Influence of elongational properties on the contraction flow of polyisobutylene in a mixed solvent

Over the last decade several international programmes have been developed around different standard fluids, one of which is the so-called S1 fluid. This is a solution of polyisobutylene in a mixed solvent and the aim of the programme has been to study the rheology of polymer solutions from the dilute solution to the melt. The focus of this paper will be on the flow visualisation of contraction flows of S1 through orifice dies and on the estimation of some of its extensional properties. The contraction ratios range from 24.4:1 and 124.3:1. The measured entry pressure drops will be correlated with contraction ratio and apparent wall shear rate. Experimental evidence will show that, when regarded as a function of wall shear rate, the entry pressure drops are independent of the contraction ratios. The flow fields for different contraction ratios, at any constant apparent wall shear rate, however, differ substantially. The evolution of the flow fields is monitored and it is shown that an initial increase in vortex size is followed by a slower decrease, this happening at a constant Weissenberg number. At the same Weissenberg number, small scale instabilities start occurring near the office. As the shear rate is increased further, these instabilities grow in size until, eventually, the flow structure is destroyed. An extensional viscosity is evaluated using a modified form of the Binding analysis for contraction flows and we show that the results are not only in qualitative agreement with those from other groups, but also that the analysis is able to predict exactly the onset of the aforementioned flow instabilities. Received: 20 March 1997 Accepted: 18 September 1997     

Optimization of the vane geometry

The use of nonstandard geometries like the vane is essential to measure the rheological characteristics of complex fluids such as non-Newtonian fluids or particle dispersions. For this geometry which is of Couette type, there is no analytical simple model defining the relation between the shear stress and the torque or relating the angular velocity to the shear rate. This study consists on calibrating a nonstandard vane geometry using a finite volume method with the Ansys Fluent software. The influence of geometrical parameters and rheological characteristics of the complex fluids are considered. First, the Newtonian fluid flow in a rotative vane geometry was simulated and a parametric model is derived therefrom. The results show an excellent agreement between the calculated torque and the measured one. They provide the possibility to define equivalent dimensions by reference to a standard geometry with concentric cylinders where the relationships between shear stress (resp. shear rate) and the torque (resp. the angular rotation) are classical. Non-Newtonian fluid flows obeying a power law rheology with different indices were then simulated. The results of these numerical simulations are in very good agreement with the preceding Newtonian-based model in some ranges of indices. The absolute difference still under 5 % provided the index is below 0.45. Finally, this study provides a calibration protocol in order to use nonstandard vane geometries with various heights, gaps, and distance to the cup bottom for measuring the rheology of complex fluids like shear thinning fluids and concentrated suspensions.     

Extensional rheology of concentrated poly(ethylene oxide) solutions

The shear and extensional rheology of three concentrated poly(ethylene oxide) solutions is examined. Shear theology including steady shear viscosity, normal stress difference and linear viscoelastic material functions all collapse onto master curves independent of concentration and temperature. Extensional flow experiments are performed in fiber spinning and opposed nozzles geometries. The concentration dependence of extensional behavior measured using both techniques is presented. The zero-shear viscosity and apparent extensional viscosities measured with both extensional rheometers exhibit a power law dependence with polymer concentration. Strain hardening in the fiber spinning device is found to be of similar magnitude for all test fluids, irrespective of strain rate. The opposed nozzle device measures an apparent extensional viscosity which is one order of magnitude smaller than the value determined with the fiber spinline device. This could be attributed to errors caused by shear, dynamic pressure, and the relatively small strains developed in the opposed nozzle device. This instrument cannot measure local kinematics or stresses, but averages these values over the non-homogenous flow field. These results show that it is not possible to measure the extensional viscosity of non-Newtonian and shear thinning fluids with this device. Fiber spin-line experiments are coupled with a momentum balance and constitutive model to predict stress growth and diameter profiles. A one-mode Giesekus model accurately captures the plateau values of steady and dynamic shear properties, but fails to capture the gradual shear thinning of viscosity. Giesekus model parameters determined from shear rheology are not capable of quantitatively predicting fiber spinline kinematics. However, model parameters fit to a single spinline experiment accurately predict stress growth behavior for different applied spinline tensions.     

