NSF-REU PROJECT AT UIC

Nadiya KlepClemson University, SCDavid Pelot, UICDr. Yarin, UIC August 2,2013

Spreading of Herschel-Bulkley fluid using lubrication approximation

Source: www.alibaba.com

OUTLINE: Purpose and applications

Background

Sample preparation

Methods of data collection

Data

Results

PURPOSE AND APPLICATION Small Angles <2˚

• Bearings• Screw extruder

Larger angles (5 ˚+)• Construction***

• Grout, mortar, joint compound

• Foods • Industrial processing

• Spreading of• Jams• Frosting• Peanut

butters• Etc.…

• Personal care products• Creams• Hair jells

BACKGROUND:

Source: www.substech.com

Source: Schlichting, Boundary-Layer Theory,McGraw-Hill,Inc,1987.

Small angles in a nutshell:• small angle between the two surfaces.• convective acceleration• viscous forces predominate over inertial forces • Navier–Stokes equations becomes simpler:

• With the use of boundary conditions :at y = 0, u = U at x = 0, p = p0

at y = h, u = 0 and at x = l, p = p0

• and the fact that volume flow must be a constant:

From this the equation for velocity (:

Where:

• Backflow occurs in areas of increasingpressure near the stationary wall

V0

2

0y H dp y yu = V 1 - - 1 - H 2μ dx H H

dpdx

 = 12μ(V0

2 H2  −  QH3 )p ( x )  =  p0  + 6 μV 0∫

0

x dxH2  − 12 μQ∫

0

x dxH3

SAMPLE PREPARATION:

Source: Noveon Source: wikipedia.com

2. Neutralized with NaOH 3. Stress yield fluid: Herschel-Bulkley 1. 1.5% Solution of Carbopol

Source: www.pharmainfo.net

Source: www.alibaba.com

CARBOPOL VISCOSITY

0.1 1 10 1001

10

100

1000 Vane Visc

Shear rate (1/s)

Visc

osity

(Pa·

s)

Power Law: fluids=µ Newtonian=non-Newtonian =µeff : eff. viscosity

METHODS OF DATA COLLECTION: Apparatus to mimic the wedge: High-speed camera Phantom video player MatLab OriginPro graphing

DATA AND ANALYSIS

Source: Schlinchting, Boundary-Layer Theory,McGraw-Hill,Inc,1987.

𝐹 𝑛=∫0

𝑙

𝜎𝑛𝑛𝑑𝑥

cos (𝛼)

2

0y H dp y yu = V 1 - - 1 - H 2μ dx H H

2 2nn n xx xy yyσ = n σ = sin (α) σ + 2sin(α)cos(α)σ + cos (α)σ

RESULTS: At larger larger amount of fluid under

wedge faster reverse flow

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00

5

10

15

20

25

30

35

40

x

0H

-0.20.00.30.50.81.0

f) 20 ˚, 1300um, 0.167m/s

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00

10

20

30

40

50

60

70

80

0H

x

-0.2

0.0

0.3

0.5

0.8

1.0

e) 20˚, 600um, 0.167m/s

0.0 0.2 0.4 0.6 0.8 1.00

3

6

9

12

15

18

x

0H

-0.2

0.0

0.3

0.5

0.8

1.0

d) 10 ˚ , 1500um, 0.167m/s

RESULTS: At same as h1 increases Force

decreases

-1 1 3 5 7 9 11 13 150

4

8

12

16

20

a

c

d

f

Time t, sec

Forc

e F

(N)

Ho=23 h1 =600um

Ho=34 h1=800um

Ho=15 h1=1500um

Ho=40 h1=1300um

RESULTS: At same h1 increases Force, F (N) decreases

Ho=23 h1=600umHo=34 h1=800um

Ho=87 h1=600um

0 2 4 6 8 10 12 14 16 180

2

4

6

8

10

12

14

16a

c

e

Time t, sec

Forc

e F,

N

0 2 4 6 8 10 12 14 16 180

4

8

12b

d

f

Time t, sec

Forc

e F,

N

Ho=10 h1=1500umHo=18 h1=1500um

Ho=40 h1=1300um

RESULTS: At same h1 & as V0 (U) increases

Force increases

0 2 4 6 8 10 12 140

1

2

3

4

5

6

7

8

9 g

h

e

f

TIme t, sec

Forc

e F,

N

V=0.167m/s

Ho=80 h1=650umV=0.24m/s

Ho=35 h1=1500um

Ho=87 h1=600um

Ho=40 h1=1300um

SUMMARY OF RESULTS

Trial (Fig. 5)

Angle (deg)

H1 (mm)

Velocity (m∙s-1)

Force (N)

Viscosity (Pa∙s)

a 5 0.60 23 0.167 19.1 4.7b 5 1.50 10 0.167 15.0 5.9c 10 0.80 34 0.167 13.5 11.4d 10 1.50 18 0.167 7.9 8.3e 20 0.60 87 0.167 8.1 20.2f 20 1.30 40 0.167 6.8 19.5g 20 0.65 80 0.240 9.8 17.2h 20 1.50 35 0.240 9.7 20.0

VISCOSITY

1

10

100

1000

0.1 1 10 100

Visc

osity

(Pa·

s)

Strain rate (1/s)

Max shear rate was calculated to be: 300s-1 : Viscosity: 0.6PasMin shear rate was calculated to be: 3s-1 : Viscosity 30 Pas

Questions?

Thank you to: NSF grant # 1062943 Dr. Yarin David Pelot Everyone in Dr. Yarin’s group Professors Takoudis and Jursich Everyone involved with the REU program at UIC