INFLUENCE OF VISCOSITY GRADIENT ON BUBBLE FORMATION AT A SUBMERGED

ORIFICE

A Thesis Presented

By

Leily Majidi

To

The Department of Mechanical and Industrial Engineering

In partial fulfillment of the requirements

For the degree of

Master of Science

In the field of

Mechanical Engineering

Northeastern University

Boston, MA

August, 2014

I

Abstract

The objective of the present work was to experimentally investigate bubble

formation in different viscosities of Silicone oil. The purpose of these experiments was to

try to understand how the shape of the bubbles, formed from a small lower orifice, is

affected by aspects of viscosity. The two major directions of investigation involved bubble

formation in (i) single and finite liquid layers of varying viscosity and (ii) multiple layers of

varying viscosities, to create a viscosity gradient. The experiments were inspired by recent

observations of Focused Ion Beam FIB movies of thermal sprayed obsidian splats, in which

different elongated ‘frozen’ bubbles exist. It was hypothesized that the rapidly cooling

obsidian would therefore have bubbles growing in a thermal gradient, leading to a viscosity

gradient from bottom to top.

The results indicated that the process of bubble formation and detachment from the

orifice is strongly affected by the viscosity gradient. Elongation in bubble shape, changes in

the geometry of bubble, growth dynamics and growth time were the parameters that

proved the effect of viscosity gradient compared to the case of finite layer of single

viscosity. The resulted bubbles were also very close in shape to those observed in FIB

movies. These findings lead to a better understanding of the process of bubble formation

occurring in splats and provide a potential to control the shape and formation of bubbles in

thermal spray process.

II

Acknowledgments

I would like to thank my advisor, Dr. Andrew Gouldstone, for all of the trust, time

and effort he provided so that I could become a better researcher. His devotion to science

inspired me along the path of my Master’s degree research. His interest in my work and

availability to discuss the challenges were always admirable to me. Meeting him and

discussing the different potentials of our project, was always exciting, productive and full of

motivation. He guided me through the path and helped me to work independently.

I would also like to thank Dr. Saeid Bashash for all of his help and ideas on

performing the image analysis section of my project.

I am thankful to the best sister in the whole world, Hasti Majidi for her love and

support. She was the very first inspiration for me to continue my studies in higher level and

to experience the taste of working hard with enjoyment as a researcher.

I am grateful to two treasures of my life, my beloved parents, Soheila Nakhostin and

Amir Majidi, for their lifetime support. Their interest in education and science made them

my role models from my childhood. I can’t imagine how brave and patient they were while

encouraging me to travel to the U.S., far from home, to fulfill my dreams. I owe them all of

the happiness I enjoy in my life today.

III

Table of Content

1. Introduction ....................................................................................................................................................... 1

1.1 Background .................................................................................................................................................. 1

1.2 Objective and Structure of This Study ............................................................................................... 1

2. Literature Review ............................................................................................................................................. 3

2.1 Liquid Droplet Impact ............................................................................................................................. 3

2.2 Bubble Formation During Thermal Spraying ................................................................................. 5

2.3 Bubble Formation in Magmas .............................................................................................................. 9

2.4 Motivation for Studying Bubble Formation from an Orifice.................................................. 10

2.5 Bubble Formation and Growth at Submerged Orifices ........................................................... 12

3. Experimental Apparatus and Methods ................................................................................................. 29

3.1 Experimental Setup for Bubble Formation .................................................................................. 29

3.1.1 Observation Box .............................................................................................................................. 31

3.1.2 Syringe Pump ................................................................................................................................... 31

3.1.3 High-Speed Camera ....................................................................................................................... 31

3.1.4 Fluid Medium (Silicone Oil) ........................................................................................................ 31

3.1.5 Soluble Dye ....................................................................................................................................... 31

3.1.6 Light Source ...................................................................................................................................... 32

3.2 Experimental Method ........................................................................................................................... 32

4. Bubble Formation and Image Analysis ................................................................................................. 34

IV

4.1 Bubble Formation in a Single Viscosity Fluid .............................................................................. 34

4.2 Image Analysis Method for The Bubble Formation Process ................................................. 35

4.2.1 Conversion of an RGB Image to a Gray Scale Image .......................................................... 37

4.2.2 2D Filtering of the Image ............................................................................................................. 38

4.2.3 Converting the Gray Scale Image into a Binary Image by Using Thresholding. ..... 38

4.2.3 Removing The Undesired Small Components From The Main Image ....................... 39

4.2.4 Filling The Holes And Pores Located In The Object .......................................................... 40

4.2.5 Determining the Position of the bubble Center of Gravity and Calculating the

Aspect Ratio ................................................................................................................................................. 41

4.2.6 Finding the Velocity of Bubble .................................................................................................. 42

4.2.7 The Method to Compare the Bubble Shape Changes in Two Different Cases ......... 43

5. Results and Discussions .............................................................................................................................. 45

5.1 Bubble Formation at a Submerged Orifice in Silicone Oil with the Liquid Level of 1

Cm. ....................................................................................................................................................................... 45

5.1.1 Bubble Formation in Silicone Oil with the Viscosity of 1000 cSt ................................. 46

5.1.3 Bubble Formation in a Viscosity Gradient ............................................................................ 49

5.2 Bubble Formation in Liquid Level of 2 cm ................................................................................... 51

5.2.1 Bubble Formation in 1000 cSt Viscosity and 2 cm Liquid Level .................................. 52

5.2.2 Bubble Formation in 60,000 cSt Viscosity and 2 cm Liquid Level .............................. 53

5.2.3 Bubble Formation in Viscosity Gradient with Liquid Level Of 2 Cm. ......................... 54

V

5.3 Comparison between Experimental Results and Thermal Sprayed Splats ..................... 58

5.4 Effect of Flow Rate on Bubble Formation and Growth ............................................................ 59

5.5 Image Processing Results .................................................................................................................... 61

5.5.1 Image Analysis of Bubble Formation in Silicone Oil with 60,000 cSt Viscosity ..... 61

6. Conclusions and Recommendations for Future Work .................................................................... 79

6.1 Conclusions ............................................................................................................................................... 79

6.2 Recommendations for Future Work ............................................................................................... 80

7. References ........................................................................................................................................................ 81

VI

List of Figures

Figure 2.1: Image sequence of an impacting droplet [9]……………………………………………………4

Figure 2.2: Schematic of thermal spray process and coating built-up [15]………………...............4

Figure 2.3: (a) Top view of the Ni splat (b) Bottom view of the splat (with the initial velocity

of 140 m/s and the thinkess of around 2 µm). (c) High magnification of the dashed circle in

(b) [15]…………………………………………………………………………………………………………………………..6

Figure 2.4: Schematic view of the processes resulting in the bubble nucleation [15]………….7

Figure 2.5: Underside of the Ni splat on Cu substrate with the high magnification of the

elongated bubbles and liquid flow direction [24]……………………………………………………………..8

Figure 2.6: Snapshot of a FIB movie showing the frozen bubbles inside the thermal sprayed

obsidian splats………………………………………………………………………………………………….................11

Figure 2.7: Forces governing the bubble growth process [64]…………………………………………14

Figure 2.8: Effect of flow rate Q on bubble formation time and volume for Ro=1mm and

constant contact angle φs for each curve [77]………………………………………………………………...18

Figure 2.9: Bubble contours in different viscosity ratios of a) µl*=0.1, b) µl*=1, and c)

µl*=150, with flow rate of Q=100ml/min and Ro=1mm and φs=70o [77]………………………..19

Figure 2.10: Photographic sequence of bubble growth with the contact angle at flow rate of

100mlph with orifice diameter of 1.6 mm [64]……………………………………………………………….20

VII

Figure 2.11: Variation of center of gravity position and bubble volume at flow rate of

100mlph and orifice diameter of 1.6 mm [64]………………………………………………………………..21

Figure 2.12: Bubble formation and growth under the influence of orifice diameters of a) 1.6

mm, b) 1.0 mm, c) 0.5 mm, with the flow rate of 10 mlph [64]………………………………………...22

Figure 2.13: Schematic of experimental setup for reduced gravity test [82]…………………….24

Figure 2.15: Effect of various surface tensions on bubble volume with +Water 0.073 N/m,

n-Propanol 0.0238 N/M × Ethanol 0.0228 N/m Methanol 0.0227 N/m i-Propanol 0.0217

N/m [86]……………………………………………………………………………………………………………………...27

Figure 3.1: Experimental setup for bubble formation showing the syringe pump that pumps

the air with the flow rate of 0.09 ml/min. The high-speed camera is located on the left side

of the observation box and the light source is placed on the right side of the observation

box……………………………………………………………………………………………………………………………….30

Figure 3.2: Schematic of the experimental setup for the bubble formation………………………30

Figure 3.3: Schematic of the experimental method showing (a) single viscosity and (b)

viscosity gradient in the medium…………………………………………………………………………………..32

Figure 4.1: Real-time observation of bubble formation and growth in Silicone oil with

viscosity of 1000 cSt, flow rate of 0.03 ml/min and liquid level of 2 cm…………………………...34

Figure 4.2: The width and height at the center of gravity point used to calculate the aspect

ratio of the bubble………………………………………………………………………………………………………...36

VIII

Figure 4.3: A true-color RGB image of a bubble right after detachment from the orifice in

Silicone oil with viscosity of 1000 cSt…………………………………………………………………………….37

Figure 4.4: Gray scale intensity image of the bubble generated with image processing tool

in MATLAB…………………………………………………………………………………………………………………...38

Figure 4.5: Binary image of the bubble generated with image processing tool, using

thresholding…………………………………………………………………………………………………………………39

Figure 4.6: Binary image of the bubble after removing undesired small components using

image processing tool in MATLAB…………………………………………………………………………………40

Figure 4.7: The binary image of the bubble after filling the holes inside the bubble using

image processing tool in MATLAB…………………………………………………………………………………41

Figure 4.8: Position of center of gravity in two dimensions is shown with a black dot in the

bubble………………………………………………………………………………………………………………………….42

Figure 4.9: Two parts of bubble inside and outside of the liquid which is separated by the

liquid free surface…………………………………………………………………………………………………………44

Figure 5.1: photographic sequence of bubble formation and growth from 2 mm orifice

diameter, in Silicone oil with the viscosity of 1000 cSt and the liquid level of 1cm…………...46

Figure 5.2: Bubble formation in 1000 and 60,000 cSt viscosity of Silicone oil with the flow

rate of 0.09 ml/min……………………………………………………………………………………………………….48

Figure 5.3: photographic sequence of bubble formation and growth from 2 mm orifice

diameter, in Silicone oil with the viscosity gradient and the liquid level of 1cm……………….50

IX

Figure 5.4: Photographic sequence of bubble formation in three cases of 1000 cSt and