Rheological properties of PDMS/clay nanocomposites and their sensitivity to microstructure

The effect of microstructure on the rheology of clay/polymer nanocomposites is investigated using dispersions of organically treated clay in nearly Newtonian poly(dimethylsiloxane). Degree of dispersion and floc size are altered by using two different dispersion procedures and by changing the shear history. The scaling for dynamic moduli of attractive colloids applies, except for a possible relaxation mechanism at very low frequencies. The time to reach the crossover at a given frequency is found to be extremely sensitive to the dispersion procedure used. Hydrodynamic and elastic components of the steady state stress, on the other hand, evolve in a very similar fashion for the different systems. Although the relaxation times of the elastic stress components change drastically with flow-induced changes in structure, the dispersion process hardly has an effect at all. Intermittent start-up flows in the forward and reverse directions show that anisotropy persists long after the flow has been arrested, even at shear rates where no large reversible flocs are present. The degree of dispersion only had a limited effect on the anisotropy. Finally, the effect of shear on structure recovery has been studied. Very low shear rates are found to increase the rate of recovery, even for small strains.     

Interfacial instability of turbulent two-phase stratified flow: Pressure-driven flow and non-Newtonian layers

We derive a flat-interface model to describe the flow of two horizontal, stably stratified fluids, where the bottom layer exhibits non-Newtonian rheology. The model takes into account the yield stress and power-law nature of the bottom fluid. In the light of the large viscosity contrast assumed to exist across the fluid interface, and for large pressure drops in the streamwise direction, the possibility for the upper Newtonian layer to display fully developed turbulence must be considered, and is described in our model. We develop a linear-stability analysis to predict the conditions under which the flat-interface state becomes unstable, and pay particular attention to characterizing the influence of the non-Newtonian rheology on the instability. Increasing the yield stress (up to the point where unyielded regions form in the bottom layer) is destabilizing; increasing the flow index, while bringing a broader spectrum of modes into play, is stabilizing. In addition, a second mode of instability is found, which depends on conditions in the bottom layer. For shear-thinning fluids, this second mode becomes more unstable, and yet more bottom-layer modes can become unstable for a suitable reduction in the flow index. One further difference between the Newtonian and non-Newtonian cases is the development of unyielded regions in the bottom layer, as the linear wave on the interface grows in time. These unyielded regions form in the trough of the wave, and can be observed in the linear analysis for a suitable parameter choice.     

Effect of phase change on the rheology and stability of paraffin wax-in-water Pickering emulsions

“Pickering” emulsions are widely found in nature and industry including food, pharmaceuticals, and oil industries. Often, Pickering emulsion studied have a Newtonian dispersed phase. However, the dispersed phase can be non-Newtonian such as one that can be subjected to a phase change under certain experimental conditions. This work examines how changing the physical state of dispersed phase alters the shear stability and bulk viscoelasticity of o/w emulsions. Model silica-stabilized, paraffin wax-in-water emulsions are synthesized. The wax, with a melting temperature of about 55 ^°C is subjected to a phase change by changing the temperature between 15 and 80 ^°C. At lower temperatures (< 55 ^°C), the droplet deformability and particle mobility at the interface are significantly restricted while at higher temperatures (> 55 ^°C), the wax melts and expands, making the emulsion droplets deformable and the particles more relaxed. These directly affect bulk emulsion rheology. Flow curves and oscillatory shear experiments indicate that emulsion droplets are flocculated and the emulsions behave as elastic solids. These properties are directly influenced by temperature, which alters the state of aggregation and network-structure of the emulsion droplets. The effect of emulsion concentration is also analyzed. Three different concentrations are tried—15, 30, and 45 vol% (as measured at 25 ^°C when the wax is solid). At a given temperature, the rheological properties seem to scale with concentration. Further, we show that the emulsions are sensitive to destabilization (gelation) under flow with the sensitivity directly varying with temperature and magnitude of shear fields (steady shear) applied.     

A Lattice Boltzmann study of non-newtonian flow in digitally reconstructed porous domains

In the present study, the Lattice Boltzmann Method (LBM) is applied to simulate the flow of non-Newtonian shear-thinning fluids in three-dimensional digitally reconstructed porous domains. The non-Newtonian behavior is embedded in the LBM through a dynamical change of the local relaxation time. The relaxation time is related to the local shear rate in such a way that the power law rheology is recovered. The proposed LBM is applied to the study of power-law fluids in ordered sphere packings and stochastically reconstructed porous domains. A linear relation is found between the logarithm of the average velocity and the logarithm of the body force with a curve slope approximately equal to the inverse power-law index. The validity of the LBM for the flow of shear thinning fluids in porous media is also tested by comparing the average velocity with the well known semi-empirical Christopher–Middleman correlation. Good agreement is observed between the numerical results and the Christopher–Middleman correlation, indicating that the LBM combined with digital reconstruction constitutes a powerful tool for the study of non-Newtonian flow in porous media.     

