Int. Symp. on Convective Heat and Mass Transfer in Sustainable Energy April 26 – May 1, 2009, Tunisia

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VISCOSITY EFFECTS ON LIQUID-LIQUID DISPERSION IN LAMINAR FLOWS

Charbel Habchi1,2, Sofiane Ouarets1, Thierry Lemenand1, Dominique Della-Valle1, Jérôme

Bellettre1 and Hassan Peerhossaini1,*

1Thermofluids, Complex Flows and Energy Research Group, Laboratoire de Thermocinétique de Nantes, CNRS UMR 6607, École Polytechnique de l’Université de Nantes, rue Christian Pauc, B.P.

50609, 44306 Nantes, France 2Agence de l’Environnement et de la Maîtrise de l’Énergie (ADEME), 20 avenue du Grésillé, B.P.

90406, 49004 Angers, France (* Corresponding author: hassan.peerhossaini@univ-nantes.fr)

ABSTRACT. Efficiency of liquid/liquid dispersion is an important stake in numerous sectors, such as the chemical, food, cosmetic and environmental industries. In the present study, dispersion is achieved in an open-loop reactor consisting of simple curved pipes, either helically coiled or chaotically twisted. In both configurations, we investigate the drop breakup process of two immiscible fluids (W/O) and especially the effect of the continuous phase viscosity, which is varied by addition of different fractions of butanol in the native sunflower oil. The global Reynolds numbers vary between 40 and 240, so that the flow remains laminar while the Dean roll-cells in the bends develop significantly. Different fractions of butanol are added to the oil in each case to examine the influence of the continuous phase viscosity on the drop size distribution of the dispersed phase (water). When the butanol fraction is decreased, the dispersion process is intensified and smaller drops are created. The Sauter mean diameters obtained in the chaotic twisted pipe are compared with those in a helically coiled pipe flow. The results show that chaotic advection intensifies the droplet breakup till 20% in droplet size reduction, and also reduces polydispersity.

NOMENCLATURE

a Radius of circular duct m Ca Capillary number

dropd Drop diameter m

maxd Maximum diameter in size distribution m

32d Sauter mean diameter m

cd /p μμ= Viscosity ratio Greek letters σ Interfacial tension N m-1

τ Viscous stress Pa

effectiveγ& Effective shear rate s-1

Deanγ& Computed shear rate in Dean flow s-1 Subscripts c Continuous phase (oil) d Dispersed phase (water)

Int. Symp. on Convective Heat and Mass Transfer in Sustainable Energy April 26 – May 1, 2009, Tunisia

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INTRODUCTION The mixing of immiscible fluids in industrial processes, for phase dispersion or emulsification, is a complex issue, since the breakup mechanisms are difficult to understand and quantify. One phase is dispersed into small droplets of various diameters. The drop size distribution is decisive for the final product properties, for instance emulsion texture and stability in a food product or the result of a chemical reaction at the interface. The dispersion process may also be aimed at producing efficiently emulsified fuel for combustion enhancement [Senthil Kumar et al. 2005, 2006, Tarlet et al. 2008]. We report on a special mixing process achieved in an open-loop reactor consisting of simple curved pipe segments in both helically coiled and chaotic twisted pipe configurations. In the present study, the effect of the continuous phase viscosity on droplet sizes is investigated in order to address the practical issue of viscosity optimization in emulsification. An aqueous phase (water) is dispersed in a continuous oily phase (commercial sunflower oil), the viscosity of which can be lowered by adding butanol without significant effect on the interfacial tension. The global effect of the viscosity reduction results in competitive effects that we call “positive” if they work toward a smaller droplet size, and otherwise “negative”. These effects are: - reduction of the external stress, and hence weakening in the external forces able to deform and split the drops (negative effect), - increase in Reynolds number and in Dean number, leading to intensification of the secondary flow and of the associated strain rates (positive effect), - lowering of the critical capillary number that governs the breakup in laminar flow, in the viscosity range of interest in experiments (positive effect). The effect of viscosity cannot be determined directly from the experimental results. In this work we attempt to interpret the experimental results through the theoretical insights provided by Taylor-Grace laminar breakup analysis [1953, 1982], and knowledge of the kinematic field in Dean flow provided by the asymptotic solutions of Jones et al. [1989]. The trends are well confirmed except for a lack of accuracy in the predictions, which can be attributed to flow complexity. Figure 1 shows the breakup mechanism in the laminar regime. In the first stage of emulsification, the dispersed phase drop is large, so that the interfacial forces do not play a significant role. The drop undergoes large deformations, stretching and folding, and the “mother” drop splits “into smaller drops whose number and size depend on the viscosity ratio and capillary number. When the size reduction is such that the Laplace forces are higher than the viscous forces, the breakup saturates and the critical size can be predicted by Taylor analysis.

