Drop Deformation in UniaxialExtensional Flow Fields in Microgravity*

By Christian Berg, Michael Dreyer, and Hans J. Rath**

A liquid bridge stretching technique for measuring thedeformation of emulsion drops in pure uniaxial extensionalflow is presented. The experiments are carried out in the drop-tower facility of ZARM at the University of Bremen whichprovides microgravity conditions of about 10±6 g for 4.7 s.

The liquid bridge is generated under microgravity and heldbetween two plates by surface tension. The initial length anddiameter of the cylindrical bridge are 30 mm. The fluid bridgeis stretched exponentially to a maximum length of one meterproviding a maximum Hencky strain of about 3.5. At the sametime, the disk diameter is reduced exponentially from 30 to10 mm in order to preserve the cylindrical bridge contour.

The new device makes drop deformation experimentspossible with emulsion drops of any density and wide-spreadviscosity ratio. Thus, drop deformation experiments with asingle drop or cluster of a few drops in a pure extensional flowfield are possible. A result of this project is the specification ofthe time dependence of the deformation in relation to thecapillary number describing the ratio between viscous stressand capillary pressure and to the viscosity ratio between dropand matrix fluid.

1 Introduction

During transport and processing of an emulsion, e.g., innozzles or extruder dies, a superposition of the uniaxialextensional flow and shear flow field occurs. In the case of asharp decrease in the pipe cross-section, the uniaxial exten-sional flow dominates and determines the deformation of theemulsion drops, which can lead to drop tearing. For the exactprediction of drop deformation in uniaxial extensional flow,rheological models are developed whose reliability should beverified by measurements. Therefore, a new device whichproduces a uniaxial extensional flow field in a cylindricalliquid bridge was constructed. The bridge consists of a modelemulsion with a few large drops whose deformation can beobserved simultaneously with the extension of the liquidbridge.

The experiment is performed in microgravity during a 4.7sfree fall period at the drop tower ªBremenº. The residualacceleration in the experimental setup is of the order of 10±6g.This is due to the equivalence of inertia and gravitationalforces in the refeence system of the falling capsule. In this case,the hydrostatic pressure in the maximal one meter long liquidbridge is disappearingly weak so that the stabilizing forces in

the bridge are always able to compensate the hydrostaticpressure. Consequently, medium viscous emulsions can bestretched in a bridge sized sufficiently large which allowsprecise visualization of the emulsion drops. Comparableexperiments under gravity producing a uniaxial extensionalflow field employ higher viscous or spinnable fluids [1], formvery narrow liquid bridges with small diameters [2] orcompensate for the hydrostatic pressure by buoyancy [3].

The liquid bridge is held between two equal disks, whosediameter can be minimized with increasing extension so thatcontour deformations as they occur in references [2] and [3]can be avoided. Consequently, the liquid bridge remainsalmost cylindrical at constant volume during the time-controlled stretching. In this way, a uniaxial extensional flowfield of constant extension rate with respect to space and timeis induced. Thereby, the flow induced tension onto the drops isindependent of the drop position and stretching time.

The problem of drop deformation is of considerablefundamental interest in cosmetics and food industry fordispersion processes in commercial blenders and mechanicalemulsifiers. In this case, long-term stable emulsions should beproduced with a power consumption as small as possible. Theemulsions are produced with precisely defined drop sizedistributions that lead to specific product qualities, such ascolor, taste, and rheological behavior.

A change of drop size distribution in an emulsion caused bystress may cause an undesired modification of the productqualities. For the exact prediction of the fluid dynamicbehavior of emulsions in uniaxial extensional flow, profoundknowledge of their deformation properties is necessary. Thepresent experimental setup allows the study of transient dropdeformation and breakup in model emulsions containingseveral drops in pure uniaxial extensional flow.

2 Experimental Setup

The new device was developed for drop tower experimentsaccording to [4] which creates a uniaxial extensional flow fieldwith a constant extension rate in space and time (Fig. 1).

The drop deformation can be observed with sufficientaccuracy (0.1 mm length error) in the large liquid bridge whichis only producible in microgravity. Since negligibly smallhydrostatic pressure in the liquid occurs under microgravity,no perceptible contour tapering of the large bridge appears.Furthermore, inertia and viscosity of the liquid stabilize thecontour of the bridge compared to the surface tension exertedto divide the bridge to minimize its surface. A predominantcylindrical liquid bridge with insignificant necking to theaccelerated disk can be achieved with medium to high viscousmatrix liquids (Fig. 2). Such a cylindrical liquid bridge canestablish a high quality uniaxial extensional flow field in anemulsion which can not be achieved in gravity, e.g., in a plateautank [3].

Before a microgravity experiment starts, the matrix liquid isconveyed between the two disks and held with the aid of two

Chem. Eng. Technol. 22 (1999) 2, Ó WILEY-VCH Verlag GmbH, D-69469 Weinheim, 1999 0930-7516/99/0202-00123 $ 17.50+.50/0 123

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[*] Poster presented at the GVC-Jahrestagung, Sept. 23±26, 1997 in Dresden,Germany.