60,000 cSt and viscosity gradient with flow rate of 0.09 ml/min and liquid level of 1 cm…51

Figure 5.5: Bubble growth in Silicone oil with low viscosity of 1000 cSt and comparison

between the two cases with liquid levels of 1 cm and 2 cm……………………………………………..52

Figure 5.6: Photographic sequence of bubble formation and growth in Silicone oil with

viscosity of 60,000 cSt and liquid level of 1 cm and 2cm…………………………………………………53

Figure 5.7: Bubble growth in Silicone oil with high of 1000 cSt and comparison between the

two cases with liquid levels of 1 cm and 2 cm…………………………………………………………………54

Figure 5.8: Photographic sequence of bubble formation in viscosity gradient with the liquid

level of 2 cm………………………………………………………………………………………………………………….55

Figure 5.9: photographic sequence of bubble formation in low viscosity, high viscosity and

viscosity gradient with the liquid level of 2 cm……………………………………………………………….56

Figure 5.10: Photographic sequence of bubble formation and growth in viscosity gradient

with two levels of liquid………………………………………………………………………………………………..57

Figure 5.11: Bubble shapes from experimental results and FIB image of frozen bubbles in

thermal spray splats. …………………………………………………………………………………………………….58

Figure 5.12: Photographic sequence of bubble formation in viscosity gradient with flow

rates of 0.03 and 0.27 ml/min and liquid level of 1.5 cm…………………………………………………59

Figure 5.13: Photographic sequence of bubble formation in Silicone oil with viscosity of

60,000 cSt and liquid level of 1.5 cm and flow rate of 0.09 ml/min………………………………….62

X

Figure 5.14: The evolution of bubble’s aspect ratio for 8 stages of bubble formation in

Silicone oil with viscosity of 60,000 cSt and flow rate of 0.09 ml/min……………………………...63

Figure 5.15: Aspect ratio evolution in normalized time for the bubble formation in Silicone

oil with viscosity of 60,000 cSt and flow rate of 0.09 ml/min…………………………………………..64

Figure 5.16: Evolution of aspect ratio versus normalized vertical position of bubble’s center

of gravity in Silicone oil with 60,000 cSt in viscosity and flow rate of 0.09 ml/min…………..65

Figure 5.17: Bubble velocity evolution during growth time in Silicone oil with 60,000 cSt

viscosity and flow rate of 0.09 ml/min…………………………………………………………………………..66

Figure 5.18: Bubble velocity through normalized time……………………………………………………68

Figure 5.19: Photographic sequence of bubble formation in Silicone oil with viscosity

gradient, liquid level of 1.5 cm and flow rate of 0.09 ml/min…………………………………………..69

Figure 5.20: Aspect ratio evolution based on image number for bubble formation in

viscosity gradient and flow rate of 0.09 ml/min……………………………………………………………..70

Figure 5.21: evolution of aspect ratio based on normalized time……………………………………..71

Figure 5.22: Aspect ratio variation versus normalized vertical position of bubble in Silicone

oil with viscosity gradient and flow rate of 0.09 ml/min…………………………………………………72

Figure 5.23: Bubble velocity versus time in a viscosity gradient and flow rate of 0.09

ml/min……………………………………………………………………………………………………………………….73

XI

Figure 5.24: Bubble velocity versus normalized time in a viscosity gradient and flow rate of

0.09 ml/min………………………………………………………………………………………………………………….74

Figure 5.25: Evolution of bubble’s aspect ratio in normalized time for two cases with flow

rate of 0.09 ml/min……………………………………………………………………………………………………….75

Figure 5.26: Evolution of bubble’s aspect ratio in normalized bubble position for two cases

with flow rate of 0.09 ml/min………………………………………………………………………………………..76

Figure 5.27: Evolution of bubble’s aspect ratio in normalized bubble position for two cases

with flow rate of 0.09 ml/min………………………………………………………………………………………..77

XII

List of Tables

Table 2.1: Developed numerical models for bubble volume……………………………………………15

1

1. Introduction

1.1 Background

Thermal spray protects mechanical parts against wear, corrosion and high

temperature when they are subjected to extreme conditions. Thermal spray coatings have

widespread applications, and can be found in the petrochemical, automotive, and

aerospace industries, and industrial gas turbines. Thermal spray is a deposition technique

where molten particles are accelerated towards a substrate. Upon this impact, through the

process of flattening, spreading and rapid cooling, a disk shaped structure called “splat” is

formed. The splat morphology and its formation process have a significant influence on the

coating structure and property.

1.2 Objective and Structure of This Study

The motivation of this effort is to experimentally investigate bubble formation and

growth in thermal sprayed splats, and develop a method to simulate its process.

This thesis is organized as follows:

Chapter 2 reviews the literature on the efforts related to 1) Aspects of droplet

impact relevant to “the bubble problem”, 2) Observations of bubbles frozen in thermal

spray coatings, 3) Bubble nucleation and growth in magmas, 4) Experimental observations

of thermal spray splats/FIB, and 5) Bubble formation and growth from a submerged orifice

and the operating parameters.

2

Chapter 3 describes the experimental setup and the methods used to simulate

bubble growth under relevant conditions.

Chapter 4 describes the bubble growth process in Silicone oil using a set of bubble

images acquired at different stages of the growth process. This chapter also presents a

sequence of image processing techniques developed to analyze these images and extract

useful information related to the bubble growth mechanics.

Chapter 5 presents the main results and discussions. Finally, Chapter 6 summarizes

the concluding remarks of this study and suggests future directions.

3

2. Literature Review

2.1 Liquid Droplet Impact

Thermal spray has been extensively used for surface protection and advanced

material forming in the past century due to its low cost, flexibility, high deposition

efficiency, easy automation, and providing desired properties such as resistance to

oxidation, corrosion, friction and wear [1]. Thermal spraying is a particulate deposition

process in which solid materials usually in the powder form are heated and then

accelerated by gas jets creating molten droplets. These liquid droplets are subsequently

propelled towards the surface of a substrate [2]. The process after the impact is followed

by flattening, spreading, rapid cooling, and solidification of the droplets [3].

Achieving an ideal implementation of thermal spray is challenging because of

various problems occurring during the process, including formation of pores between the

droplets and the substrate leading to an unsuccessful bond between the droplets.

Therefore, developing a high quality thermal sprayed coating is extremely dependent on

controlling the droplet impact process and its key parameters including particle radius,

temperature and initial velocity [4]. Effects of other parameters on the quality of bonding

have been extensively studied, such as the effect of plasma arc power [5], the effect of spray

distance [6], deposition temperature [7] and substrate roughness [8]. Figure 2.1 depicts a

set of sequential images for a droplet impact.

4

Figure 2.1: Image sequence of an impacting droplet [9].

When a molten droplet impacts a solid surface, its kinetic energy converts into a

work which contains the work of viscous forces and surface energy. Immediately upon the

impact, the droplet solidifies and expands radially, taking the form of a disk or a pancake

which is called a “splat”. These observations were gained by various analytical models

developed by different researchers including Jones [10], Madjeski [11], Trapaga and

Szekely [12], Chandra and Avedisian [13] and Yoshid et al. [14]. Eventually, successive

droplet impacts and splat formations result in building a coating as shown in Figure 2.2.

Figure 2.2: Schematic of thermal spray process and coating built-up [15].

Splats are the foundational parts of thermal spray coatings, and the formation of a

splat has the potential of being studied independently. Hence, different studies have been

5

centered around the splat morphology due to the effect of splat formation on coatings

properties and the quality of the adhesion between the coatings and the substrates. It is

challenging to study the liquid droplet impact phenomena experimentally, because the

process occurs only in a few mirco seconds and at a very high temperature, which imposes

other limitations [16]. Therefore, numerical models have been developed to solve the

governing fluid dynamics (conservation of mass and momentum) and heat transfer

equations [17]. The extensive number of studies available on these models and their

modifications indicates that most of the attention of research on the droplet impact

problem has focused on understanding the solidification and spreading process during the

droplet impact.

2.2 Bubble Formation During Thermal Spraying

There has been a rapid growth on the investigation of single splat formation and its

morphology because of the recent technological advancements. However, just a few

observations have been performed on the underside structure of the splat. Qu et al. [15]

closely studied the underside of the removed thermal sprayed Ni splats from the substrate,

and reported a unique structure which had not been predicted before. This structure

contained a large number of small pores ranging between 20-100 nm in diameter as shown

in Figure 2.3. They described these pores as frozen gas bubbles generated as a result of a

rapid decompression during the droplet impact process.

6

Figure 2.3: (a) Top view of the Ni splat (b) Bottom view of the splat (with the initial velocity of

140 m/s and the thinkess of around 2 µm). (c) High magnification of the dashed circle in (b)

[15].

Figure 2.4 schamtically suggests the bubble generation sources. The velocity of the

impacting droplet is approximately 100 m/s. The air between the droplet and the substrate

is squeezed to a large amount, and is then dissolved in it (Figure 2.4 (a) and (b)). Upon the

rapid impact, the hydrostatic pressure increases adversely to 1 GPa, and a huge amount of

depressurization happens in a very small period of time in the scale of 10-8 to 10-7 s [18,

19]. This causes the supersaturation and nucleation of bubbles with a high rate at the

interface of droplet and the substrate as shown in Figure 2.4 (c). While the droplet spreads

radially, the bubbles grow untill they soldify and freeze.

7

Figure 2.4: Schematic view of the processes resulting in the bubble nucleation [15].

By applying the nucleation studies performed by Toramaru [20], Qu et al. [15]

calculated the maximum nucleation rate for the bubbles observed in molten Ni at 2500°C.

This rate is approximately two bubbles per 100×100×100 nm3/100ns.

The change in the structure of bubbles is dependent on bubble nucleation, growth

and motion. Various conditions of substrate would affect the cooling and solidification

rates and eventually the morphology of the bubbles [17, 21-23]. Figure 2.5 illustrates the

underside of the Ni splats on the Cu substrate. In this case, the pore size is smaller on

avarage. Moreover, a number of the nucleated bubbles are elongated, which indicates the

solidfication of the liquid on the bubble’s final structure during motion [24].

8

Figure 2.5: Underside of the Ni splat on Cu substrate with the high magnification of the

elongated bubbles and liquid flow direction [24].

Qu and Gouldstone [24] experimentally studied the nanoporous structure on the

underside of Ni splats, and concluded that the bubble formation and shapes are

significantly dependent on the substrate’s thermal properties and roughness, and other

parameters of the process such as initial droplet velocity.

The size, the number, and the structure of the bubbles nucleated in thermal sprayed

splats have a significant impact on the adhesion of the coating to the substrate and the

coating quality. These observations and methods can provide a potential for a new pore

design process which may lead to developing a novel coating technology [15, 24].