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The forces due to the continuous-flow velocity gradients in the main flow create deformation strains. Grace [1982] underlines the existence of two strain modes, shear strain and extensional strain, whose effects on the breakup mechanism are quite different. The internal viscous forces depend on the ratio p of the viscosities of the dispersed and continuous phases:

c

dpμμ

= (2)

In order to characterize the relative effect of the different forces, a dimensionless parameter Ca , called capillary number, is defined:

σ

τ2forcesCapillary

forcesViscous dropdCa == (3)

Grace [1982] considered that drop breakup occurs when the capillary number exceeds some critical value that depends upon the viscosity ratio p , which reflects the drop’s internal viscous resistance. Hinze et al. [1955] reported that the difference in density between the dispersed and continuous phase has an important effect on droplet breakup, and must be taken in account in experiments. The influence of rheological properties of both dispersed and continuous phases on droplet size was investigated by Walstra [1974], who showed that the average droplet sizes increase with dispersed phase viscosity. Peters [1992] suggested several modes for drop deformation and breakup in idealized laminar flow, all of which depend on the viscosity ratio p . It was found [Grace 1982 and Rallison 1984] that elongational flows are more effective than simple shear flows to break up the droplets in liquid-liquid dispersion.

Pure

shea

r flo

w

Small p

p~1

Large p

Flow direction

Pure

elo

ngat

iona

l flo

w

Small p

Large p

Figure 1. Schematic diagram of single drop deformation in

idealized flows (adapted from Peters [1992])

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De Roussel et al. [2001] modeled the drop formation process in continuous flow systems by using particle advection simulation, a model that provides information on deformation rates and residence time distribution in the mixer. Lemenand et al. [2003] studied the formation of droplets of two immiscible fluids in a HEV static mixer and found experimentally that the variation in the dispersed-phase Sauter mean diameter is independent of the volume fraction of the dispersed phase, which ranged from 0 to 15%. Previous work by the present group [Habchi et al. 2008] studied the dispersion in both helically coiled and chaotic twisted pipe flows. It was shown that an increase in flow rate decreases drop size, and that chaotic advection flow intensifies the emulsification process and provides smaller and more homogeneously dispersed droplets. Both Eulerian and Lagrangian analytical studies showed that chaotic advection causes fluid particles to visits regions of high shear and elongation rates, thus intensifying emulsification. However, this study was limited to low Reynolds numbers (not above 70). Therefore, in order to increase the Reynolds numbers range, we decreased the continuous phase viscosity by adding butanol fraction, eliminating the need to increase the flow rate. In this paper we investigate the effect of the continuous phase viscosity on droplet breakup in both helically coiled and chaotic twisted pipe flows. The experiments carried out in both configurations allow comparison between the two cases. It appears that the latter, which has already been shown to improve heat transfer [Mokrani et al. 1998], also provides better performance for liquid/liquid dispersion. This paper is organized as follows: in section 2, experimental apparatus and measurement methods are described. Results and discussion are given in section 3, and section 4 is devoted to conclusions.

EXPERIMENTAL APPARATUS AND METHODS Hydraulic Loop A schematic diagram of the hydraulic loop used in the experiments appears in Figure 2. Experiments were carried out for two-phase flow using immiscible fluids. The experimental setup consists of two similar loops. Each working fluid is contained in a tank. The oil is pumped by a centrifugal pump, and the water is supplied by a constant-level feed tank connected to the water supply. Flow rates are controlled by valves and measured with two flowmeters. The same experimental setup was used by Lemenand et al. [2005], for turbulent dispersion and Habchi et al. [2008] for laminar and chaotic advection flows. Water is injected at the test section inlet by an injection needle designed not to disturb the main flow and not to create additional breakup of the dispersed phase. For accurate evaluation of breakup performance, the volume fraction of the dispersed aqueous phase is very low (about 1%) so that coalescence phenomena are negligible.

