The deformation of disc-shaped particles by a shearing fluid with application to the red blood cell

The shear stress distribution at the surface of an oblate spheroid in Couette flow is obtained using the hydrodynamical solutions of Jeffery to the Navier-Stokes creeping flow equations in the presence of ellipsoidal particles. The maximum hydrodynamic compression experienced by the precessing spheroid in a direction perpendicular to the particle's symmetry axis is calculated when the thickness-to-diameter ratio is made extremely small. Euler's differential equation for the bending moments about a column is integrated for a disc-shaped lamina of uniform thickness to obtain the critical diametric loading under which the disc would buckle in a sinusoidal mode. The resulting buckling load is equated to the maximum hydrodynamical compression force and the corresponding shear stress in the fluid obtained. An application of the foregoing principles to the erythrocyte is then discussed.