9

Therefore, understanding the interactions in gas-liquid environments and the sources of

bubble formation would be a useful approach.

2.3 Bubble Formation in Magmas

Thermal spray and volcanic phenomena might seem different at the first glance;

moreover, studying the volcanic eruptions is not the main objective of this thesis. However,

there is a phenomenon which thermal sprayed splats and volcanic eruption have in

common, that is bubble formation and growth. Investigation on bubble nucleation, and the

interaction and coalescence of bubbles in ascending magma chambers and their growth can

potentially improve our understanding of vesiculation, and the unknown parameters of

volcanic eruptions [25-28].

The volcanic eruption occurs in a diverse range due to the wide range of magma

viscosities [29]. When the highly viscous magma rises and the decompression occurs, the

volatiles dissolve, and the supersaturation leads to bubble nucleation and growth [30].

Manga and Stone [31] experimentally studied the interactions between two bubbles

to model the actual conditions happening in magma and lava. They also developed a model

in order to approximately estimate the rate of coalescence between deformable bubbles.

Toramaru [20] numerically studied the nucleation and growth of bubbles in viscous

magmas by using a formulation that considers the effect of viscosity on nucleation and

moments of bubble size distribution. Before that, he developed a model to simulate the

vesiculation process in rising magma with constant velocity which led to a better

understanding of bubble nucleation and growth [21]. Various numerical and experimental

10

models have been developed to simulate the bubble nucleation in lava flows and highly

viscous melts [32].

Aside from the bubble formation, and along the line of viscosity effects and viscosity

gradient influence on the dynamics of magmas, Huppert [33] experimentally investigated a

two layer liquid with a viscosity difference. He reported that this is the viscosity ratio

between the more viscous upper layer and the less viscous lower layer (as in magmas),

which can affect the interaction between the two layers, the mixing, the overturning, and

the motion of the liquid.

When bubbles are formed in magma, narrow rinds of highly viscous melt are

created around them because of the melt dehydration. Some numerical simulations studied

the effect of the varying viscosity around the bubble [34, 35]. As an example of a more

recent study, Lensky et al. [30] studied the influence of radial viscosity gradient on the

bubble growth dynamics in vesiculation magmas.

2.4 Motivation for Studying Bubble Formation from an Orifice

Along the path of studying the porous structure of the thermal sprayed splats,

various observations have been made. One of the most interesting observations, and the

main inspiration of the present work, is the view of images extracted from Focused Ion

Beam (FIB) movies of the thermal sprayed obsidian splats developed by Prof. Gouldstone’s

group at Northeastern University. These movies depict the frozen bubbles from the bottom

to the top of the splat. Figure 2.6 shows a cross sectional view of the bubbles observed in

the splats.

11

Figure 2.6: Snapshot of a FIB movie showing the frozen bubbles inside the thermal sprayed

obsidian splat.

The cross sectional areas observed in the bubbles show that the bubbles are

different from those observed in metal splats. Firstly, the bubbles are larger and secondly,

the bubbles are significantly elongated. One reason for the size of the bubbles observed in

obsidian splat is that magma does not solidify with decreasing the temperature. With

temperature decreasing, the viscosity of magma increases, and the magma becomes

thicker, thereby making the bubbles in obsidian splats larger.

Besides, we hypothesize that these elongated bubbles are formed in a viscosity

gradient as a result of a temperature gradient. Since the splats are the result of molten

droplet impacts on a substrate and then their solidification, the bottom layers of the splats

are cooler and this rapid cooling penetrates to the upper layers. Therefore, there exists a

temperature gradient in the splats from bottom to top. This temperature gradient causes a

12

difference in the viscosity of the lower and the upper layers in the form of a viscosity

gradient.

These interesting bubble shapes inspired us to think about a method to form

bubbles with non-spherical shapes. We thought of an orifice from which we could form and

grow a bubble inside a liquid. However, we considered two major parameters which

provide a better simulation of the actual conditions in the splats:

1) Liquid thickness: Since the splats are very thin, we applied a finite and thin layer of

liquid in which we could grow the bubble.

2) Viscosity gradient: We decided to form and grow the bubble inside a liquid with

different layers and different viscosities in order to develop a viscosity gradient.

The details of the experiments and results will be discussed in the subsequent

chapters. Next section reviews some of the studies on bubble formation at a submerged

orifice and its specific parameters.

2.5 Bubble Formation and Growth at Submerged Orifices

The gas bubble formation process at submerged orifices plays a significant role in

vast array of industries with the applications accompanied by gas-liquid contacting devices.

These applications are found in metallurgy, waste water treatment, biochemical and

chemical processing, and procedures involving transfer phenomena such as heat and mass

transfers. An example is nucleate boiling which is applied in different heat transfer

applications. Therefore, understanding the bubble formation process, which has been

13

investigated widely in the past 50 years, leads to improvement in domestic and industrial

technologies [36, 37].

The study on the formation of a single bubble or one stage bubble formation traces

back to the works of Tate [38] and Bashforth and Adams [39]. A significant attention was

paid to the area of bubble formation at submerged orifice(s) over a wide range of design

and operation parameters (Davidson and Schuler [40, 41] Tan et al. [42-47]. Most of those

studies were performed based on the operating conditions pertaining to the gas phase,

such as the constant flow, constant pressure, and intermediate condition. In the late 1960s,

Kumar et al. studied the mechanism of bubble formation for different conditions, mainly,

the various methods of measuring bubble sizes experimentally [48-51]. Tsuge worked on

the hydrodynamics of bubble formation from submerged orifices and discussed various

models proposed for the mechanism of bubble formation [52-59].

An extensive investigation has been performed on different parameters and their

effects on the bubble formation process. These parameters include orifice diameter [40, 41,

58, 56, 60], surface characteristic and wettability [61], Viscosity [42, 48, 56, 59, 62, 63],

liquid density [61], surface tension [41, 48, 59, 56].

One of the main objectives of the previous studies was to predict the bubble size and

volume under the influence of various parameters. Therefore, various models have been

developed to calculate the bubble volume. These models have been modified over time.

These analytical models of bubble volume have been created by solving the force equations

that govern the bubble formation process. The most important forces acting on the bubble

are accompanied by the lifting forces and restraining forces.

The lifting forces are described as follows:

14

Buoyancy force FB= (π/6)db3(ρl-ρg)g

Contact pressure force FCP= (π/4)do2(ρg- ρl)

Gas momentum force FM= (π/4)do2ρgU02

The restraining forces include:

Surface tension force FC= πdoσ

Drag force FD= FI+Fviscous

Inertial force FI≈ (99/32π+ (9/2π)ρg/ρl)ρlQG2/db

Viscous force Fviscous= (π/4) db2 CD (ρl Ub2/2),

where d, U, ρ, σ, CD, µ, and Q are the diameter, velocity, density, surface tension, drag

coefficient, viscosity, and flow rate, respectively. The subscripts b, o, l and g also relate to

the bubble, orifice, liquid, and gas, respectively [36].

Figure 2.7: Forces governing the bubble growth process [64].

15

The drag coefficient CD is an important parameter in calculating the viscous forces

which affect the bubble volume. CD decreases when the Reynolds number increases. For

example, for high Reynolds numbers, Miyahara et al. [65, 66] and Al Hayes [67] calculated

the drag coefficient as CD=16/(Re+1), which becomes close to 1 in practice. As a result of

very low flow rate and small gas density, the gas momentum force FM is negligible in

comparison with the other forces [36].

When the bubble is going to detach from the orifice there is a balance between all

the described lifting and restoring forces:

FB+FCP=FC+FD

Table 2.1 presents different bubble volume models developed by different

researches through time including Davidson and Schueler, [41], Davidson and Harrison

[68], Kumar and Kuloor [50], Gaddis and Vogelpohl [69] and Jamialahmadi et al. [70].

Table 2.1: Developed numerical models for bubble volume [36].

16

All of these models assume that the process involves a single bubble formation

which happens as a result of low gas flow rates. At higher flow rates, the bubbles that forms

first, affects the formation and growth of the next bubble [36].

There are several important dimensionless numbers defined to characterize the bubble

formation process as described below.

1) Bond number Bo: ρlgdo2/ σ

Bond number becomes significant in lower gas flow rates, which characterizes the static

bubble formation regime. It defines the ratio of buoyancy forces to the surface tension

force.

2) Froude number Fr=Uo2/gdo

Froude number characterizes the bubble formation process when the gas flow rate

increases and inertial forces become dominant compared to surface tension forces. It

indicates the ratio of inertial forces to the gravitational forces.

3) Capillary number Ca=µlQg/σdo2

Capillary number represents the relation of viscous forces versus surface tension forces

acting on the bubble.

4) Reynolds number Re=ρlUodo/µl

Reynolds number measures the importance of inertial forces relative to the viscous

forces.

5) Weber number We= ρlUo2do/σ

Weber number measures the importance of the inertial forces relative to the surface

tension forces.

17

As mentioned before, the effects of different parameters on the bubble formation

process has been widely studied, both numerically and experimentally. Terasaka and Tsuge

[71] experimentally investigated the effect of parameters including gas flow rate, gas

chamber volume, orifice diameter and liquid viscosity on bubble formation process in a

highly viscous liquid. They concluded that increasing those parameters would increase the

bubble volume. This volume increase was found as a result of an increase in the bubble

formation and growth time in a highly viscous liquid compared to a liquid with low

viscosity. Snabre and Magnifotcham [72] studied the continuous emission of a bubble

stream from a submerged orifice in a viscous liquid. They presented a model to predict the

bubble volume under constant flow rate by solving the force balance at the time of

detachment. They experimentally estimated the bubble rise velocity and investigated its

variation versus gas flow rate. With the use of the force balance characteristics, Gerlach et

al. [73] studied bubble formation using a shadow imaging technique. They investigated the

influence of Young contact angle and surface wettability on bubble formation in three

different materials. Young contact angle is defined as the angle formed where a

liquid/vapor phase meets a solid in equilibrium. The angle accounts for the amount of the

solid wettability by the liquid. A non-wetting plate made of Teflon was used to distinguish

the difference between various values of contact angles. A big difference in bubble volume

was reported between two cases with different roughness.

The majority of the bubble formation studies have focused on liquids with low

viscosity. However, bubble formation in highly viscous fluids is also important for different

applications such as polymer melts [74], molten glasses and magmas [75]. Higurea [76]

investigated the periodic bubble formation from an orifice in a highly viscous liquid,

18

numerically. He reported the results based on the contact angle, Bond number, and the

Capillary number. It was concluded that pairing and coalescence of bubbles would happen

when the capillary number exceeds critical value which is dependent on the Bond number.

Continuing the effort to study the bubble formation process, Gelarch et al. [77] carried out a

numerical simulation by using the volume-of-fluid technique in water and air as the gas.

