A continuum model for a red blood cell transformation: sphere to crenated sphere

The evolution of crenations on the spherical red blood cell, which is part of the reversible disc-sphere transformation of these cells, is considered here. A continuum model is developed where the cell is treated as a small viscous droplet encapsulated by a viscoelastic solid membrane. When a small amount of material is deposited into the membrane, the drop responds by increasing its surface area as manifested by the appearance of ripples. A preferred number of crenations form and they are sustained for long time periods. The inception of crenations is due to a dynamic instability in the governing set of nonlinear equations, and depends on the rheological properties of the droplets' interior and membrane.