Efficient computation of micro-particle dynamics including wall effects

Abstract This study describes an effective method for one-way coupled Eulerian–Lagrangian simulations of spherical micro-size particles, including particle–wall interactions and the quantification of near-wall stasis at possibly elevated concentrations. The focus is on particle-hemodynamics simulations where particle suspensions are composed of critical blood cells, such as monocytes, and the carrier fluid is non-Newtonian. Issues regarding adaptive time-step integration of the particle motion equation, relevant point-force model terms, and adaptation of surface-induced particle forces to arbitrary three-dimensional geometries are outlined. By comparison to available experimental trajectories, it is shown that fluid-element pathlines may be used to simulate non-interacting blood particles removed from wall boundaries under dilute transient conditions. However, when particle–wall interactions are significant, an extended form of the particle trajectory equation is required which includes terms for Stokes drag, near-wall drag modifications, or lubrication forces, pressure gradients, and near-wall particle lift. Still, additional physical and/or biochemical wall forces in the nano-meter range cannot be readily calculated; hence the near-wall residence time (NWRT) model indicating the probability of blood particle deposition is presented. The theory is applied to a virtual model of a femoral bypass end-to-side anastomosis, where profiles of the Lagrangian-based NWRT parameter are illustrated and convergence is verified. In order to effectively compute the large number of particle trajectories required to resolve regions of particle stasis, the proposed particle tracking algorithm stores all transient velocity field solution data on a shared memory architecture (SGI Origin 2400) and computes particle trajectories using an adaptive parallel approach. Compared to commercially available particle tracking packages, the algorithm presented is capable of reducing computational time by an order of magnitude for typical transient one-way coupled blood particle simulations in complex cyclical flow domains.