Hydrodynamics of domain size equilibration in monolayers

Coexisting thermodynamic phases of lipid molecules at the air-water interface often exhibit microscopically observable domains with a variety of sizes and shapes. The size and shape equilibration of these domains generally involve fluid flow in the monolayer as well as in the aqueous subphase. The present work treats the problem of the rate of size equilibration of a circular solid domain surrounded by a liquid composed of the same substance. The pressure at large distances from the domain is maintained constant, so that there is monolayer flow toward or away from the central domain. The central domain accordingly increases or decreases in size until a state of stable or metastable equilibrium is reached. Calculated rates of domain size change are discussed in terms of different experimental conditions, including applied electric fields.