The effect of various operating parameters including surface wettability, orifice radius and

flow rate on bubble growth was investigated. All of these parameters were varied step by

step to encounter a transition from single periodic (SP) formation to double periodic (DP)

bubble formation.

Figure 2.8: Effect of flow rate Q on bubble formation time and volume for Ro=1mm and

constant contact angle φs for each curve [77].

It was observed that with increasing the contact angle, the transition from SP to DP

is delayed. This occurs because the bubble volume and size increases with φs, therefore, the

bubble growth time increases, and successive bubbles have less interactions.

19

Gelarch et al. also studied the effect of liquid density and viscosity on the bubble formation

time and volume and the change they impose on the bubble shape. Figure 2.9 depicts the

change of bubble shape with viscosity ratio of µl*= µl/ µl,aw where aw refers to the viscosity

of air-water phase.

Figure 2.9: Bubble contours in different viscosity ratios of a) µl*=0.1, b) µl*=1, and c) µl*=150,

with flow rate of Q=100ml/min and Ro=1mm and φs=70o [77].

It was observed that the bubble volume and detachment time is not very different in

three cases. However, there is a significant difference in the bubble shape when the

viscosity increases. Figure 2.9(c) shows that the bubble detaching from orifice is clearly

elongated compared to the other cases. The reason is related to the detachment or pinch-

off time that was calculated by Wong et al. [78]. This parameter was reported to have a

proportional relationship with viscosity. Therefore, when the viscosity increases, the pinch-

off time increases as well, thereby forcing the bubble to elongate when the lifting forces are

trying to pull the bubble upward. Based on Figure 2.9 it was also concluded that the time of

detachment T is almost constant when the viscosity ratio µl* is less than 1.

20

Other interesting experimental studies have been carried out to achieve a better

understanding of the bubble formation phenomenon. Di Bari and Robinson [64] used an

experimental setup to inject air into water in order to record the images of the formed

bubbles. They used an image processing tool to define different geometrical specifications

including bubble volume, center of gravity position, bubble interface coordinates, and the

contact angle.

Figure 2.10 depicts the video sequence of bubble growth in Di Bari and Robinson’s

experiment. They also plotted the evolution of bubble center of gravity and volume with

time as shown in Figure 2.11.

Figure 2.10: Photographic sequence of bubble growth with the contact angle at flow rate of

100mlph with orifice diameter of 1.6 mm [64].

21

Figure 2.11: Variation of center of gravity position and bubble volume at flow rate of 100mlph

and orifice diameter of 1.6 mm [64].

It is shown that in the initial stages when t ≤ 0.2s, the bubble comes out of the orifice

with a hemispherical shape. When the bigger portion of the bubble grows in the liquid, the

effect of buoyancy becomes significant and tends to pull the bubble to detach from the

orifice. This effect causes the bubble to elongate. As shown in Figure 2.11a during this

elongation time (0.2 ≤ t ≤ 0.8s) the variation rate of the bubble center of gravity is constant.

In the final stage where the necking happens and the detachment starts (t ≥ 0.8s), the

center of gravity accelerates upward because of the dominant lifting forces. These changes

all happen while the rate of change in the bubble volume through time is constant (Figure

2.11b).

Di Bari and Robinson [64] also studied the influence of orifice diameter on the

bubble shape and the detachment time. They verified that the bubble is more spherical and

smaller in size when the orifice diameter is smaller, and detaches from the orifice sooner.

Figure 2.12 illustrates the effect of orifice diameter on bubble shape and growth.

22

Figure 2.12: Bubble formation and growth under the influence of orifice diameters of a) 1.6

mm, b) 1.0 mm, c) 0.5 mm, with the flow rate of 10 mlph [64].

In another attempt, using the finite-volume method, Di Bari et al. [37] studied the

effect of gravity on the bubble formation process. They reported the effect would be

significant. When the gravity increases, the bubble formation and growth time decreases,

resulting in a smaller bubble volume in the time of detachment.

The formation of bubbles under reduced gravity can contribute to space

applications including thermal energy, power generation, and increasing the life support.

23

Few studies have been done on the bubble formation under reduced gravity. Buyevich and

Webbon [79] concluded that under reduced gravity conditions, the frequency of bubble

formation increases with gas flow rate while the bubble volume at the time of detachment

does not depend on gas flow rate. Pamperin and Rath [80] investigated the bubble

formation under microgravity conditions, both experimentally and theoretically, and

observed that the bubble detachment from the orifice does not occur in low gas flow rates.

Another work performed by Chakarborty et al. [81] explored the dynamics of bubble

formation from a submerged orifice and compared the results in normal and reduced

gravity conditions. They investigated different levels of gravity by categorizing the

experiments with the ratio of the governing gravity (g) to the gravitational acceleration

(ge). They observed that at a specific flow rate, while detachment increases, the frequency

of bubble formation decreases and the detachment time is delayed under reduced gravity

conditions. Also, they reported that under high air flow rates, the bubble formation process

under normal gravity conditions is similar to the results under reduced gravity levels.

Nahra et al. [82] have experimentally investigated the effect of liquid cross-flow

velocity, gas flow rate, and orifice diameter on the bubble formation in a wall-bubble

injection configuration under reduced gravity conditions. The reduced gravity experiment

was conducted aboard the NASA DC-9 Reduced Gravity Aircraft (see Figure 2.13). Their

results show that the process of bubble formation and detachment depends on gravity, the

orifice diameter, the gas flow rate, and the liquid cross flow velocity (Figure 2.14). They

analyzed their data based on a force balance, and identified two different detachment

mechanisms: when the gas momentum is large, the bubble detaches from the injection

orifice as the gas momentum overcomes the attaching effects of liquid drag and inertia. The

24

surface tension force is much reduced because a large part of the bubble pinning edge at

the orifice is lost as the bubble axis is tilted by the liquid flow. On the other hand, when the

gas momentum is small, the force balance in the liquid flow direction is important, and the

bubble detaches when the bubble axis inclination exceeds a certain angle.

Figure 2.13: Schematic of experimental setup for reduced gravity test [82].

25

Figure 2.14: Bubble diameter at detachment as a function of superficial liquid velocity in

reduced gravity [82].

They concluded that under low gravity, the surface tension force is much reduced

because a large part of the bubble pinning edge at the orifice is lost as the bubble axis is

tilted by the liquid flow. However, for lower momentum force or lower gas flow rates (DN =

0.15 and 0.076 cm) when the bubble axis inclination angle exceeds a certain value, or when

the front side of bubble surface becomes nearly normal to the wall, the bubble bottom is

pinched of starting from the front side, and the bubble detaches from the orifice.

The following properties of liquid in which the bubble grows have major effects on

the process and have been considered in various studies.

Liquid viscosity: With comparing various studies carried out on the bubble

formation process in different arbitrary viscosity [40, 56, 59, 83], it was observed that the

viscosity variation considerably affects the bubble volume and size, however, the effect

26

becomes insignificant in high gas flow rates and bigger orifice diameters. Jamialahmadi et

al. [70] concluded that the bubble size is dependent on viscosity with the relation of ∼µ0.66.

Liquid surface tension: When bubbles form and grow at a submerged orifice, their

rear surfaces are dragged backward along with the liquid while the surface is stretched in

the front part; therefore, the new surface is constantly generated. In the vicinity of the

orifice, the bubble surface is compressed and the liquid is pushed toward the orifice edges.

As a result, the surface forces on a bubble arise out of the linear surface tension acting on it,

helping the bubble to adhere to the edge of orifice delaying the detachment process [84].

There are two types of surface tension forces acting on a bubble: dynamic and static.

Initially, the surface tension is dynamic and its contact angle with the orifice changes

continuously. In the later part, it reaches to a constant contact angle approaching to static

surface tension. Although the surface tension forces are small, they vary significantly with

gas flow rate through the orifice [85-87], and because of the dynamic surface tension effect

on the stretching of the bubbles, sudden motion resulting in a reduced pressure at the tip of

the capillary initiating the next bubble occurs. It was observed that the surface tension

increases with the orifice diameter getting bigger, affecting the bubble contact and

adherence. Figure 2.15 shows influence of surface tension on the bubble volume in some

studies.

27

Figure 2.15: Effect of various surface tensions on bubble volume with +Water 0.073 N/m, n-

Propanol 0.0238 N/M × Ethanol 0.0228 N/m Methanol 0.0227 N/m i-Propanol 0.0217 N/m

[86].

Liquid density: There have been two different observations on the effect of density

on bubble formation:

1) When the liquid density increases, the bubble volume decreases. This result happened

under two conditions. One condition is that the liquid viscosity and flow rate are both

small. The other condition is when the orifice diameter and the liquid viscosity are both

small [87].

28

2) The bubble volume does not depend on liquid density. The volume is independent from

the density whenever the orifice diameter and liquid viscosity are both small while the

gas flow rate is high [87].

Further researchers have contributed their work to examine the effect of other

operating parameters on bubble formation process. However, to our knowledge, the effect

of viscosity gradient on bubble formation at a submerged orifice has not been studied.

Therefore, we carried out experiments to study the bubble formation and growth both in

single viscosity and viscosity gradient. Then, we developed a MATLAB-based image

processing tool to quantitatively analyze the geometry of the bubble during this process.

29

3. Experimental Apparatus and Methods

This chapter gives a detailed description of the experimental setup and methods

used in this study. The primary objective of these experiments is to monitor the bubble

formation process and to investigate the effect of viscosity and viscosity gradient of the

medium on nucleation and growth of the bubble. The first section of this chapter explains

the experimental setup, and the second section describes the experimental method and our

approach to create a viscosity gradient in the medium.

3.1 Experimental Setup for Bubble Formation

The experimental setup and its schematic to study the bubble formation dynamics is

shown in Figure 3.1 and Figure 3.2. Bubbles are created by forced air from the syringe

pump. The same flow that creates the bubble, then injects it into the observation box. The

nucleated bubble at the bottom of the observation box then grows and rises up to the free

surface of fluid medium. The entire process of bubble formation is recorded by a high-

speed camera. The movie is stored in a computer connected to the camera. The rest of this

section will give a detailed description of each component and its role in the bubble

formation experimental setup.

30

Figure 3.1: Experimental setup for bubble formation showing the syringe pump that pumps the

air with the flow rate of 0.09 ml/min. The high-speed camera is located on the left side of the

observation box and the light source is placed on the right side of the observation box.

Figure 3.2: Schematic of the experimental setup for the bubble formation.

31

3.1.1 Observation Box

The bubble grew and detached from the bottom of a crystal clear Polystyrene box,

made in U.S.A., with base dimensions of 4.5 cm × 9 cm and a height of 6.5 cm. The top of the

box is open to atmosphere. There is a hole at the bottom of the box, locating 1 cm from the

outside edge of the front (camera side) of the box. The hole is large enough to fit a capillary

syringe tube with inner diameter of 2 mm fitting for supplying air from a syringe pump.

