Flow past an array of cells that are adherent to the bottom plate of a flow channel

Parallel-plate flow channels are used extensively in cell-biological research to investigate cell-substrate adhesion. However, an analytical relationship between the fluid force acting on a cell that is adherent to the bottom plate of a channel and the Bow rate into the channel is yet to be established. A finite-difference scheme was used to evaluate the three-dimensional laminar flow past an array of uniformly distributed cells that are adherent to the bottom plate of a parallel-plate Bow channel. Computational results indicated that the fluid force acting on a spherical cell can be computed within 10% accuracy by using the solution given by Goldman et al. [Goldman, A. J., Cox, R. G. and Brenner, H., Slow viscous motion of a sphere parallel to a plane wall. I. Motion through quiescent fluid. Chem. Engng Sci., 1967, 22, 637-651. Goldman, A. J., Cox, R. G. and Brenner,H., Slow viscous motion of a sphere parallel to a plane wall. II. Couette Bow. Chem. Engng Sci., 1967, 22, 653-660.] - for a single sphere in contact with a planar wall in infinite shear flow - when the ratio of the cell radius (R(s)) to the gap thickness between parallel plates (h) is less than (1/15). Goldman et al.'s solution begins to significantly overestimate the actual fluid force as the (R(s)/h) ratio becomes larger than 1/15. When (R(s)/h) = 1/5, the fluid force computed by Goldman et al. is greater than the actual force by 30%. As an originally spherical cell aligns and elongates in the direction of flow, the fluid force acting on it decreases by 25%. In all cases, cell spreading leads to a more uniform distribution of fluid shear stress on the cell surface. Further computations indicate that fluid force on a spherical cell with surface projections (rough cell) is slightly smaller than that for a smooth spherical cell whose radius is equal to the maximum radial dimension of the rough cell. Copyright (C) 1996 Elsevier Science Ltd.