The axisymmetric deformation of a red blood cell in uniaxial straining Stokes flow

Abstract

The axisymmetric deformation of a red blood cell placed in a uniaxial straining Stokes flow is considered. The cell is modelled as a fluid capsule that contains a Newtonian fluid, and is bounded by an area-preserving membrane with negligible resistance to bending. First, it is theoretically demonstrated that spheroidal cells with isotropic membrane tension constitute stationary configurations. To compute transient cell deformations, a numerical procedure is developed based on the boundary-integral method for Stokes flow. Calculations show that initially prolate or oblate cells with isotropic membrane tension deform into stationary spheroids. Cells with a highly oblate initial shape may develop a persistent small pocket along their axis during the deformation. The shear elasticity of the membrane prevents folding, but may cause the formation of sharp corners and concave regions along the cell contour. A decrease in the membrane shear elasticity results in substantial increase in the magnitude of the transient and asymptotic membrane tensions. The maximum strain rate below which a red blood cell remains intact is estimated to be e_x = 10⁵ s⁻¹.