3.1.2 Syringe Pump

A syringe pump, purchased from Kats Enterprises Scientific Division (model NE-

300-U), allowed changing the flow rate of room-temperature air. The pump has a Maximum

pumping rate of 1500 mL/hr with a 60 mL syringe.

3.1.3 High-Speed Camera

Since the bubble formation is a rapid process, a high-speed microscopic camera,

2MP Andonstar (model NV1-30W-USB), was utilized to capture the changes in the shape of

the bubble. The camera is capable of taking up to 30 image frames per second, and its

resolution is in the range of 640X480 to 1600 X 1200.

3.1.4 Fluid Medium (Silicone Oil)

The fluid medium used in the experiments was Silicone oil, purchased from

CLEARCO, with viscosities of 1000 cSt and 60,000 cSt. Silicone oil offers the benefit of being

transparent, cheap, readily available, and having various viscosities and densities.

3.1.5 Soluble Dye

A yellow-colored dye, purchased from Pylam Products Company, Inc., and soluble in

Silicone oil was used to distinguish between the silicon oil with different viscosities.

32

3.1.6 Light Source

A lamp located behind the box was utilized as a light source to provide a better

contrast and homogeneity of the pixels around the circumference of the bubble.

3.2 Experimental Method

The bubble formation process was performed in two general sets:

1) The bubble was formed in a single layer of oil with single viscosity of 1000 cSt and

60,000 cSt, each time. (Figure 3.3.a)

2) The bubble was formed in a double-layered fluid with 1000 cSt layer of oil on top and

60,000 cSt oil at the bottom. (Figure 3.3.b)

Figure 3.3: Schematic of the experimental method showing (a) single viscosity and (b) viscosity

gradient in the medium.

These three sets of experiments were repeated at the flow rates of 0.03 ml/min,

0.09 ml/min and 0.27 ml/min with the liquid levels of 1cm, 1.5 cm and 2cm.

In order to characterize the regimes of bubble formation process and to understand

the forces acting on the bubble during nucleation and growth, non-dimensional numbers

such as Bond and capillary numbers were calculated.

a) Single viscosity

Fluid (µ)

Air Fluid (µ)

Air

Fluid (µ’) b) Viscosity gradient

(µ’>µ )

33

By comparing capillary and Bond numbers, two different regimes were defined for

the bubble formation process: hydrostatic regime that corresponds to Ca«1/ B01/3 and

Davidson & Schuler high-flow rate regime that is attained for Ca»1/ B01/3. [90] The

calculated capillary and Bond number in the present work are 0.0011≤Ca≤0.068 and

0.4462≤ B0≤0.4483. Comparison of these two numbers depicts that the hydrostatic forces

dominate the bubble formation process for the current study. (Ca»1/ B01/3)

34

4. Bubble Formation and Image Analysis

The first section of this chapter describes the details of bubble formation and

growth observed experimentally in a single viscosity fluid and the second section discusses

the image analysis method, developed using MATLAB image processing tool in order to

quantitatively analyze the shape of the bubble during the nucleation and growth.

4.1 Bubble Formation in a Single Viscosity Fluid

A bubble starts to nucleate and grow when the gas pressure in the chamber or tube

becomes larger than the sum of the hydrostatic pressure and surface tension. As a result of

the difference in the pressure of outside and inside of the bubble, the surface of the bubble

moves and its volume gets bigger. [85]

Figure 4.1 includes a photographic sequence of a bubble, forming and growing from

a submerged orifice in Silicone oil with the viscosity of 1000 cSt. During the early stage

(t≤0.92 s), the bubble is formed and exits the orifice. In this stage, the shape of the bubble is

approximately close to a sphere.

Figure 4.1: Real-time observation of bubble formation and growth in Silicone oil with viscosity

of 1000 cSt, flow rate of 0.03 ml/min and liquid level of 2 cm.

35

In the middle stage of growth (0.92≤t≤2.33), as the bubble grows, its volume

increases and therefore, the buoyancy force acts on a bigger part of the bubble. The

buoyancy force lifts the main portion of the bubble while the other end of the bubble is still

attached to the bottom of the box. Hence, an elongation happens and the bubble shape

deviates from the initial spherical shape. The amount of elongation also depends on the

viscosity and surface tension of the fluid which will be discussed in the following chapters.

During the final stage (t≥2.33), the buoyancy effect is dominant enough to form a

neck close to the attached part of the bubble to the bottom of the box. As the buoyancy

force becomes larger, the neck diameter decreases and finally the bubble detaches from the

orifice.

After the detachment happens, if the bubble is small enough or the fluid level is deep

enough, as the case shown in Figure 4.1, it rises until it hits the free surface of the fluid.

4.2 Image Analysis Method for The Bubble Formation Process

Monitoring the geometry of the bubble during the nucleation and growth by real-

time image recording helps to understand different stages of the process. However, to

calculate the geometric characteristics of the bubble and have the capability of comparing

these values for different conditions, a quantitative analysis is required. In this thesis, the

objective is to observe how the geometry of bubble varies under the change of viscosity

and also in a viscosity gradient. One of the important specifications of the geometry of

bubble is the aspect ratio. The aspect ratio is defined as:

Aspect ratio= H/W.

36

The parameters W and H are depicted schematically in Figure 4.2.

Figure 4.2: The width and height at the center of gravity point used to calculate the aspect ratio

of the bubble.

Investigating aspect ratio reveals the amount of elongation in different viscosities. In

order to quantify the geometry of observed bubbles and calculate the aspect ratio, we have

developed an image processing algorithm based on MATLAB image processing tool. Figure

4.3 shows the sample image used in this section to explain the details of the image

processing tool step by step.

H

W

37

Figure 4.3: A true-color RGB image of a bubble right after detachment from the orifice in

Silicone oil with viscosity of 1000 cSt.

4.2.1 Conversion of an RGB Image to a Gray Scale Image

In this step, a true-color RGB image is converted into a gray scale intensity image

using MATLAB “rgb2gray” operation. “rgb2gray” eliminates the hue and saturation of a

colored image while maintaining the luminance. Figure 4.4 shows the gray scale image

converted from Figure 4.3.

38

Figure 4.4: Gray scale intensity image of the bubble generated with image processing tool in

MATLAB.

4.2.2 2D Filtering of the Image

In this step, a 2 dimensional filtering is applied on the image by using “imfilter”

operation in MATLAB. “imfilter” allows mitigating the image noise.

4.2.3 Converting the Gray Scale Image into a Binary Image by Using Thresholding.

During this section, the tool provides the possibility to convert the gray scale image

into a black and white (binary) image using the operation “im2bw” and thresholding.

Thresholding performs segmentation on the image. In other words, it divides the image

into two segments: 1) background and 2) object that is the bubble. The Threshold value is

defined as the minimum point between the two major peaks related to the bubble and the

background data in the histogram. Thresholding provides the segmentation to make the

39

desired object separated from the background. Image 4.5 shows the binary image with

thresholding.

Figure 4.5: Binary image of the bubble generated with image processing tool, using

thresholding.

4.2.3 Removing The Undesired Small Components From The Main Image

As it is shown in Figure 4.5, there are some smaller white components in the image

which are separate from the bubble and it is necessary to remove them. These components

can include smaller bubbles or noise. “bwareaopen” operation is a very useful tool in

MATLAB that removes any object that occupies any number of pixels which is smaller than

“P”. Figure 4.6 depicts the result with the removed small white components.

40

Figure 4.6: Binary image of the bubble after removing undesired small components using image

processing tool in MATLAB.

4.2.4 Filling The Holes And Pores Located In The Object

There are black closed areas existing in the image in Figure 4.6. These black areas

are a part of the bubble. However, since their gray scale values were similar to the

background and above the threshold value, they were colored black. To include them in the

bubble, they have to be filled with white color. “imfill” operation in MATLAB allows filling

these holes and illustrates a consistent view of the bubble. Figure 4.7 shows the result after

using “imfill”. The entire bubble is now white and the background is black. This process is

necessary for further geometric analysis on the bubble.

41

Figure 4.7: The binary image of the bubble after filling the holes inside the bubble using image

processing tool in MATLAB.

4.2.5 Determining the Position of the bubble Center of Gravity and Calculating the Aspect

Ratio

The position of the bubble center of gravity is calculated based on the two

dimensional image of the bubble. Using the two dimensional image for center of gravity can

only be valid if the bubble has a symmetric shape. The center of gravity is calculated in both

x and y directions. The coordinate of center of gravity in the x direction ( ) is defined as

∑

∑

Where n is the number of pixels in the x direction, pi is the binary value of pixel i (either 1

or 0), and xi is the coordinate of pixel i. The same calculation is carried out for y direction.

Figure 4.8 shows the bubble with its center of gravity, marked with a small black dot.

42

Figure 4.8: Position of center of gravity in two dimensions is shown with a black dot in the

bubble.

Aspect ratio is then calculated based on the coordinates of the center of gravity,

described in Figure 4.2. For this particular example, the aspect ratio is:

H/W=0.6113

Finally, the change of aspect ratio can be plotted for every group of bubble images

during the bubble formation and growth. The aspect ratio was plotted as a function of

normalized time and normalized position. These type of plots quantitatively analyses the

geometrical changes in the bubble and can be used to compare the geometry of bubbles

formed in different media with different viscosities.

4.2.6 Finding the Velocity of Bubble

Velocity of bubble was defined based on the position of the center of gravity and has

the unit of “number of pixel/s”. It indicates the number of pixels through which the position

43

of center of gravity travels in one second. If desired, this unit can be converted to m/s by

using the approximate distance between two pixels.

4.2.7 The Method to Compare the Bubble Shape Changes in Two Different Cases

In order to compare two sets of results under various experimental conditions, 8

different snapshots were provided for each set to cover different stages of bubble

formation and growth. Each individual image was analyzed by the image processing tool.

As each bubble has a different formation and growth time in every new condition,

the initial time of bubble formation or t=0 was set as the first moment that the bubble

began to emerge from the orifice into the box and camera frame.

Since the fluid level is not high enough for some particular cases, such as the single

high viscosity and viscosity gradient, the bubbles formed in these media hit the free surface

and push the fluid free surface to a higher level. Thus, portions of the bubble went above

the initial level of the fluid. Figure 4.9 vividly illustrates the two parts of the bubble that are

inside and outside of the fluid. As implementing the image processing for the object that

had two separate parts was difficult and caused errors, we applied the image analysis code

only to the part of the bubble which is inside the fluid. These conditions were applied to all

sets of results to provide a consistent method for comparing different sets of results with

each other.

