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

• Published in: Computers & fluids 1996-01, Vol.25 (8), p.741-757
• Main Authors: Brooks, Steven B., Tozeren, Aydin
• Format: Article
• Language: English
• Subjects: Biological and medical sciences; Cell interactions, adhesion; Fundamental and applied biological sciences. Psychology; Molecular and cellular biology
• ISSN: 0045-7930; 1879-0747
• DOI: 10.1016/S0045-7930(96)00024-2

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 flow 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 flow 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 flow. 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.