Molecular network model for the rheology of gelling polymer solutions

A molecular network model is proposed to describe the rheology of macromolecular solutions undergoing chemical or physical gelation. The model is based on the Bird—Carreau network model [1] with the addition of chemical reaction kinetics to predict the formation of chemical crosslinks among the polymer molecules in solution. The goal is to provide a framework for describing the rheology of gels, that are currently used as fracturing fluids in oil well simulation, formed from polymer solutions that are crosslinked by the addition of transition metal ions. The model has the ability to predict an increase in storage modulus with time, shear thinning viscosity, stress overshoot upon the inception of shear flow, and viscosity changes during the simulation of flow histories that are representative of those encountered in fracturing operations.     

Dynamic properties of shear thickening colloidal suspensions

The transient shear rheology (i.e., frequency and strain dependence) is compared to the steady rheology for a model colloidal dispersion through the shear thickening transition. Reversible shear thickening is observed and the transition stress compares well to theoretical predictions. Steady and transient shear thickening are observed to occur at the same value of the average stress. The critical strain for shear thickening is found to depend inversely on the frequency at fixed applied stress for low frequencies (high strains), but is limited to an apparent minimum critical strain at higher frequencies. This minimum critical strain is shown to be an artifact of slip. Lissajous plots illustrate the transition in material properties through the shear thickening transition, and the energy dissipated by a shear thickening suspension is analyzed as a function of strain amplitude.     

Rheology of an emulsion of viscoelastic drops in steady shear

Steady shear rheology of a dilute emulsion with viscoelastic inclusions is numerically investigated using direct numerical simulations. Batchelor's formulation for rheology of a viscous emulsion is extended for a viscoelastic system. Viscoelasticity is modeled using the Oldroyd-B constitutive equation. A front-tracking finite difference code is used to numerically determine the drop shape, and solve for the velocity and stress fields. The effective stress of the viscoelastic emulsion has three different components due to interfacial tension, viscosity difference (not considered here) and the drop phase viscoelasticity. The interfacial contributions – first and second normal stress differences and shear stresses – vary with Capillary number in a manner similar to those of a Newtonian system. However the shear viscosity decreases with viscoelasticity at low Capillary numbers, and increases at high Capillary numbers. The first normal stress difference due to interfacial contribution decreases with increasing drop phase viscoelasticity. The first normal stress difference due to the drop phase viscoelasticity is found to have a complex dependence on Capillary and Deborah numbers, in contrast with the linear mixing rule. Drop phase viscoelasticity does not contribute significantly to effective shear viscosity of the emulsion. The total first normal stress difference shows an increase with drop phase viscoelasticity at high Capillary numbers. However at low Capillary numbers, a non-monotonic behavior is observed. The results are explained by examining the stress field and the drop shape.     

Flow of wormlike micelle solutions through a periodic array of cylinders

Solutions of self-assembled wormlike micelles are used with ever increasing frequency in a multitude of consumer products ranging from cosmetic to industrial applications. Owing to the wide range of applications, flows of interest are often complex in nature; exhibiting both extensional and shear regions that can make modeling and prediction both challenging and valuable. Adding to the complexity, the micellar dynamics are continually changing, resulting in a number of interesting phenomena, such as shear banding and extensional flow instabilities. In this paper, we present the results of our investigation into the flow fields generated by a controllable and idealized porous media: a periodic array of cylinders. Our test channel geometry consists of six equally spaced cylinders, arranged perpendicular to the flow. By systematically varying the Deborah number, the flow kinematics, stability and pressure drop were measured. A combination of particle image velocimetry in conjunction with flush mount pressure transducers were used to characterize the flow, while flow induced birefringence measurements were used to determine micelle deformation and alignment. The pressure drop was found to decrease initially due to the shear thinning of the test fluid, and then exhibit a dramatic upturn as other elastic effects begin to dominate. We present evidence of the onset of an elastic instability in one of the test fluids above a critical Deborah number manifest in fluctuating transient pressure drop measurements and asymmetric streamlines. We argue that this disparity in the two test fluids can be attributed to the measurable differences in their extensional rheology.     

