Pair collisions of fluid-filled elastic capsules in shear flow: Effects of membrane properties and polymer additives

Pranay, Pratik; Anekal, Samartha G.; Hernández-Ortiz, Juan P.; Graham, Michael D.

doi:10.1063/1.3524531

Cited by 46 publications

(61 citation statements)

References 53 publications

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“…A great number of numerical analyses have been conducted in recent years to study large deformation of capsules; for example, the boundary integral simulations of Pozrikidis (1995), Ramanujan & Pozrikidis (1998), Pozrikidis (2001), Lac et al (2004), Foessel et al (2011) and , immersedboundary/front-tracking simulations of Eggleton & Popel (1998), Li & Sarkar (2008), Sui et al (2008) and Le (2010), accelerated boundary integral simulation of Pranay et al (2010), spectral boundary integral simulations by Wang & Dimitrakopoulos (2006), Kessler, Finken & Seifert (2008) and Zhao et al (2010), to name a few. Of particular interest is the work by Lac et al (2004) who observed that the capsule buckled at low shear rates with wrinkles forming near the equator similar to the experimental observation of Walter et al (2001).…”

Section: Introductionmentioning

confidence: 99%

Influence of membrane viscosity on capsule dynamics in shear flow

2013

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Most previous numerical studies on capsule dynamics in shear flow have ignored the role of membrane viscosity. Here we present a numerical method for large deformation of capsules using a Kelvin-Voigt viscoelastic model for the membrane. After introducing the model and the related numerical implementation, we present a comprehensive analysis of the influence of the membrane viscosity on buckling, deformation and dynamics. We observe that the membrane viscosity leads to buckling in the range of shear rate in which no buckling is observed for capsules with purely elastic membrane. For moderate to large shear rates, the wrinkles on the capsule surface appear in the same range of the membrane viscosity that was reported earlier for artificial capsules and red blood cells based on experimental measurements. In order to obtain stable shapes, it is necessary to introduce the bending stiffness. It is observed that the range of the bending stiffness required is also in the same range as that reported for the red blood cells, but considerably higher than that estimated for artificial capsules. Using the stable shapes obtained in the presence of bending stiffness, we analyse the influence of membrane viscosity on deformation, inclination and tank-treading frequency of initially spherical capsules. Membrane viscosity is observed to reduce the capsule deformation, and introduce a damped oscillation in time-dependent deformation and inclination. The time-averaged inclination angle shows a non-monotonic trend with an initial decrease reaching a minimum and a subsequent increase with increasing membrane viscosity. A similar non-monotonic trend is also observed in the tank-treading frequency. We then consider the influence of the membrane viscosity on the unsteady dynamics of an initially oblate capsule. The dynamics is observed to change from a swinging motion to a tumbling motion with increasing membrane viscosity. Further, a transient dynamics is also observed in which a capsule starts with one type of dynamics, but settles with a different dynamics over a long time.

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Section: Introductionmentioning

confidence: 99%

Influence of membrane viscosity on capsule dynamics in shear flow

2013

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“…Equations (2) and (3) are solved by a hybrid boundary Integral-Mesh method, the General Geometry Ewald like method (GGEM) [1,31,32], used in a variety of micromultiphase simulations [33][34][35]. In our implementation, the mesh-based part (responsible for the long-range part of the Green's function) is calculated by the spectralelement solver NEK5000 [36] which allows us to cope with non-trivial boundaries.…”