44

Figure 4.9: Two parts of bubble inside and outside of the liquid which is separated by the liquid

free surface.

45

5. Results and Discussions

This chapter discusses the experimental results of investigation into bubble

formation and the effect of viscosity, viscosity gradient, liquid level and flow rate on the

process. The first section focuses on bubble formation with the liquid level of 1 cm. This

section describes the behavior of the bubble under the influence of viscosity when formed

in a single layer of Silicone oil and also when formed in two layers of Silicone oil with a

viscosity gradient. The second section covers the results of the first section for the liquid

level of 2 cm. The third section describes the visual results of bubble behavior in three

different flow rates.

For each set of experiment a new tube was used in order to avoid any error caused

by air entrapment. In the sequence of forming different bubbles, for each experiment, the

movie for the first bubble emerging from the orifice was recorded to have as much as

consistency needed. Five snapshots for each case were provided with the specific time of

the recorded image.

5.1 Bubble Formation at a Submerged Orifice in Silicone Oil with the Liquid Level of 1 Cm.

The air was pumped through the syringe tube and into the Silicone oil with the

constant flow rate of 0.09 ml/min. The diameter of the orifice was 2 mm. Bubbles were

formed in a relatively small (Finite) thickness. For 5.1.1 and 5.1.2 sections the focus is on

two viscosities of Silicone oil (1000 and 60,000 cSt), separately and the 4.1.3 section

discusses the liquid with viscosity gradient. Since the thickness in thermal sprayed splats is

very thin the liquid level of 1 cm was used to provide a finite thickness in order to reduce

the effect of gravity and buoyancy force on the movement of bubble.

46

5.1.1 Bubble Formation in Silicone Oil with the Viscosity of 1000 cSt

Figure 5.1 depicts the photographic sequences of the bubble formation and growth

in Silicone oil with the viscosity of 1000 cSt. Five different snapshots have been presented

to include all the stages of bubble formation and growth, including the post detachment

phase where the bubble rises upward through the bulk liquid.

Figure 5.1: photographic sequence of bubble formation and growth from 2 mm orifice

diameter, in Silicone oil with the viscosity of 1000 cSt and the liquid level of 1cm.

The results confirm the previous theories and experimental studies performed on

bubble formation. As the bubble grows, its volume increases and it fills the space

previously occupied by the liquid. The process involves the three general expansion,

detachment and dynamic stages.

During the early growth stage, the bubble is small and around the size of the orifice

and very close to a spherical or hemi-spherical shape. During this stage the influences of

the gravity and the hydrostatic pressure difference in the liquid around the bubble are

negligible.

However, in the middle stages when the bubble gets larger and elongated, the

pressure difference from the bottom of the bubble to the top of it, becomes more significant

47

which gets in line with the buoyancy effects increasing. These effects squeeze the bubble

and because the bottom of it is still attached to the orifice, the result is an elongated bubble

which is deviated from the spherical shape it had before. (t=1.79 in Figure 5.1) with this

elongation happening, the center of gravity position moves upward which is a suitable

parameter to study the geometrical changes in the bubble shape. The elongation is followed

by a necking that occurs right before the bubble detachment. (t=2.33 in Figure 5.1)

In the last stage and for this case with a constant air injection rate, the bubble starts

to detach from the orifice when the lifting forces including gas momentum and buoyancy

force become more significant and can conquer the retarding forces including viscous

force, surface tension force and inertia force. As a result of further addition of mass into the

bubble volume, there would be no stable state for the bubble unless it detaches from the

orifice.

5.1.2 Bubble Formation in Silicone Oil with the Viscosity of 60,000 cSt and Comparing the

Results with 1000 cSt Case.

After verifying the previous studies of bubble formation experimentally in the last

section, in this part we provide the results for bubble formation in Silicone oil with 60,000

cSt and compare it with the case for 1000 cSt viscosity. This viscosity difference is capable

of presenting the good visualization for the effects of viscosity on the shape and behavior of

the bubble. Moreover, as the solidification in splats occur very rapidly, the viscosity

difference between upper and lower layers of splat becomes significant. Therefore,

choosing these two values for viscosity of Silicone oil could provide the high enough

viscosity difference.

48

Figure 5.2 shows the photographic sequence for bubble formation in the two

viscosities of 1000 and 60,000 cSt next to each other. The yellow dye is also used to

distinguish the 1000 cSt oil from the 60,000 cSt oil. The yellow colored liquid represents

the 1000 cSt oil for the rest of figures.

Figure 5.2: Bubble formation in 1000 and 60,000 cSt viscosity of Silicone oil with the flow rate of

0.09 ml/min.

With reconsidering the forces acting on a bubble when formed at an orifice from

chapter 2:

There is a balance between these forces at the time of detachment:

FB+FCP=FC+FD,

FB=Buoyancy force, FCP =Pressure force and FM= force due to gas momentum which is

negligible in low gas flow rates and FC= surface tension force and FD= Drag forces

With the drag force getting stronger, it takes more time for the lifting forces (Gas

momentum and buoyancy force) to move the bubble upward. Therefore, the bubble

49

formation period increases in a liquid with higher viscosity. The result that was verified in

this set of experiment with Silicone oil and viscosity of 60,000 cSt.

Based on table 1 from chapter 2 which presents various models defined for bubble

volume, it is shown that the bubble size gets bigger in a liquid with higher viscosity. The

bubble spreads more on the edge of the orifice at the bottom of the box and the neck

formation process is delayed which eventually results in a longer time for the bubble to

detach.

Figure 2 clearly shows that bubble in the early stage of formation with higher

viscosity has the same features and behavior when formed in a liquid with smaller

viscosity. However, in the middle stages, the elongation happening in the shape of the

bubble is more significant than the elongation in the 1000 cSt oil. The width of the bubble

also in this stage is bigger than the bubble’s width in the less viscous liquid. The interesting

part of this experiment is that because we chose a relatively thin liquid level (1 cm), the

bubble in the 60,000 cSt viscosity, doesn’t have enough time to detach completely from the

orifice and travel through the liquid in the final stages. Instead, the bubble hits the free

surface, while still being attached to the orifice.

5.1.3 Bubble Formation in a Viscosity Gradient

As described in chapter 2, in one set of our experiments the bubble is formed in a

liquid with two layers. The bottom layer is Silicone oil with 60,000 cSt and the upper layer

is 1000 cSt. The injection flow rate is 0.09 ml/min and the liquid level is 1 cm. Figure 5.3

shows the photographic sequence of bubble growth in the viscosity gradient.

50

Figure 5.3: photographic sequence of bubble formation and growth from 2 mm orifice

diameter, in Silicone oil with the viscosity gradient and the liquid level of 1cm.

When the bubble forms in the viscosity gradient, at the early stage (t≤0.60), it is still

in the medium with higher viscosity (60,000 cSt). Hence, the bubble shape is close to a

sphere, like other cases with single viscosity. In the middle stages (0.60≤t≤6.00), when

additional air is injected into the bubble and increases the bubble volume, the bubble tends

to show the same behavior as the case with 60,000 cSt viscosity. The bubble tends to

expand as much as possible because of the stronger viscous forces and elongate afterwards.

However, comparing the viscosity gradient case with the case of single high

viscosity (60,000 cSt) shows when the bigger portion of the bubble enters the upper layer

of the liquid with less viscosity (1000 cSt) the decrease in drag force turns the balance in

favor of buoyancy force effects. This stronger lifting force which tends to move the top of

the bubble upward, squeezes the bubble from sides so that the bubble can elongate, but

with a smaller width than the case with higher viscosity (60,000 cSt). This process also

causes the bubble formation period become shorter than the case with higher viscosity and

as a result, the volume of the bubble becomes smaller and necking occurs sooner in the

final stage (t≤13.03). The bubble is still attached to the orifice when it hits the free surface

of the liquid. (The same behavior observed in the high viscosity liquid.) But the cross

sectional area that hits the free surface is smaller. (Figure 5.4)

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Figure 5.4: Photographic sequence of bubble formation in three cases of 1000 cSt and 60,000

cSt and viscosity gradient with flow rate of 0.09 ml/min and liquid level of 1 cm.

In comparison with single low viscosity case (1000 cSt), the bubble formation time

increases in the viscosity gradient case, because the higher viscosity in the bottom layer,

increases the drag force and it takes more time for the lifting forces to move the bubble

upward. This also delays neck formation and detachment. The bubble size is also bigger

and the shape deviates from spherical shape more significantly. (Figure 5.4)

5.2 Bubble Formation in Liquid Level of 2 cm

In the last set of experiments it was observed that the bubble in two cases (high

viscosity and viscosity gradient) doesn’t detach from the orifice when it hits the free

surface of the liquid. Therefore, another set of experiments was performed to let the bubble

have more time before hitting the free surface in order to highlight possible changes in the

shape and behavior of the bubble. Similar to the previous section, this section includes the

52

results for the three cases of low single viscosity (1000 cSt), high single viscosity (60,000

cSt) and viscosity gradient.

5.2.1 Bubble Formation in 1000 cSt Viscosity and 2 cm Liquid Level

Figure 5 shows the bubble formation and growth in a sequential time in 1000 cSt

Silicone oil and the height of 2 cm compared to the results gained from the last section. The

only difference is the liquid level. Increasing the liquid level simply increases effect of

buoyancy forces and accelerates the bubble to move upward.

Figure 5.5: Bubble growth in Silicone oil with low viscosity of 1000 cSt and comparison between

the two cases with liquid levels of 1 cm and 2 cm.

Therefore, with the same flow rate, the bubble in the higher liquid level, faces

stronger lifting forces and grows and rises faster than the bubble in a lower liquid level. As

a result, the neck formation and detachment from the orifice occurs sooner. For example

Figure 5.5 depicts that the bubble in the liquid level of 1 cm detaches from the orifice

approximately 4.10s after the emergence. On the other hand, in the liquid level of 2 cm, the

bubble detachment happens approximately 2.33s after the early stage.

53

5.2.2 Bubble Formation in 60,000 cSt Viscosity and 2 cm Liquid Level

Figure 5.6 indicates the photographic sequence of bubble growth in Silicone oil with

the viscosity of 60,000 cSt and liquid level of 2cm, compared to the case with 1000 cSt

viscosity.

Figure 5.6: Photographic sequence of bubble formation and growth in Silicone oil with viscosity

of 60,000 cSt and liquid level of 1 cm and 2cm.

Figure 5.6 clearly shows the highlighted difference in bubble behavior under the

effect of viscosity. With higher viscosity, the bubble size increases and with stronger

viscous forces, there is more time needed for the buoyancy force to act on the bubble.

Therefore, the necking is delayed in higher viscosities and the bubble formation period

lasts longer. For this case, the detachment of bubble in higher viscosity occurs after 22.26 s

and the bubble detachment in less viscous liquid happens after 2.33 s.