[**] Dipl.-Phys. C. Berg, Dr.-Ing. M. Dreyer, Prof. Dr.-Ing. H. J. Rath, ZARMUniversität Bremen, Am Fallturm, 28359 Bremen, Germany.

0930-7516/99/0202-00123 $ 17.50+.50/0

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supporting cylinders including the cylindrical start volume. Inthe center of each disk is placed a vertical injection cannulawhich allows the precise positioning of the injected drops. Inthis case the drop density has to differ from the matrix density.Two lateral injections mounted at the supporting cylindersallow additionally a lateral drop positioning of density equaldrops of 1±3 mm radius Rdrop into the closed liquid bridge.1)

After a few seconds damping time, the capsule drop occurs.

The supporting cylinders are withdrawn and the liquid bridgeis only held adhesively between both disks. In the first 1.2 s ofthe 4.7 s of weightlessness, disturbances in the bridge inducedby opening of the supporting cylinders can relax by viscousdissipation and fade away in the medium to the high viscousliquid.

After this in the following 3.5 s, the lower disk is axiallyaccelerated with exponentially increasing velocity vz (Eq. (1)).In this way, the cylindrical liquid bridge with initial lengthL0 = 30 mm is stretched to a maximum final length of 1000 mm.The final length attainable at the measuring time t depends onthe default extension rate G which can vary from 0.3±1.0 s±1.Simultaneously, a variable disk geometry reduces the diskradius from the 15 mm starting radius R0 to a minimum of 5mm with an appropriate increasing extension as in Eq. (2). Insuch a way, the liquid maintains its cylindrical shape, and anextension constant in space and time is implemented.

vz(t) = L0G exp[Gt] (1)

vR(t) = ±R0 G

2exp ÿGt

2

� �(2)

Since the experiment is carried out in microgravity, dropliquids of any density can be inserted for the observation ofdrop deformation in uniaxial extensional flow free of buoy-ancy forces. Moreover, the drops may have any viscosity, onlythe matrix liquid must have a medium to high viscosity forstabilization of the bridge.

Moreover, several drops with different densities can beinserted on top of each other in the bridge. Because of thespatial constant extension rate the viscous stress along thedrop interfaces is nearly the same for all drops. The drops inthe uniaxial extensional flow are followed by a moveablevideo camera recording the transient deformation in detail(Fig. 3). A second video camera observes the contour of the

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Figure 1. Stretched fluid bridge with emulsion drops connected with twovariable disk areas (animated picture).

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1) List of symbols at the end of the paper.

Figure 2. Video picture of the stretched liquid bridge with emulsion drops inmicrogravity.

Figure 3. Detail view of four deformed drops in the uniaxial extensional flow.

liquid bridge and a laser light sheet allows the verification ofthe uniaxial extensional flow field around the liquid drop.

3 Drop Deformation in Uniaxial Extensional Flow

First, drop deformation investigations were carried out atdifferent model emulsions with the components castor oil andsilicon fluid as the matrix and drop liquid in variouscombinations. Here, of special interest is the verification ofthe critical capillary number Ca (Eq. (3)) determined bynumerical simulations and describing the boundary valuebetween the limited stretched drop form and tearing byelongational stress.

(3)

Up to now in this work, the drop deformation was examinedat capillary numbers ranging from 0.2±3.5 where elliptical andpointed-end drop shapes depending on the viscosity ratio l =Zdrop/Zmatrixwere observed. This ratio varies in the measure-ments from 3×10±4±1.2×100.

Fig. 4 shows exemplary the transient drop deformation of acolored silicon oil drop in a castor oil matrix at a capillarynumber of 0.3.

Figure 4. Transient drop deformation of a colored silicon oil drop in a castor oilbridge at different elongation times.

In these video pictures, the drop and the background scalingare represented in a distorted manner, which is caused byrefraction on the curved surface of the liquid bridge. Theactual drop dimensions can be calculated by taking intoconsideration the refraction.

Fig. 5 represents exemplary two differently strong dropdeformation processes at almost the same viscosity ratios inconsideration of the refraction. The curves describe thechange of the drop length Ldrop in the direction of flow scaledto the initial diameter of the spherical drop 2Rdrop. Themeasurement at Ca = 1.2 describes a continuous dropdeformation. On the other hand, the drop apparently achievessteady state at Ca = 0.2; no further deformation could beobserved within the observation period.

4 Conclusion

The new device can provide a uniaxial extensional flowfield of high quality in a cylindrical liquid bridge over ameasurement duration of 3.5 s. This is achieved by theexponential stretching function of the liquid bridge and thesimultaneous adaptation of the disk areas. The size of theliquid bridge allows the precise observation of drops orparticles of 1±5 mm diameter in the extensional flow. Sincethe experiment is carried out in microgravity, drops with anydensity can be inserted and its deformation in uniaxialextensional flow observed free from buoyancy forces.Moreover, the drops may have any viscosity; only the matrixliquid must have medium to high viscosity for stabilization ofthe bridge.

