Small deformation of a nearly circular lipid-raft in the stagnation flow

A lipid-raft-a non-caveolar microdomain enriched with sphingolipids and cholesterol-is thought to be unable to grow beyond a certain size in the biomembrane in vivo. The membrane can accommodate two-dimensional flow, which could break up a larger raft. As a fundamental problem of this mechanism, a small raft-deformation in the stagnation flow is studied in this paper. The capillary number-a relevant dimensionless factor in this problem-involves viscosity of the surrounding fluids for a large enough raft, and instead that of the membrane for a small enough raft. Discussing the breakup condition of a raft, we also show that an estimate of the critical raft-size is consistent with previous observations in vivo.