Figure 5.7 shows the photographic sequence of bubble formation and growth in

Silicone oil with the viscosity of 60,000 cSt and liquid level of 2cm, compared to the case

with 1cm of liquid level.

54

Figure 5.7: Bubble growth in Silicone oil with high of 1000 cSt and comparison between the two

cases with liquid levels of 1 cm and 2 cm.

With adding 1 cm to the liquid level, buoyancy effects become more dominant than

the viscous effects. Hence, the bubble forms, grows and detaches sooner than the case with

1 cm liquid level. As it is shown in Figure 7, the bubble’s shape is closer to spherical shapes

in higher liquid level. The bubble in the final stage is detached at 27.26 s. on the other hand

bubble in the same final stage in 1cm liquid level is still attached to the orifice while it has

already hit the free surface. This thin liquid layer forces the bubble shape to deviate from

the spherical shapes predicted and studied for the bubble formation process.

5.2.3 Bubble Formation in Viscosity Gradient with Liquid Level Of 2 Cm.

This time the bubble was formed in a two layer liquid with a viscosity gradient and

in the liquid level of 2 cm. the flow rate is the same as the previous case. (0.09 ml/min)

Figure 5.8 shows a photographic sequence of the bubble forming and growing in the

viscosity gradient where the lower layer is the high viscosity of 60,000 cSt and the upper

layer is the low viscosity of 1000 cSt.

55

Figure 5.8: Photographic sequence of bubble formation in viscosity gradient with the liquid level

of 2 cm.

As we observed for the previous set of experiments in a viscosity gradient, the

bubble shape at the early stage (t≤1.10) is spherical and after a portion of bubble enters the

less viscous layer, the decrease in viscous forces expedites the movement of upper portion

of the bubble upward and the bubble elongates. This elongation is vividly highlighted as the

liquid level increases for 1 cm. for example at 3.71 s, the bubble is very close to a cylinder

and then the necking occurs in the following stages.

Here we can compare the new set of results with the previous results in different

point of views: Figure 5.9 shows the complete three sets of results for bubble formation

and growth in liquid level of 2 cm. It contains the snapshots of bubble formation in low

viscosity (1000 cSt), high viscosity (60,000 cSt) and viscosity gradient.

56

Figure 5.9: photographic sequence of bubble formation in low viscosity, high viscosity and

viscosity gradient with the liquid level of 2 cm.

Compared to the single low viscosity case (1000 cSt), when the bubble is formed in

the viscosity gradient, the volume gets bigger, the necking is delayed and therefore, the

bubble formation and growth time increases. For instance, the bubble neck detaches from

the orifice at 2.33 s when formed in the 1000 cSt oil, while the bubble in the viscosity

gradient hasn’t been detached completely from the orifice 12.31 s after the formation.

Observing the viscosity gradient results and the high viscosity (60,000 cSt), on the other

hand, shows that the viscosity gradient decreases the bubble formation and growth time

and expedites the neck formation and detachment.

Figure 5.10 presents the results of bubble behavior in viscosity gradient with two

liquid levels.

57

Figure 5.10: Photographic sequence of bubble formation and growth in viscosity gradient with

two levels of liquid.

Figure 5.10 readily depicts how an additional 1 cm of height can distort the normal

shape of bubble and deviate it further from the spherical shape. Moreover, increasing the

liquid level makes the buoyancy forces stronger. When the buoyancy forces are weaker, as

the case with 1 cm liquid level, the expansion stage of bubble is more pronounced than the

bubble detachment stage and as mentioned in the previous sections of this chapter, weaker

lifting forces, need more time to detach the bubble from the orifice. The neck formation is

delayed in a medium with decreased buoyancy. As it is shown in Figure 5.10, the bubble in

the smaller liquid level starts the necking at the 13.03 s and while the bubble in the higher

liquid level starts the necking approximately at 5.24 s. besides, the decreased buoyancy

forces make the bubble diameter detachment smaller. The elongation of the bubble is also

more projected in the higher liquid level and it more vividly proves our hypothesis that the

bubble shape changes in a great amount under the influence of viscosity gradient.

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5.3 Comparison between Experimental Results and Thermal Sprayed Splats

As mentioned in the previous chapters, our main inspiration was the images

achieved from the FIB movies out of the thermal sprayed obsidian splats. The frozen

bubbles in these splats are large, they don’t have the spherical shape and they are mainly

elongated along the splat thickness. Figure 5.11 puts the results of bubble formation in

viscosity gradient next to the one sample snapshot of the bubbles observed in splats.

Figure 5.11: Bubble shapes from experimental results and FIB image of frozen bubbles in

thermal spray splats.

The bubbles from the experimental results which were formed in the viscosity

gradient become more distorted and deviated from the spherical shapes in the middle and

final stages of growth and they get closer in shape to what actually was observed in FIB

59

movies of frozen bubbles in thermal sprayed obsidian splats. This verifies our hypothesis

that the bubbles observed in obsidian splats are formed in a viscosity gradient.

5.4 Effect of Flow Rate on Bubble Formation and Growth

After performing the experiments with the pumping flow rate of 0.09 ml/min, the

experiments were repeated with two other flow rates, one higher and one lower than 0.09

ml/min in order to observe whether the bubble formation process was going under any

transition and the results would be consistent in a reliable range of flow rate.

Figure 5.12 depicts the photographic sequence of bubble formation and growth for

two new flow rates of 0.03 and 0.27 ml/min. the liquid level is also chosen equal to 1.5 cm

to be in the range of 1-2 cm that was studied before.

Figure 5.12: Photographic sequence of bubble formation in viscosity gradient with flow rates of

0.03 and 0.27 ml/min and liquid level of 1.5 cm.

Based on the previous studies and the modified models developed for predicting the

bubble volume during time, the bubble volume becomes bigger when the flow rate

increases. The amount of change in the bubble volume depends on the regime of the bubble

60

formation and how big or small the flow rate is. In the present study, in order to simulate

the bubble growth in thermal sprayed splats, the flow rates chosen are as small as possible.

In the range of the chosen flow rates in this study, when the flow rate increases, the change

in the bubble is not significant, but it is still visible, as it is shown in Figure 5.12. The bubble

volume with the 0.27 ml/min flow rate is bigger than the case with 0.03 ml/min flow rate.

As mentioned in the previous chapters and based on other researchers’ results,

increasing the flow rate, decreases the bubble formation time, neck formation time,

detachment time and the bubble growth period. Based on Figure 5.12, these results were

verified. The bubble in the 0.03 ml/min flow rate, begins to detach completely from the

bottom at 19.42 s, on the other hand it takes less time for the bubble to detach from the

orifice in the higher flow rate of 0.27 ml/min(It take 15.93 seconds for detachment).

Increasing the flow rate empowers the gas momentum and therefore, the lifting forces

become stronger and detachment of bubble occurs sooner.

Three sets of visual results of bubble formation in viscosity gradient with three flow

rates of 0.03, 0.09 and 0.27 ml/min indicated a consistent behavior and shape change for

the bubble. No other significant change was observed besides the results mentioned above.

In the first stage, the bubble is spherical, after entering the low viscous layer, the bubble

elongates and the shape deviates from the previous spherical shape and still there is

similarities observed between the bubbles formed in these experiments and the frozen

bubbles in the FIB movies of thermal sprayed obsidian splats.

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5.5 Image Processing Results

As discussed earlier with details in chapter 4, a MATLAB code was developed to

implement the image analysis for a set of images of bubbles. In this section the results for

two different sets of results will be discussed: 1) Bubble formation in single high viscosity

of 60,000 cSt 2) Bubble formation in viscosity gradient.

As the bubble in higher viscosity is bigger and the changes might be visually closer

to the case with viscosity gradient, the case with 60,000 cSt was chosen to highlight the

viscosity gradient effect on bubble geometry. The liquid level for each set of experiment is

1.5 cm.

5.5.1 Image Analysis of Bubble Formation in Silicone Oil with 60,000 cSt Viscosity

Figure 5.13 shows 8 different stages of bubble formation in Silicone oil with

viscosity of 60,000 cSt. With applying all the stages of MATLAB image processing tool

described in chapter 4, there are 5 different sets of results provided to understand the

behavior of bubble.

1) Aspect ratio vs image number:

Figure 5.14 illustrates the variation of aspect ratio of the bubble versus the image

numbers. Aspect ratio has a slight decrease while travelling from image 1 to image 2

because of the great amount of size difference. However, the aspect ratio clearly increases

afterwards.

62

Figure 5.13: Photographic sequence of bubble formation in Silicone oil with viscosity of 60,000

cSt and liquid level of 1.5 cm and flow rate of 0.09 ml/min.

13.00 [s] 24.81 [s] 27.86 [s]

36.06 [s] 33.40 [s] 39.30 [s]

41.05 [s] 44.58 [s]

63

Figure 5.14: The evolution of bubble’s aspect ratio for 8 stages of bubble formation in Silicone

oil with viscosity of 60,000 cSt and flow rate of 0.09 ml/min.

2) Aspect ratio vs normalized time:

In order to provide consistent criteria to compare the two cases in this chapter for

different viscosity conditions, instead of plotting the evolution of aspect ratio versus real

time, a normalized time range was used between 0 and 1.

Tnorm=Time of every recorded image/maximum time for the last recorded image

Figure 5.15 depicts the change in aspect ratio versus normalized time. It is useful to

reemphasize that the very first moment that the bubble emerges from the orifice is

considered as t=0. Therefore, at t=0 there is actually no image of bubble available which

64

can be used in MATLAB image processing tool. That’s why in plots of bubble aspect ratio

versus normalized time, the curve doesn’t start at tnorm=0.

Figure 5.15: Aspect ratio evolution in normalized time for the bubble formation in Silicone oil

with viscosity of 60,000 cSt and flow rate of 0.09 ml/min.

Figure 5.15 indicates that after experiencing a small amount of decrease at the first

stage, the bubble aspect ratio will start increasing at tnorm≈0.55. First, the amount of this

increase is moderate, but after tnorm≈0.62 the slope is high enough that changes the amount

of aspect ratio from AR≈0.45 to AR≈0.92. The increase becomes significant as a result of

buoyancy effects at the early stages of neck formation.

3) Aspect ratio versus normalized position:

65

Relating the change of the aspect ratio to the position of bubble has the potential to

provide interesting results on understanding the effect of viscosity on bubble geometry.

Figure 5.16 shows the aspect ratio variation along the change of bubble position. Here, the

bubble position is considered as the center of gravity vertical position Ynorm. Again, in order

to present comparable data, this position is normalized.