Shear Rate Determination from Pore-Scale Flow Fields

Aqueous solutions with polymer additives often used to improve the macroscopic sweep efficiency in oil recovery typically exhibit non-Newtonian rheology. In order to predict the Darcy-scale effective viscosity \(\mu _{\mathrm{eff}} \) required for practical applications often, semi-empirical correlations such as the Cannella or Blake–Kozeny correlation are employed. These correlations employ an empirical constant (“C-factor”) that varies over three orders of magnitude with explicit dependency on porosity, permeability, fluid rheology and other parameters. The exact reasons for this dependency are not very well understood. The semi-empirical correlations are derived under the assumption that the porous media can be approximated by a capillary bundle for which exact analytical solutions exist. The effective viscosity \(\mu _{\mathrm{eff}} (v_{\mathrm{Darcy}} )\) as a function of flow velocity is then approximated by a cross-sectional average of the local flow field resulting in a linear relationship between shear rate \(\gamma \) and flow velocity. Only with such a linear relationship, the effective viscosity can be expressed as a function of an average flow rate instead of an average shear rate. The local flow field, however, does in general not exhibit such a linear relationship. Particularly for capillary tubes, the velocity is maximum at the center, while the shear rate is maximum at the tube wall indicating that shear rate and flow velocity are rather anti-correlated. The local flow field for a sphere pack is somewhat more compatible with a linear relationship. However, as hydrodynamic flow simulations (using Newtonian fluids for simplicity) performed directly on pore-scale resolved digital images suggest, flow fields for sandstone rock fall between the two limiting cases of capillary tubes and sphere packs and do in general not exhibit a linear relationship between shear rate and flow velocity. This indicates that some of the shortcomings of the semi-empirical correlations originate from the approximation of the shear rate by a linear relationship with the flow velocity which is not very well compatible with flow fields from direct hydrodynamic calculations. The study also indicates that flow fields in 3D rock are not very well represented by capillary tubes.     

Rheology of immiscible blends with particle-induced drop clusters

We consider the effects of 2.7-μm-diameter hydrophobic silica particles added to droplet–matrix blends of polyethylene oxide (PEO) and polyisobutylene (PIB). The particles adsorb on the surface of the PEO drops but protrude considerably into the PIB phase. Hence, it is possible for a single particle to adsorb onto two PEO drops simultaneously. Such particles are called “bridging” particles, and they the glue drops into noncoalescing clusters. Flow visualization studies show that shearing the sample promotes bridging-induced clustering of drops and that the structure of the clusters depends on the shear rate. Rheologically, the most significant consequence of bridging-induced drop clustering appears to be a plateau in G′ at low frequencies characteristic of gel-like behavior. The gel-like behavior develops fully after shearing the sample, and the kinetics of gel formation are faster with increasing shear stress or increasing drop volume fraction. The gel-like behavior suggests that the bridging-induced drop clusters form a weak network. Apart from particle bridging, optical microscopy also reveals that particles can organize into a hexagonal lattice on the drops’ surfaces, a phenomenon that has only been noted in aqueous systems previously. Finally, rheology and flow visualization both suggest that particles promote coalescence of drops. This is surprising in light of much past research that shows that particles that are preferentially wetted by the continuous phase generally hinder coalescence in droplet–matrix systems.     

Extended irreversible thermodynamics,generalized hydrodynamics,kinetic theory,and rheology

The gist of extended irreversible thermodynamics and generalized hydrodynamics is presented within the context of rheology of complex molecules (e.g., polymers) in this paper. Then, the constitutive equation for stress developed for polyatomic fluids in a previous paper is applied to rheology of polymeric fluids. This constitutive equation is fully consistent with the thermodynamic laws. It is shown that the collision bracket integrals appearing in the constitutive equation can be recast in terms of friction tensors of beads and equilibrium force-force correlation functions if the momentum relaxation is much faster than the configuration relaxation and there exist such relaxation times. The force-force correlation functions reduce to those related to the mean square radius of gyration of the polymer if the Hookean model is taken for forces. By treating the recast collision bracket integrals in the constitutive equation as empirical parameters, we analyze some experimental data on shear rate and elongation rate dependence of polymeric melts and obtain excellent agreement with experiment. We show that the empirical parameters can be related to the zero shear rate viscosity and the ratio of the secondary to the primary normal stress coefficient. Therefore, for the plane Couette flow geometry considered in the paper, the constitutive equation is completely specified by the limiting material functions at zero shear rate and relaxation times.Work supported in part by the Natural Sciences and Engineering Research Council of Canada and Fonds FCAR, Quebec. This paper was presented at the Symposium on Recent Developments in Structured Continua II held at Magog, Quebec, Canada, May 23–25, 1990.     