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Test Sections The test section, composed of a succession of 90° bends, is designed to be arranged in two configurations: helically coiled pipe and chaotic twisted pipe, where each bend is rotated by 90° with respect to the preceding one. In laminar flow through curved pipes, centrifugal forces create a secondary flow in the radial direction consisting of a pair of counter-rotating roll-cells known as Dean roll-cells [Dean 1927, 1928]. Chaotic advection is achieved by alternating the bend orientation of ± 90°, as shown in Figure 3. This geometrical perturbation greatly increases the heat and mass transfer [Jones et al. 1989, Acharya et al. 1992, Peerhossaini et al. 1993, Castelain et al. 1997, Mokrani et al. 1998, Lemenand and Peerhossaini 2002, Habchi et al. 2008].

The test section dimensions are summarized in Table 1.

Flowmeters

Test section

Setting tank

Visualization box

Oil tank

Water tank

Centrifugal pump

Flowmeters

Test section

Setting tank

Visualization box

Oil tank

Water tank

Centrifugal pump

Figure 2. Schematic diagram of the hydrodynamic loop for droplet formation

Figure 3. Chaotic twisted pipe mixer

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Working Fluids Experiments were carried out for a two-phase flow using immiscible fluids. Working fluids are vegetable oil for the continuous phase and water for the dispersed phase. Different mass fractions of butanol are added to the continuous phase in order to modify the continuous phase viscosity cμ . Physical properties of the fluids and measurement methods are given in Table 2.

Oil viscosity is sensitive to temperature variation; this effect is taken into consideration. The oil temperature is controlled by a chromel/alumel (type K) thermocouple in the oil admission circuit. Studies show that a 25% addition of butanol decreases halves the continuous phase viscosity; increasing the Reynolds number while conserving the flow rate:

⎥⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−=

0Toiloil

110 TTR

Eexp,μμ (4)

Where E is activation energy, 0μ is viscosity at a reference temperature 0T , and -1-1molKJ 8.314=R . The variation of the continuous phase viscosity with temperature and butanol fraction is graphed in Figure 4. As shown, an addition of 25% of butanol halves the continuous phase viscosity, increasing the Reynolds number while conserving the flow rate. This addition decreases the deformation strain rates in the main flow. Moreover, the continuous phase viscosities decrease when temperature is increased, with the same variation, whatever the butanol fraction. The consequence of varying the continuous phase viscosity is detailed in section 3.

Table 1 Test section dimensions

Radius of circular pipe 4 mm Bend curvature radius 44 mm Curvature angle in bend plane 2/π radNumber of bends 25 Total curved length 1.8 m Total straight length between bends 0.2 m

Total length 2 m

Table 2 Characteristics of working fluids

Properties (at 298 K) Values Measurement methods

waterbutanol25%oil −+σ 0.036 ± 0.003 N/m Krüss™ tensiometer (K12) by ring method

cρ 889 Kg/m3 Data Technical™

cμ 0.052 Pa s Mettler™ RM180 rheometer

dρ 1000 Kg/m3 Data Technical™

dμ 0.001 Pa s Mettler™ RM180 rheometer

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Measured viscosities are fitted with continuous lines in Figure 4 by using Arrhenius’ law, as given by equation (4).

The activation energies E correlated from measurements are given in Table 3.

Droplet Diameter Measurement Emulsion pictures are taken by a high-frequency digital Canon™ camera whose optical axis of the camera is perpendicular to the plane of the rectangular visualization window. The visualization system, a parallelepiped box with 2D diffuser at the entrance and 2D nozzle at the exit, is placed directly at the test section outlet (shown in Figure 2). The visualization system is designed to minimize flow disturbances and to maintain the same deformation strain levels as in the test section. For each operating condition, the sequence of independent images recorded constitutes our statistical sample of the drops. Drop diameters are measured from the recorded images. At least 400 measured drop diameters are retained for each run; beyond this number, the measurements are stable. Reproducibility testing was carried out to check the effect of a new operator and new trial on the measured diameters of the final size distribution. The maximum standard deviation based on Sauter mean diameter was found to be less than 7%, implying that the measurements are reproducible. To summarize the experimental protocol adopted for droplet diameter measurement, three main parameters are taken into consideration:

- oil temperature is continuously measured to prevent errors due to dependence of oil viscosity with temperature.

