Steady shear rheology of a viscous emulsion in the presence of finite inertia at moderate volume fractions: sign reversal of normal stress differences

Srivastava, Priyesh; Malipeddi, Abhilash Reddy; Sarkar, Kausik

doi:10.1017/jfm.2016.561

Cited by 14 publications

(20 citation statements)

References 63 publications

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“…[18], while the black circles are the results for drops with Ca = 0.15 from Ref. [27] and the dashed line Pal's empirical relation [23]. We observe that the effective viscosity is a monotonic non-linear function of both variables, and in particular, it in- creases with the volume fraction Φ and decreases with the Capillary number Ca.…”

Section: Resultsmentioning

confidence: 61%

“…Indeed, we define the effective suspension viscosity For comparison we also plot the same data for rigid particles [18] (Ca = 0 (color circles), the results for drops with Ca = 0.15 from Ref. [27] (black circles) and Pal's empirical relation [23] (black dashed line).…”

Section: Resultsmentioning

confidence: 99%

“…Later analytical calculations [20,21,22,23] attempted to extend the result to higher order in Φ and Ca, similarly to what done by Batchelor for rigid particles, using perturbative expansions. Only recently high-fidelity numerical simulations have been used to study such problem [24,25,26,27,28].…”

Section: Introductionmentioning

confidence: 99%

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Suspensions of deformable particles in a Couette flow

Rosti

Brandt

2018

Journal of Non-Newtonian Fluid Mechanics

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We consider suspensions of deformable particles in a Newtonian fluid by means of fully Eulerian numerical simulations with a one-continuum formulation. We study the rheology of the visco-elastic suspension in plane Couette flow in the limit of vanishing inertia and examine the dependency of the effective viscosity µ on the solid volume-fraction Φ, the capillary number Ca, and the solid to fluid viscosity ratio K. The suspension viscosity decreases with deformation and applied shear (shear-thinning) while still increasing with volume fraction. We show that µ collapses to an universal function, µ (Φ e ), with an effective volume fraction Φ e , lower than the nominal one owing to the particle deformation. This universal function is well described by the Eilers fit, which well approximate the rheology of suspension of rigid spheres at all Φ. We provide a closure for the effective volume fraction Φ e as function of volume fraction Φ and capillary number Ca and demonstrate it also applies to data in literature for suspensions of capsules and red-blood cells. In addition, we show that the normal stress differences exhibit a non-linear behavior, with a similar trend as in polymer and filament suspensions. The total stress budgets reveals that the particle-induced stress contribution increases with the volume fraction Φ and decreases with deformability.

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Section: Resultsmentioning

confidence: 61%

Section: Resultsmentioning

confidence: 99%

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Suspensions of deformable particles in a Couette flow

Rosti

Brandt

2018

Journal of Non-Newtonian Fluid Mechanics

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“…For these cases we also observe that the dynamics of the dispersed phase flow is substantially unaffected by the volume fraction and has always components of rotational flow (inside the deforming droplets). We conclude our analysis by computing the normal stress difference following the Batchelor's formulation (Batchelor 1970;Srivastava et al 2016). Here, however, we cannot follow the same methodology used for the shear stress, because it is not possible to obtain the integration constant needed to determine the function G when integrating in the homogeneous directions.…”

Section: Flow Topology and Normal Stressmentioning

confidence: 99%

On the effect of coalescence on the rheology of emulsions

et al. 2019

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We present a numerical study of the rheology of a two-fluid emulsion in dilute and semidilute conditions. The analysis is performed for different capillary numbers, volume fraction and viscosity ratio under the assumption of negligible inertia and zero buoyancy force. The effective viscosity of the system increases for low values of the volume fraction and decreases for higher values, with a maximum for about 20% concentration of the disperse phase. When the dispersed fluid has lower viscosity, the normalised effective viscosity becomes smaller than 1 for high enough volume fractions. To single out the effect of droplet coalescence on the rheology of the emulsion we introduce an Eulerian force which prevents merging, effectively modelling the presence of surfactants in the system. When the coalescence is inhibited the effective viscosity is always greater than 1 and the curvature of the function representing the emulsion effective viscosity vs. the volume fraction becomes positive, resembling the behaviour of suspensions of deformable particles. The reduction of the effective viscosity in the presence of coalescence is associated to the reduction of the total surface of the disperse phase when the droplets merge, which leads to a reduction of the interface tension contribution to the total shear stress. The probability density function of the flow topology parameter shows that the flow is mostly a shear flow in the matrix phase, with regions of extensional flow when the coalescence is prohibited. The flow in the disperse phase, instead, always shows rotational components. The first normal stress difference is positive, except for the smallest viscosity ratio considered, whereas the second normal difference is negative, with their ratio being constant with the volume fraction. Our results clearly show that the coalescence efficiency strongly affects the system rheology and neglecting droplet merging can lead to erroneous predictions. † Email address for correspondence: fdv@mech.kth.se

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“…Fully resolved three-dimensional simulations of emulsions in shear flow, with same physical parameters as in experiments, are therefore extremely expensive. Numerical studies of emulsions at moderate concentration in literature have mostly been conducted with methods that do not allow droplets to coalesce 24,25 whereas simulations which resolve the liquid films are mostly in the dilute regime 26,27 .…”

Section: Introductionmentioning

confidence: 99%

Numerical simulations of vorticity banding of emulsions in shear flows

et al. 2020

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Multiphase shear flows often show banded structures that affect the global behavior of complex fluids e.g. in microdevices. Here we investigate numerically the banding of emulsions, i.e. the formation of regions of high and low volume fraction, alternated in the vorticity direction and aligned with the flow (shear bands). These bands are associated with a decrease of the effective viscosity of the system. To understand the mechanism of banding observed in the experiments by Caserta and Guido (Langmuir, 2008, 100), we simulate the multiphase flow using a one-fluid formulation, solving the incompressible Navier-Stokes equations coupled with a Volume of Fluid technique. The experiments were perfomed starting with a random distribution of droplets which, under the applied shear, evolves in time resulting in a phase separation. To numerically repoduce this process, the banded structures are initialized in a narrow channel confined by two walls moving in opposite direction. We find that the initial banded distribution is stable when droplets are free to merge and unstable when coalescence is prevented. In this case, additionally, the effective viscosity of the system increases, resembling the rheological behavior of suspensions of deformable particles. Droplets coalescence, on the other hand, allows emulsions to reduce the total surface of the system and hence the en-ergy dissipation associated to the deformation, which in turn reduces the effective viscosity. arXiv:1902.05448v1 [physics.flu-dyn]

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Steady shear rheology of a viscous emulsion in the presence of finite inertia at moderate volume fractions: sign reversal of normal stress differences

Cited by 14 publications

References 63 publications

Suspensions of deformable particles in a Couette flow

Suspensions of deformable particles in a Couette flow

On the effect of coalescence on the rheology of emulsions

Numerical simulations of vorticity banding of emulsions in shear flows

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