Ynorm= (Ymax-Yn)/ (Ymax-Yn) max

Also the subscript n varies from 1 to 8, to consider every image for finding the

center of gravity’s vertical position at each stage.

Figure 5.16: Evolution of aspect ratio versus normalized vertical position of bubble’s center of

gravity in Silicone oil with 60,000 cSt in viscosity and flow rate of 0.09 ml/min.

66

Figure 5.16 is in agreement with past observations of bubble geometry in different

stages of growth. It is vividly shown that when the bubble rises, the aspect ratio increases

and approximately the second half of its path is accompanied by a significant increase of

the aspect ratio. This proves what we have observed in previous sections as the bubble

elongated and the shape deviated from the spherical shape.

4) Velocity of the bubble versus time

The velocity of center of gravity position is simply defined as described below:

Vc.o.g=dnorm/t

Figure 5.17: Bubble velocity evolution during growth time in Silicone oil with 60,000 cSt

viscosity and flow rate of 0.09 ml/min

67

Where Vc.o.g is the velocity of center of gravity, dnorm is the normalized distance

between every two positions of center of gravity between two consequent images or

stages, t is the time difference between the two stages.

In the present study, as it was not possible to implement the image processing for

t=0, the velocity related to the first image at t=13 s wasn’t available. However, the velocities

for all other images starting from the second image could be approximated by MATLAB.

Figure 5.17 shows the variation of velocity based on time for the stages of bubble formation

presented in this case, excluding the first stage.

The velocity of center of gravity has the unit of normalized position per second,

because the normalized distance between two consequent positions is calculated based on

the number of pixels existing between two consequent centers of gravity. If desired, this

normalized distance unit can be converted into meter (m) upon the distance between every

two pixels.

5) Velocity of the bubble versus normalized time

The bubble velocity defined in the previous section is plotted versus normalized

time in figure 5.18.

68

Figure 5.18: Bubble velocity through normalized time.

First, in Figure 5.18 the velocity of bubble increases. This is because of the pressure

of air injected into the volume of bubble at first stages of growth. On the other hand, the

velocity decreases after this stage. Comparing the velocity trend with Figure 5.13 reveals

that the behavior change occurs when the bubble is going under transition from t=27.86 s

to t=33.40 s where it is no longer spherical and tends to attach from the orifice by starting

the neck formation. The bubble grows with decreasing velocity till it faces an increase in

the velocity again in tnorm≈0.87 when the bubble is growing from t=39.30 s to t=41.05 s in

Figure 5.13. In this period, the bubble has already hit the liquid free surface and it seems

that the cohesive forces of surface tension in this high viscosity oil, accompanied by

buoyancy force pulls the bubble to detach faster from the orifice and this makes the

69

velocity to increase. The bubble’s velocity decreases again in the last stage, because it is

almost completely detached from the orifice and moreover, the liquid free surface

completely acts as an obstacle to prevent the bubble to rise further.

5.5.2 Image Analysis of Bubble Formation in Silicone Oil with Viscosity Gradient

Figure 5.19: Photographic sequence of bubble formation in Silicone oil with viscosity gradient,

liquid level of 1.5 cm and flow rate of 0.09 ml/min.

Figure 5.19 shows 8 different stages of bubble formation in Silicone oil with

viscosity gradient. As explained before, the lower layer is the oil with high viscosity (60,000

1.05 [s] 2.53 [s] 3.54 [s]

4.52 [s] 5.13 [s] 5.75 [s]

6.03 [s] 6.48 [s]

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cSt), the upper layer is the oil with low viscosity (1000 cSt). The liquid level is 1.5 cm and

the flow rate is constant and equal to 0.09 ml/min.

The same 5 sets of results obtained for the single high viscosity in the last section

are presented in this section:

1) Aspect ratio vs image number:

Figure 5.20 depicts the variation of bubble aspect ratio through the sequence of

images or stages.

Figure 5.20: Aspect ratio evolution based on image number for bubble formation in viscosity

gradient and flow rate of 0.09 ml/min

71

It is shown that aspect ratio increases in a great amount stage by stage. It varies

approximately from 0.5 to 10.5. Hence, at the first glance, figure 5.20 proves the

significant elongation happening in the bubble shape in a liquid with viscosity gradient.

2) Aspect ratio vs normalized time:

The bubble aspect ratio is plotted versus the normalized time in Figure 5.21.

Figure 5.21: evolution of aspect ratio based on normalized time

Again, it is important to note that the curve doesn’t start at 0, because there was

no image of bubble available to apply image processing on for t=0 in MATLAB.

3) Aspect ratio versus normalized position:

72

In figure 5.22 the geometrical behavior of the bubble is shown based on

normalized vertical position of the center of gravity. The definition of the normalized

vertical position is the same as described in the previous section.

Figure 5.22: Aspect ratio variation versus normalized vertical position of bubble in Silicone oil

with viscosity gradient and flow rate of 0.09 ml/min

It is shown that as the bubble rises, the aspect ratio increases. The aspect ratio

increases smoothly until the final stages. When normalized position is 0.8 the aspect

ratio changes become significant. It agrees with the fact that when the bigger portion of

the bubble enters the low viscosity layer, the buoyancy force becomes more powerful

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and the elongation in the bubble is very significant in a way that the aspect ratio

reaches around 10.5.

4) Velocity of the bubble versus time

Figure 5.23 shows the evolution of bubble’s center of gravity velocity through

growth time.

Figure 5.23: Bubble velocity versus time in a viscosity gradient and flow rate of 0.09 ml/min

Comparing Figure 5.17 and Figure 5.23 restates that the bubble formation and

growth time becomes significantly small when the high viscosity liquid changes into a

liquid with viscosity gradient. Moreover, observing the velocity values reveals that the

bubble velocity in high single viscosity liquid (60,000 cSt) is much smaller than the bubble

74

velocity in a viscosity gradient. In a high single viscosity, the bubble velocity changes in the

range of 0.021-0.058 normalized position/s while the velocity change in viscosity gradient

is in the range of 0.1-0.27 normalized position/s.

5) Velocity of the bubble versus normalized time

Figure 5.24 depicts the bubble velocity variation in normalized time.

Figure 5.24: Bubble velocity versus normalized time in a viscosity gradient and flow rate of 0.09

ml/min

After the second stage, the velocity decreases as the bigger portion of bubble is still

in the high viscous layer, but when the bubble rises and the bigger portion of it enters the

low viscosity layer, the velocity increases. This behavior continues till the bubble hits the

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liquid free surface. After hitting the free surface, the velocity drops again. After the neck is

completely formed, the bubble is going to detach from the orifice, the effect of buoyancy

also pulls the bubble and the velocity increases again.

5.5.3 Comparison between the Two Discussed Cases

Plotting the bubble aspect ratio and velocity in normalized time and normalized

position is helpful to compare two or more cases that occur in different time ranges. Figure

5.25 depicts the variation of bubble aspect ratio in normalized time for two cases of single

high viscosity (60,000 cSt) and viscosity gradient.

Figure 5.25: Evolution of bubble’s aspect ratio in normalized time for two cases with flow rate

of 0.09 ml/min

76

Taking a glance at two vibrational curves for two discussed cases, clearly agrees

with what have been found from the bubble formation and growth images. In the case of

high single viscosity, the aspect ratio increases in a very small amount and doesn’t exceed

1. It means the height of center of gravity never becomes equal to or bigger than the width

of the bubble at center of gravity position. On the other hand, for the viscosity gradient

case, the aspect ratio exceeds 10 and this proves the elongation and the significant effect of

viscosity gradient on the geometry of the bubble.

Figure 5.26 illustrates the change in aspect ratio with change in normalized vertical

position of the bubble for two different cases.

Figure 5.26: Evolution of bubble’s aspect ratio in normalized bubble position for two cases with

flow rate of 0.09 ml/min

77

Comparison between two cases in Figure 5.26 indicates the significant difference in

behavior of the bubble. The aspect ratio for two cases increases. However, the aspect ratio

at late stages of bubble growth increases significantly for the viscosity gradient case, while

it increases slightly for the high viscosity case. This difference happens after the normalized

position is equal to 0.8 and it shows the main elongation happens in the viscosity gradient

at final stages.

Figure 5.27 depicts bubble velocity change for two cases.

Figure 5.27: Evolution of bubble’s aspect ratio in normalized bubble position for two cases with

flow rate of 0.09 ml/min

78

As it is shown, the bubble velocity for the single high viscosity liquid varies very

smoothly while the velocity for viscosity gradient changes in a bigger range and fluctuates

more significantly.

This method and described findings are interesting tools to quantify visual results of

bubble growth in different conditions which can be applicable to achieve a better

understanding of bubble formation in thermal spray process and also the bubble formation

from an orifice in general.

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6. Conclusions and Recommendations for Future Work

6.1 Conclusions

We investigated the bubble formation process at a submerged orifice and observed

the effects of different parameters on bubble shape and growth. The purpose of this work

was to simulate the conditions governing the bubble nucleation in thermal sprayed

obsidian splats.

We experimentally studied the effects of flow rate, liquid level, viscosity and

viscosity gradient on bubble growth and dynamics; and by applying the image analysis tool

on the images, we verified the effect of viscosity gradient on the bubble geometry. The

following are the major results obtained:

With increasing the liquid viscosity, the bubble volume and the bubble growth time

increases.

With increasing the liquid level, the effects of buoyancy forces become significant

and the bubble growth time decreases.

The liquid with viscosity gradient makes the bubble to detach later than the single

low viscosity and sooner than the single high viscosity.

Viscosity gradient elongated the bubble and deviated the shape of bubble further

from spherical shapes.

The bubbles resulted in the viscosity gradient were the closest in shape to the

bubbles observed in FIB movies of thermal sprayed obsidian splats.

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The image analysis on the bubble images indicated that the aspect ratio of the

bubble exceeds 10 in a viscosity gradient while the aspect ratio never becomes

equal to or more than 1 in a single layer of high viscosity.

The image analysis showed the bubble velocity in viscosity gradient fluctuates in a

wider range than that of the case with single high viscosity.

These findings provide a potential to control the shape and growth dynamics of the

bubbles and a better understanding of bubble formation in thermal spray coatings

and magma columns while volcano eruption.

6.2 Recommendations for Future Work

The path of studying bubble formation in various conditions has different

undiscovered directions. Different changes in operating parameters and conditions can

lead to a big change in bubble dynamics and shapes. In this section there are a few

suggestions presented which has a good potential for further investigations:

Studying the effect of viscosity gradient on behavior and coalescence of two bubbles

growing from two neighboring orifices.

Studying the influence of viscosity gradient on bubble formation process by

applying a liquid with more than two layers of different viscosities.

Studying the effect of viscosity gradient on bubble shape and dynamics with higher

flow rates with focusing on break up occurring in the bubble and dividing it into two

parts.

81

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