2.9x10-3 3.0x10-3 3.1x10-3 3.2x10-3 3.3x10-3 3.4x10-35.0x10-3

1.0x10-2

1.5x10-2

2.0x10-2

2.5x10-2

3.0x10-2

3.5x10-2

4.0x10-2

4.5x10-2

5.0x10-2

5.5x10-2

Oil with: 0% butanol 5% butanol 10% butanol 15% butanol 20% butanol 25% butanol Exponential fitted curves

Increasing butanol fraction

µ (P

a.s-1

)

1/T (K-1)

Figure 4. Continuous phase viscosity

Table 3 Activation energy for different butanol fractions

Butanol to oil fraction 0% 5% 10% 15% 20% 25% E (kJ) 26.15 23.48 25.24 23.79 22.07 22.82 Fitting accuracy (%) 99.22 99.53 99.09 99.34 99.45 99.05

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- water injection flow rate is small enough to prevent the coalescence that can occur in the visualization box, and to minimize the main flow disturbance. Bigger drop diameters appear when smaller droplets enter in collision.

- Samples of diameter distribution should be independent of the population (number of droplets). Therefore, we measured at least 400 drops in each run.

RESULTS AND DISCUSSIONS Experimental Plan The objective of the present study is to investigate the effect of the continuous phase viscosity on the final drop size distribution. The viscosity variation depends of several parameters such as temperature and the addition of surfactants. The interfacial tension is modified due to the addition of butanol: as shown in Table 2, for 25% butanol fraction in the oil, the interfacial tension changes by about 30%. However, in present butanol range [0% - 12.5%], the interfacial tension variation is less than 4% and can be neglected. As a consequence, the flow rate and the continuous phase viscosity are the only parameter contributing to the emulsification process. The drop size distribution in the flow is characterized by the Sauter mean diameter. This diameter, given in equation (5), represents the characteristic drop diameter as:

∫∫=

lll

lll

d)(f

d)(fd

2

3

32 (5)

Here )(lf is the distribution function representing the proportion of drops having a given diameter l in the observed emulsion. The integral operates over the whole of the observed emulsion. Experimental data The measured Sauter mean diameters are represented in Figure 5 as functions of the continuous phase viscosity and the butanol fraction for all flow rates. On this figure, one finds several Sauter diameters for each continuous phase viscosity. In fact since the continuous phase temperature varied during experiments, each viscosity gave rise to several Sauter diameters each corresponding to one temperature. As shown, the addition of butanol to the oil strongly affects the continuous phase viscosity and the Sauter mean diameter in both helically coiled and chaotic twisted pipe flows. To assess the effect of the continuous phase viscosity on drop breakup, a Grace diagram [1982] is adopted to recalculate the critical capillary number.

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Drop diameters seem to depend strongly on the flow rate. A fixed Reynolds number of 60 is used in Figure 6 to plot Sauter mean diameters versus continuous phase viscosity cμ for both helically coiled and twisted pipe flows. The Sauter mean diameter 32d decreases with μc, showing that the emulsification process is greatly enhanced in both regular and chaotic flows by the butanol addition. The physical interpretation of this phenomenon is explained below using Grace [1984] theory.

1.0x10-2 1.5x10-2 2.0x10-2 2.5x10-2 3.0x10-2 3.5x10-2 4.0x10-20.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Helically coiled: Habchi et al. [2008] oil + 10% butanol oil + 12.5% butanol

Chaotic twisted pipe: Habchi et al. [2008] oil oil + 5% butanol oil + 10% butanol oil + 12.5% butanol

Saut

er m

ean

diam

eter

, d32

(mm

)

Continuous phase viscosity, µc (Pa s)

Figure 5. Sauter mean diameter as a function of continuous phase viscosity μc

0.025 0.03 0.04 0.05 0.06 0.070.4

0.6

0.8

1

1.2

1.4

1.6

1.8 Helically coiled pipe Chaotic twisted pipe

Saut

er m

ean

diam

eter

, d32

(mm

)

Continuous phase viscosity, µc (Pa s)

Figure 6. Sauter mean diameter as a function of viscosity ratio for

fixed Reynolds number 60 Re =

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Interpretation by Grace-Taylor breakup diagram To interpret the physical effect of the continuous phase viscosity on drop breakup, a Grace diagram is adopted by recalculating the critical capillary number as:

σ

γμ2

maxeffectiveccritical

dCa

&= (6)

In the range of Reynolds number studied here, the effective deformation strain rate effectiveγ& is considered equal to the maximum shear rate in a helically coiled pipe flow, Deanγ& , which has been computed by Habchi et al. [2008] as:

502

Dean 2150114

.

