(297b) Self-Sustained Oscillations in the Flow of a Suspension through a Capillary Network

A numerical method is implemented for computing the unsteady flow of a suspension through a capillary tube network. The evolution of the local particle concentration along each network segment is computed by integrating in time a convection equation. Boundary conditions for the particle concentration at a bifurcation arise from a partitioning law. Data on the tube to discharge hematocrit ratio and effective viscosity are either borrowed from the literature or computed using a boundary-element method for Stokes flow. The continuum model is validated for the case of blood flow through a microvascular capillary network by comparison with a discrete model where the motion of the individual particles is followed through the network. Simulations for a tree-like network reveal a supercritical Hopf bifurcation yielding self-sustained oscillations for red blood cells and suspensions of rigid, spherical particles. A phase diagram is presented to establish conditions for unsteady flow.