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.