Section: Methodsmentioning

confidence: 99%

Motion of an elastic capsule in a constricted microchannel

et al. 2015

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We study the motion of an elastic capsule through a microchannel characterized by a localized constriction. We consider a capsule with a stress-free spherical shape and impose its steady state configuration in an infinitely long straight channel as the initial condition for our calculations. We report how the capsule deformation, velocity, retention time, and maximum stress of the membrane are affected by the capillary number, Ca, and the constriction shape. We estimate the deformation by measuring the variation of the three-dimensional surface area and a series of alternative quantities easier to extract from experiments. These are the Taylor parameter, the perimeter and the area of the capsule in the spanwise plane. We find that the perimeter is the quantity that reproduces the behavior of the three-dimensional surface area the best. This is maximum at the centre of the constriction and shows a second peak after it, whose location depends on the Ca number. We observe that, in general, area-deformation correlated quantities grow linearly with Ca, while velocity-correlated quantities saturate for large Ca but display a steeper increase for small Ca. The velocity of the capsule divided by the velocity of the flow displays, surprisingly, two different qualitative behaviors for small and large capillary numbers. Finally, we report that longer constrictions and spanwise wall bounded (versus spanwise periodic) domains cause larger deformations and velocities. If the deformation and velocity in the spanwise wall bounded domains are rescaled by the initial equilibrium deformation and velocity, their behavior is undistinguishable from that in a periodic domain. In contrast, a remarkably different behavior is reported in sinusoidally shaped and smoothed rectangular constrictions indicating that the capsule dynamics is particularly sensitive to abrupt changes in the cross section. In a smoothed rectangular constriction larger deformations and velocities occur over a larger distance.

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“…For extensional flow with Wi 1, the Trouton ratio for high molecular weight long-chain polymers is 1; indicating that a solution of this polymer in which the polymer makes a negligible contribution to the stress in shear flow may nevertheless exhibit large stresses in extensional flow. Recent numerical simulations of pair collisions of capsules in polymer solutions by Pranay et al 66 showed a dramatic effect of DRAs on collision dynamics-polymers attenuated the net displacement of capsules after the collision. The uniaxial extensional flow generated in the gap of the departing capsules as they leave each other after the collision stretched the polymers significantly and the stretching worked against the separation of the departing capsules after the collision.…”

Section: Introductionmentioning

confidence: 99%

Depletion layer formation in suspensions of elastic capsules in Newtonian and viscoelastic fluids

2012

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Motivated by observations of the effects of drag-reducing polymer additives on various aspects of blood flow, suspensions of fluid-filled elastic capsules in Newtonian fluids and dilute solutions of high molecular weight (drag-reducing) polymers are investigated during plane Couette flow in a slit geometry. A simple model is presented to describe the cross-stream distribution of capsules as a balance of shear-induced diffusion and wall-induced migration due to capsule deformability. The model provides a theoretical prediction of the dependence of capsule-depleted layer thickness on the capillary number. A computational approach is then used to directly study the motion of elastic capsules in a Newtonian fluid and in polymer solutions. Capsule membranes are modeled using a neo-Hookean constitutive model and polymer molecules are modeled as bead-spring chains with finitely extensible nonlinearly elastic springs, with parameters chosen to loosely approximate 4000 kDa poly(ethylene oxide). Simulations are performed with a Stokes flow formulation of the immersed boundary method for the capsules, combined with Brownian dynamics for the polymer molecules. Results for an isolated capsule near a wall indicate that the wall-induced migration depends on the capillary number and is strongly reduced by addition of polymer. Numerical simulations of suspensions of capsules in Newtonian fluid illustrate the formation of a capsule-depleted layer near the walls. The thickness of this layer is found to be strongly dependent on the capillary number. The shear-induced diffusivity of the capsules, on the other hand, shows only a weak dependence on capillary number. These results thus indicate that the mechanism of wall-induced migration is the primary source for determining the capillary number dependence of the depletion layer thickness. Both the wall-induced migration and the shear-induced diffusive motion of the capsules are attenuated under the influence of polymer; reduction of migration dominates, however, so the net effect of polymers on the capsule suspension is to reduce the thickness of the capsule-depleted layer. This prediction is in qualitative agreement with experimental observations. C 2012 American Institute of Physics. [http://dx.

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Pair collisions of fluid-filled elastic capsules in shear flow: Effects of membrane properties and polymer additives

Cited by 46 publications

References 53 publications

Influence of membrane viscosity on capsule dynamics in shear flow

Influence of membrane viscosity on capsule dynamics in shear flow

Motion of an elastic capsule in a constricted microchannel

Depletion layer formation in suspensions of elastic capsules in Newtonian and viscoelastic fluids

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