Three-dimensional simulations of a platelet-shaped spheroid near a wall in shear flow

Abstract

We have investigated the three-dimensional motion of an oblate spheroid-shaped particle or “platelet” close to an infinite planar wall in shear flow. The completed double layer-boundary integral equation method modified to include a flat surface boundary was used to compute the effects of the wall on the flow behavior of a platelet of aspect ratio 0.25. Platelet simulations were initiated with the platelet having its axis of symmetry normal to the surface. The platelet is observed to demonstrate three distinct regimes of flow, the dominant regime of flow being dependent on its initial height from the surface. Platelets further than 1.2 platelet radii from the surface display a “modified” Jeffery orbit with periodic rotational motion in the direction of flow (regime I). The presence of the wall retards platelet flow and more importantly introduces periodic lateral motion normal to the wall. When the platelet starts flowing at a height between 1.1 and 0.75 platelet radii from the surface (regime II), it is found to dip down and then “pole vault” off of the surface. Periodic platelet rotation and contact with the surface then ensues with no drift of the platelet away from the surface. In the third regime of flow, a platelet with an initial height of 0.7 platelet radii and below demonstrates wobble motion. The platelet neither rotates nor contacts the surface, but instead, moves laterally in a periodic manner as it translates in the direction of flow. Flow behavior typical of regime III is not observed at all spheroid aspect ratios. The range of initial heights that demonstrate regime III flow diminishes with increasing aspect ratio and regime III disappears completely above an aspect ratio of 0.41. If a platelet located at heights relevant to regime III is given an initial tilt about the y axis or x axis (where x is the flow direction), the resulting flow may either continue in regime III or shift to regime II, depending on the tilt angle. There is a small critical angle of tilt, the magnitude of which depends on the initial platelet height, above which the platelet flow behavior immediately transitions from regime III flow to that of regime II. Tilts about the x axis induce fully three-dimensional flow with rotational motion occurring about all three axes. Therefore, even small tilts about the x axis that are below the critical tilt angles can cause platelet flow to transform from regime III to II eventually at some point downstream. Thus, a platelet flowing close to the surface in linear shear has ample opportunity to contact the surface, an important event for initiating receptor-ligand binding of blood platelets to the injured vascular endothelium during the onset of hemostasis.