Shear-flow induced deformation of an elastic particle adhering to a wall: Modeling leukocyte adhesion to the endothelium

The study of blood cell physiology motivates an analysis of the physical nature of steady flow past an elastic particle fixed to a boundary. The analysis of this system also has relevance to the fields of particle mechanics and collector flows. A parametric study was performed to examine the steady state deformation of an elastic particle adhered to a rigid wall under stresses applied by a viscous linear shear flow. The two parameters varied are the initial contact radius ratio {dollar}(lambda){dollar} defined as the ratio of a particle radius to its contact area radius when adhesion is initiated in the absence of flow, and the capillary number {dollar}(Omega){dollar} defined by the ratio of the fluid viscous shear stress to the elastic modulus of the particle.; The flow field was computed numerically by the Boundary Element Method (BEM). Finite displacement solutions to a Finite Element Analysis (FEA) grid using a commercially available solid mechanics solver were employed to compute the deformations of the elastic particle. An iterative method was developed to match the linearized fluid stress solution to the computed deformation response of the particle.; For the contact radius ratio case {dollar}lambda{dollar} = 0.25, it was possible to compute a critical capillary number, Ca = {dollar}416 cdot 10sp{lcub}-6{rcub}{dollar}, where a transition in the contact line continuity demonstrated numerical instability. The {dollar}sigmasb{lcub}rm {lcub}zz{rcub}{rcub}{dollar} stress distributions were computed on the flow-deformed solids and demonstrated variations consistent with the increasing residual stress of increasing initial contact radius ratio: The three-dimensional stress values were plotted. Flow fields around the particles were computed from tabulated fluid force values evaluated for the solved solid deformations. For the extreme capillary number cases of each contact radius ratio studied, plots were made. The results are relevant to the adhesion and rolling of white blood cells in small venules.