Sailing the surfactant sea: Membrane hydrodynamics, geometry, and red blood cells

The dynamics of viscous or viscoelastic membranes surrounded by a viscous fluid plays an important biophysical role in, e.g., understanding the mobility of proteins in cell membranes. These fluid membranes also provide an interesting physical system in which low Reynolds number hydrodynamics acquires an inherent lengthscale, and where membrane curvature can dramatically change the mobility of membrane-bound particles. In this talk I first discuss the hydrodynamics of flat fluid membranes surrounded by bulk fluids, initially developed by Saffman and Delbrück (SD). I then extend these theories to study flows in curved membranes, showing how curvature modifies the SD picture. Finally, I use these geometric ideas to study the effect of curvature on the fluctuation spectrum of (visco-)elastic membranes, and apply that analysis to membrane microrheology. Using this theory, I analyze the fluctuation spectrum of human red blood cell membranes (measured by G. Popescu, UIUC) in order to extract their mechanical properties in various morphological states of the cell.