Flow-induced deformation of two-dimensional biconcave capsules
Numerical simulations of the flow-induced deformation of a two-dimensional biconcave capsule enclosed by an elastic membrane that exhibits flexural stiffness are conducted using the boundary-integral method for Stokes flow. The capsule represents an idealized red blood cell suspended in plasma. When the internal and external fluid viscosities are matched, a capsule immersed in infinite shear flow deforms to obtain a nearly steady elongated shape. A transition from flipping to tumbling is observed as a dimensionless shear rate, defined with respect to the membrane bending modulus, becomes smaller. When the internal fluid viscosity exceeds a critical threshold, the capsule engages in periodic tumbling motion as it stretches and compresses while rotating under the action of the shear flow. Simulations of the capsule motion in simple shear flow near a plane wall reveal that the capsule monotonically migrates away from the wall in the case of equal viscosities, and exhibits undulatory migration in the case of high interior viscosity. The behavior of two-dimensional capsules is qualitative similar to that exhibited by the mid-plane contour of three-dimensional biconcave capsules resembling red blood cells.