Velocity distribution on the membrane of a tank-treading red blood cell

The kinematics of an area-conserving tank-treading disk-shaped red blood cell membrane is studied using the stream function method suggested by Secomb and Skalak (Q. Jl Mech. appl. Math. 35, Pt 2, 233-247, 1982). Two simple area-conserving velocity fields are superimposed to satisfy the continuity condition at the curved edges of the disk. A differential equation for the trajectory of any material point of the membrane is derived. The requirement of synchrony of the cycle for all membrane points leads to an integral equation which determines a magnitude function. An approximate solution is made possible by assuming small trajectory deflections.