The 3.5 s measuring time is sufficient for observation of thetransient deformation of drops with a low viscosity ratio. Inthis way, the critical capillary number indicating the boundaryof the stable drop can be limited. A result of the measurementsis to verify drop deformation theories and predict dropdeformation, so that drop tearing by extensional flow may beprevented, for example, in production line nozzles.

Acknowledgments

We thank the German Aerospace Center (DLR) whichsupports this project under contract 50 WM 9443.

Received: January 16, 1998 [K 2360]

Symbols used

Ca [±] capillary numberG [s±1] extension rate

Chem. Eng. Technol. 22 (1999) 2, Ó WILEY-VCH Verlag GmbH, D-69469 Weinheim, 1999 0930-7516/99/0202-00125 $ 17.50+.50/0 125

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Figure 5. Transient drop deformation in uniaxial extensional flow at differentcapillary numbers.

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L0 [m] initial length of the fluid bridgeLdrop [m] drop length in flow directionR0 [m] initial radius of the fluid bridgeRdrop [m] drop radius of the initial spherical dropg [m s±2] acceleration of gravity = 9.81t [s] measurement timevR [m s±1] rate of change of the bridge radiusvz [m s±1] rate of change of the bridge length

Greek symbols

Zmatrix [Pa s] matrix shear viscosityZdrop [Pa s] drop shear viscosityl [±] ratio of drop and matrix viscositysmatrix-drop [N m±1] surface tension between drop and

matrix fluid

References

[1] Hudson, N.E.; Ferguson, J.; Mackie, P., The Measurement of theElongational Viscosity of Polymer Solutions Using a Viscosimeter ofNovel Design, Trans. Soc. Rheol. 18 (1974) No. 4, pp. 541±562.

[2] Tirtaatmadja, V.; Sridhar T., A Filament Stretching Device for Measure-ment of Extensional Viscosity, J. Rheol. 37 (1993) No. 6, pp. 1081±1102.

[3] Kröger, R.; Berg, S.; Delgado, A.; Rath, H.J.; Stretching Behaviour ofLarge Polymeric and Newtonian Liquid Bridges in Plateau Simulation, J.Non-Newtonian Fluid Mech. 45 (1992) pp. 385±400.

[4] Berg, S.; Kröger, R.; Rath H.J., Measurement of Extensional Viscosity byStretching Large Liquid Bridges in Microgravity, J. Non-Newtonian FluidMech. 55 (1994) pp. 307±319.

This paper was also published in German in Chem. Ing. Tech. 70 (1998) No. 8.

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Investigating the Synthesis Potential inSupercritical Water

By Petra Krammer, Sabine Mittelstädt, and Herbert Vogel*

1 Introduction

In many chemical reactions, water plays an important role asa solvent, a reaction partner or a catalyst. It is cheap, nontoxic,it is neither combustible nor explosive, and it is environmen-tally friendly. Consequently, reactions in water contribute towaste-avoidance and the conservation of resources. Manyorganic substances do not react or react only insufficientlywith or within water at lower temperatures. This behaviorchanges dramatically when the temperature is increased:

water then proves to be an extremely reactive partner. Abroad scope of the characteristics of the aqueous reactionmixture (e.g., density, solubilities, dielectric constant, ionproduct, heat capacity, and transport properties), especiallynear the critical point, can be changed through minortemperature and pressure variations (Tab. 1). This canprovide alternative reaction pathways, i.e., the chemicalenvironment can be adapted without having to find alter-natives for the solvent water.

Table 1. Properties of water under different conditions [1,2].

One cause is the change of the intermolecular interaction ofthe water molecules (three-dimensional hydrogen-bondednetwork) during the transition into the supercritical condition.In the past, the industrial application of supercritical water(SCW) was limited predominately to the destruction of poorlydegradable and toxic wastes by using ªsupercritical wateroxidationº (SCWO) [3,4]. In order to investigate the synthesispotential of SCW, hydration and dehydration reactions as wellas hydrolyses of various model compounds (alcohols, esters,nitriles, amides) were carried out under sub- and supercriticalconditions. These reactions were carried out without involvingcatalysts (acids, bases) to overcome the disadvantages ofcommon reaction conditions (e.g., the use of mineral acids, saltyields and low space-time yields). Small autoclaves orcapillary-tube reactors have been used for most of theresearch on SCW up to now [5,6,7], and that is why walleffects of the corresponding reactor material could not alwaysbe excluded. For this reason, a continuous miniplant with ªtechnicalº dimensions was set up for the series of tests, withmaximum working conditions of 500 bar and 500 �C, which canbe regarded as realistic upper limits for industrial applications.

This article describes the miniplant and the first results ofreactions of simple model substances with supercritical water.

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[*] P. Krammer, S. Mittelstädt, H. Vogel, Technische Universität Darmstadt,Fachbereich Chemie, Institut für Chemische Technologie, ChemischeTechnologie I, Petersenstr. 20, D-64287 Darmstadt, Germany.