Spatiotemporal pattern formation in thin layers and membranes: critical focal size

Abstract

A theory for the determination of the focal nucleation size of oscillatory membrane (or thin layer) reactions is developed on the assumption that the focal domain is square planar. From this, one can estimate that, for a period of the oscillatory mode of, say, 5 min and lateral diffusion coefficient of approximately 10(-9) cm2/sec, the critical focal area would be of the order of 148 micrometer2, corresponding to a linear dimension of approximately 12.2 micrometer2. An alternative general expression for the critical focal size, involving explicitly the viscosity of the membrane, is also given.