Dissipative particle dynamics simulation of polymer drops in a periodic shear flow

The steady-state and transient shear flow dynamics of polymer drops in a microchannel are investigated using the dissipative particle dynamics (DPD) method. The polymer drop is made up of 10% DPD solvent particles and 90% finite extensible non-linear elastic (FENE) bead spring chains, with each chain consisting of 16 beads. The channel’s upper and lower walls are made up of three layers of DPD particles, respectively, perpendicular to Z-axis, and moving in opposite directions to generate the shear flow field. Periodic boundary conditions are implemented in the X and Y directions. With FENE chains, shear thinning and normal stress difference effects are observed. The “colour” method is employed to model immiscible fluids according to Rothman–Keller method; the χ-parameters in Flory–Huggins-type models are also analysed accordingly. The interfacial tension is computed using the Irving–Kirkwood equation. For polymer drops in a steady-state shear field, the relationship between the deformation parameter (D_def) and the capillary number (Ca) can be delineated into a linear and nonlinear regime, in qualitative agreement with experimental results of Guido et al. [J. Rheol. 42 (2) (1998) 395]. In the present study, Ca<0.22, in the linear regime. As the shear rate increases further, the drop elongates; a sufficiently deformed drop will break up; and a possible coalescence may occur for two neighbouring drops. Dynamical equilibrium between break-up and coalescence results in a steady-state average droplet-size distribution. In a shear reversal flow, an elongated and oriented polymer drop retracts towards a roughly spherical shape, with a decrease in the first normal stress difference. The polymer drop is found to undergo a tumbling mode at high Schmidt numbers. A stress analysis shows that the stress response is different from that of a suspension of solid spheres. An overshoot in the strain is observed for the polymer drop under extension due to the memory of the FENE chains.     

Investigation on heavy crude-water two phase flow and related flow characteristics

In this paper, heavy crude oil–water flows are studied in a horizontal stainless steel test section with 25.4 mm ID and overall length of 50 m. Crude oil (viscosity = 628.1 mPa s, interfacial tension with water = 10.33 mN/m at 60 °C) and water, collected from an oilfield, were used as test fluids. Visual observations, local sampling and pressure drop measurements were used to identify the flow patterns and their transitions. It was found that in all conditions studied there was a water-in-oil emulsion present. At low mixture velocities and water fractions this occupied the whole pipe cross section. As the velocity or the volume fraction increased water appeared to segregate. At high water fractions and mixture velocities annular flow appeared with the water-in-oil emulsion in the core surrounded by a water layer. The results were compared with those from a model oil with the same viscosity. At low water fractions there was a similarity between the patterns observed with the two oil systems characterized by water segregation from an oil continuous dispersion with increasing water fraction or mixture velocity. However, at high water fractions an oil-in-water dispersion formed with the model oil that was not seen with the crude oil. Pressure drop was generally higher for the crude oil system compared to the model one, while in both cases it decreased when water started to segregate and form layers in contact with the pipe wall. The differences between the two oil systems are attributed to the natural surfactants present in the heavy crude oil (such as asphaltenes and resins), which tend to accumulate on the water/oil interface, retard film drainage and maintain the stability of water drops in oil.     

Numerical simulations of Boger fluids through different contraction configurations for the development of a measuring system for extensional viscosity

This paper reports the flow behaviour of Newtonian and Boger fluids through various axisymmetric contraction configurations by means of numerical predictions. A principal aim has been to evaluate the geometrical design choice of the hyperbolic contraction flow. The FENE-CR model has been used to reflect the behaviour of Boger fluids, with constant shear viscosity, finite (yet large) extensional viscosity and less than quadratic first normal stress difference. Numerical calculations have been performed on six different contraction configurations to evaluate an optimized geometry for measuring extensional viscosity in uniaxial extensional flow. The influence of a sharp or rounded recess-corner on the nozzle has also been investigated. Few commercial measuring systems are currently available for measurement of the extensional rheology of medium-viscosity fluids, such as foods and other biological systems. In this context, a technique based on the hyperbolic contraction flow would be a suitable alternative. The pressure drop, the velocity field, the first normal stress difference and the strain rate across the geometry have each been evaluated for Newtonian and Boger fluids. This numerical study has shown that the hyperbolic configuration is superior to the other geometry choices in achieving a constant extension rate. In this hyperbolic configuration, no vortices are formed, the measuring range is broader and the strain rate is constant throughout the geometric domain, unlike in the alternative configurations tested. The difference between sharp and rounded recess-corner configurations proved to be negligible and a rise in excess pressure drop (epd) for increasing deformation rates has been observed.     

