Modeling And Simulation Of Capsules And Biological Cells PDF Download

Three-dimensional computational modeling and simulation are presented on the flow-induced motion of highly deformable particles which are representative of biological cells, such as red blood cells. We focus on the dynamics of capsules, that is, liquid drops surrounded by hyperelastic membranes. Unlike liquid drops where the fluid-fluid interface is characterized by isotropic surface tension, that for a capsule is governed by more complex constitutive laws. The numerical method is based on a front-tracking/immersed boundary method forcapsule deformation, and a finite-difference/fourier-transform method for the flow solver. The methodology is able to consider large deformation of capsules, capsule-capsule interaction, semi-dense suspension, and inertial effect. Using the simulation tool, we address a sequence of problems: (a) Capsule motion in wall-bounded pressure-driven flows: The motion of a capsule in a channel flow is investigated in absence of inertia and under large deformation. It is shown that a deformable capsule slowly drifts lateral to the flow and away from the wall while moving axially with the flow. Based on the theory of small deformation, and the present numerical results, an approximate expression for migration velocity under large deformation is developed. (b) Binary interaction in wall-bounded pressure-driven flows: Hydrodynamic interaction between two capsules in a channel flow is investigated in absence of inertia. Effect of wall proximity on the shear-induced diffusion process, in which one capsule rolls over the other, is studied for spherical and ellipsoidal resting shapes. (c) Effect of inertia on binary collision: Hydrodynamic interaction between two capsules in a linear shear flow is investigated in presence of inertia. The shear-induced diffusion process is shown to be absent. Instead, a new interaction mode is found in which the capsules engage in spiraling motion. (d) Simulation of semi-dense suspension: We then consider direct numerical simulations (DNS) of suspension of multiple capsules of spherical and biconcave resting shapes. Detailed analysis of the numerical results and their relevance to in vitro blood flow are presented. It is shown that the two-phase model of blood in microvessels underpredicts the DNS flow rate. We proceed to develop a three-layer model based on the microrheology extracted from the DNS, and show that it accurately predicts the DNS velocity.