R. Murthy Kalluri

Dynamic rheology of a dilute suspension of elastic capsules: effect of capsule tank-treading, swinging and tumbling

Three-dimensional numerical simulations are used to study the effect of unsteady swinging and tumbling motion on the rheology of a dilute suspension of oblate-shaped elastic capsules. Unlike a suspension of initially spherical capsules undergoing the steady tank-treading motion for which the rheology is constant in time, the suspension of non-spherical capsules is time-dependent due to the unsteady capsule motion. In a simple shear flow, the non-spherical capsules undergo a transition from the tank-treading/swinging to the tumbling motion with a reduction in the shear rate or an increase in the ratio of the internal to external fluid viscosities. We find that the time-averaged rheology obtained for the non-spherical capsules undergoing the unsteady motion is qualitatively similar to that obtained for the spherical capsules undergoing the steady tank-treading motion, and that the tank-treading-to-tumbling transition has only a marginal effect. The time-averaged rheology exhibits a shear viscosity minimum when the capsules are in a swinging motion at high shear rates but not at low shear rates. This is a remarkable departure from the behaviour of a vesicle suspension which exhibits a shear viscosity minimum at the point of transition. We find that the shear viscosity in a capsule suspension can decrease as well as increase with increasing viscosity ratio during both tank-treading and tumbling motions, while that of a vesicle suspension always decreases in tank-treading motion and increases in tumbling motion. We then seek to connect the time-dependent rheology with the time-dependent membrane tension, capsule orientation, deformation and tank-treading velocity. At low shear rates, the numerical results exhibit a similar trend to that predicted by analytical theory for rigid ellipsoids undergoing tumbling motion. The trend differs during swinging motion due to the periodic deformation and time-dependent variation of the membrane stress. The elastic component of the shear stress is minimum when the capsules are maximally compressed, and is maximum when the capsules are maximally elongated. In contrast, the viscous component is related to the periodic variation of the tank-treading velocity synchronized with the swinging motion, and the rate of capsule elongation or compression. The swinging or tumbling velocity makes no contribution to the time-dependent rheology.

Binary Interaction of Liquid Capsules in a Shear Flow

Three-dimensional numerical simulations using front-tracking method are presented on the hydrodynamic interaction between two deformable particles suspended in simple shear flow. Particles are modeled as liquid capsules, that is, liquid drops surrounded by elastic membranes. Small and finite inertia are considered. Two sets of simulations are presented. In the first set, interaction between two identical capsules are considered. In the limit of zero inertia, it has been known from past research that the hydrodynamic interaction between two deformable particles results in an irreversible shift in the trajectories of the particles as one particle rolls over the other. We show that the presence of inertia can significantly alter the capsule trajectories, and the capsules engage in a symmetric spiraling motions. In the second set of simulations, we consider the interaction between two non-identical capsules which differ from each other in terms of capillary number. The interaction between them results in greater lateral separation as compared to that of an identical pair. This result suggests that the shear-induced diffusion mechanism may play an even greater role in mixing in suspension of bidisperse particles. The long-time trajectory of the non-identical capsules at finite Re shows that they move in spirals with different radii while translating along the streamwise direction. The more deformable capsule moves with smaller radius, and vice versa.Copyright

Rheology of a Suspension of 1000 Liquid Capsules in Channel Flow

Three-dimensional numerical simulations are presented on the motion of large ensembles of deformable particles (up to 1096 in number) in a channel flow at small inertia. Particles are modeled as capsules, that is, liquid drops surrounded by elastic membranes. Unlike liquid drops where the fluid-fluid interface is characterized by isotropic surface tension, that of a capsule is governed by more complex constitutive laws. Here we assume that the capsule membrane follows the neo-Hookean constitutive law. The particle volume fraction considered is up to 29%. The numerical methodology is based on a mixed finite-difference/Fourier transform method for the flow solver and a front-tracking method for fluid/membrane interaction. In the simulations, the flow field is resolved using up to 288×288×288 grid points, and each particle surface is resolved by 1280 triangular elements. The simulations are computation- and data-intensive, and the first of their kind in the context of deformable capsule suspension. The database generated from the simulations provides a wealth of information on the dynamics of semi-dense suspension of liquid capsules, in particular, and of deformable particles, in general. Preliminary results on flow visualization, particle trajectory, deformation, mean velocity and suspension viscosity are presented.Copyright

Direct Numerical Simulation of 1000 Deformable Capsules in a Channel Flow at Finite Inertia

Three-dimensional numerical simulations are presented on the motion of large ensembles of deformable particles (up to 1096 in number) in a channel flow in presence of inertia. Particles are modeled as capsules, that is, liquid drops surrounded by hyperelastic membranes. Unlike liquid drops where the fluid-fluid interface is characterized by isotropic surface tension, that of a capsule is governed by more complex constitutive laws. Here we assume that the membrane follows the neo-Hookean constitutive law. The particle Reynolds number, based on the centerline velocity of the undisturbed flow, the undeformed particle diameter, and suspending fluid viscosity, is in the range 0.1 to 25. The particle volume fraction considered is 9 and 26%. The ratio of the particle diameter to channel height varies from 0.08 to 0.16. The numerical methodology is based on a mixed finite-difference/Fourier transform method for the flow solver and a finite-element based fluid-structure interaction, and front-tracking method. In the simulations, the flow field is resolved using up to 2883 grid points, and each particle surface is resolved by 1280 triangular elements. Instantaneous snapshots of particle distribution from the simulations are analyzed to study the interaction between the deformable particles in a multi-particle environment. Results are presented on the time-dependent and mean quantities such as particle velocity and trajectory, deformation and orientation, rms fluctuations in lateral velocity, location, and deformation. The simulations are computation- and data-intensive, and the first of their kind in the context of deformable particle suspension. The database generated from the simulations provides a wealth of information on the dynamics of semi-dense suspension of liquid capsules, in particular, and of deformable particles, in general.Copyright