The axisymmetric contraction–expansion: the role of extensional rheology on vortex growth dynamics and the enhanced pressure drop

The flow of a polystyrene Boger fluid through axisymmetric contraction–expansions having various contraction ratios (2≤β≤8) and varying degrees of re-entrant corner curvatures are studied experimentally over a large range of Deborah numbers. The ideal elastic fluid is dilute, monodisperse and well characterized in both shear and transient uniaxial extension. A large enhanced pressure drop above that of a Newtonian fluid is observed independent of contraction ratio and re-entrant corner curvature. Streak images, laser Doppler velocimetry (LDV) and digital particle image velocimetry (DPIV) are used to investigate the flow kinematics upstream of the contraction plane. LDV is used to measure velocity fluctuation in the mean flow field and to characterize a global elastic flow instability which occurs at large Deborah numbers. For a contraction ratio of β=2, a steady elastic lip vortex is observed while for contraction ratios of 4≤β≤8, no lip vortex is observed and a corner vortex is seen. Rounding the re-entrant corner leads to shifts in the onset of the flow transitions at larger Deborah numbers, but does not qualitatively change the overall structure of the flow field. We describe a simple rescaling of the deformation rate which incorporates the effects of lip curvature and allows measurements of vortex size, enhanced pressure drop and critical Deborah number for the onset of elastic instability to be collapsed onto master curves. Transient extensional rheology measurements are utilized to explain the significant differences in vortex growth pathways (i.e. elastic corner vortex versus lip vortex growth) observed between the polystyrene Boger fluids used in this research and polyisobutylene and polyacrylamide Boger fluids used in previous contraction flow experiments. We show that the role of contraction ratio on vortex growth dynamics can be rationalized by considering the dimensionless ratio of the elastic normal stress difference in steady shear flow to those in transient uniaxial extension. It appears that the differences in this normal stress ratio for different fluids at a given Deborah number arise from variations in solvent quality or excluded volume effects.     

Non-linear viscoelasticity and temporal behavior of typical yield stress fluids: Carbopol, Xanthan and Ketchup

The viscoelastic properties of yield stress fluids are difficult to measure outside the linear viscoelastic regime, in particular above their yield stress. These properties are investigated for several common yield stress fluids using inertio-elastic oscillations. From this coupling between the instrument’s inertia and the viscoelasticity of the materials, the complete simple shear rheology can be determined, including viscoelasticity under flow. Findings show that the tested materials have an almost constant elasticity below and above the yield stress, even for applied stresses several times larger than the yield stress. Moreover, the temporal behavior of the materials is unambiguously determined. Concentrated Xanthan is shown to be thixotropic, while Ketchup mainly shows retarded viscoelasticity. Carbopol does not show long-term temporal dependance but apparently exhibits fracturation.     

Direct numerical simulation of surfactant-stabilized emulsions

A 3D lattice Boltzmann model for two-phase flow with amphiphilic surfactant was used to investigate the evolution of emulsion morphology and shear stress in starting shear flow. The interfacial contributions were analyzed for low and high volume fractions and varying surfactant activity. A transient viscoelastic contribution to the emulsion rheology under constant strain rate conditions was attributed to the interfacial stress. For droplet volume fractions below 0.3 and an average capillary number of about 0.25, highly elliptical droplets formed. Consistent with affine deformation models, gradual elongation of the droplets increased the shear stress at early times and reduced it at later times. Lower interfacial tension with increased surfactant activity counterbalanced the effect of increased interfacial area, and the net shear stress did not change significantly. For higher volume fractions, co-continuous phases with a complex topology were formed. The surfactant decreased the interfacial shear stress due mainly to advection of surfactant to higher curvature areas. Our results are in qualitative agreement with experimental data for polymer blends in terms of transient interfacial stresses and limited enhancement of the emulsion viscosity at larger volume fractions where the phases are co-continuous.