ReR

aa

W⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛+=γ& (7)

The study by Habchi et al. (2008), however, gives only an order of magnitude for criticalCa in a small range of viscosity ratio p . The theory is established in pure flows (simple shear or simple elongation) that allow homogeneous deformation rates. In the present study, the flows are more complex, and the heterogeneity distribution of the effective strain rates adopted here limits the accuracy in calculating criticalCa . Therefore effectiveγ& is merely an indicative value for the deformation strain rates, and uncertainty appears when calculating criticalCa . The experimental maximum diameters obtained from the Sauter diameters are given by [Habchi et al. 2008]:

⎪⎪⎩

⎪⎪⎨

⎧

=

=

860 :pipe twistedChaotic

80 :pipe coiledHelically

32max

32max

.dd

.dd

(8)

In Figure 7, the critical capillary numbers are represented for both mixers; they merge to a master curve in the Grace [1982] diagram.

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Figure 7 shows that the present results for criticalCa are located in the zone where p should increase to transmit the deformation forces more effectively from the continuous to dispersed phase. This explains the intensification of the emulsification process, due to the decrease in continuous phase viscosity, which is caused here by the addition of butanol. To recapitulate, when the continuous phase viscosity decreases, three parameters are modified: - The deformation rate, given in eq. (1), increases - The Reynolds number increases, thus intensifying the strain rate in the Dean flow Deanγ& given in eq. (7) - The viscosity ratio p tends to the optimum value of 1 Therefore, the emulsification process is highly intensified by decreasing the continuous phase viscosity. Chaotic Advection Effect To analyze the emulsification process in Dean flow, we refer to Figure 8, a schematic representation of the different deformation stages of a single drop (Figure 8(a)) injected in the main continuous flow. The initial drop of the dispersed fluid is stretched and folded over, due to secondary flow formed by Dean roll-cells. When the fluid filament is situated at the median plane separating Dean roll-cells, it is subject to the maximum elongation rate due to the opposite rotation of Dean roll-cells (Figure 8(b)). The drop is stretched less if injected inside a Dean roll-cell and will stay trapped in a rotating cell. As mixing proceeds, shear and elongation strain rates in the radial cross section break the droplet up into smaller drops (Figures 8(c), (d)).

10-3 10-2 10-1 100 101 10210-2

10-1

100

101

102

103

Ca

Viscosity ratio, p

Helically coiled pipe Chaotic twisted pipe

Simple shear flow [Grace 1982]

Elongational flow [Grace 1982]

Figure 7. Drop breakup diagram

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In the twisted pipe configuration, Dean roll-cells are reoriented after each bend, and stretching and folding are more intense than in the helically coiled pipe. This geometrical perturbation creates chaotic advection trajectories whereby the dispersed-phase fluid visits the whole mixer cross section, passing by the maximum values of shear and elongation rates. Droplet breakup is then enhanced and the final drop diameters are smaller in twisted-pipe Dean flow than in regular Dean flow (i.e., in the helically coiled mixer). This effect is shown in Figure 9, which compares the two mixers for different Reynolds numbers. Considering the relative improvement over regular laminar flows, we see droplet diameters about 20% lower in chaotic advection twisted pipe flow than in helically coiled tube flow.

(a) (b)

(c) (d)

Figure 8. Deformation of a drop in Dean

flow by elongation and shear rates

40 80 120 160 200 2400.2

0.4

0.6

0.8

1

1.21.41.6

Saut

er m

ean

diam

eter

, d32

(mm

)

Reynolds number, Re

Helically coiled pipe Chaotic twisted pipePower law fitted curves:

Helically coiled pipe Chaotic twisted pipe

Figure 9. Sauter diameters: comparison between helically coiled and chaotic twisted pipe flows

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CONCLUSION The reduction of the continuous phase viscosity intensifies the emulsification process in the two geometries considered, helically coiled and chaotic twisted pipe flows: the Dean flow effect is decisive in this process. When 25% butanol is added to the oil, the continuous phase viscosity is halved, so that it was possible to increase the Reynolds number without needing to increase the flow rate. The chaotic advection strongly enhances mass transfer and gives raise to smaller droplet size distribution (by about 20%) than in regular Dean flow. Theory provides useful support for process design and future improvements or optimization, for example in fuel production. Future work will focus on varying the interfacial tension over a large Reynolds number range, since this is an important parameter in the breakup process.

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