The role of convection in the standard fluid-mechanical model for morphogenesis
The effect of convection on reaction-diffusion instabilities in a visco-elastic medium is studied by using the standard continuum theory of a fluid mixture. The medium is assumed to be in local mechanical equilibrium, and convection is generated by pressure forces which arise if the equilibrium density of the medium changes with its composition. A linear stability analysis shows that reaction-diffusion instabilities proceeding from homogeneous steady states at rest are unmodified by induced convection to first order in concentration changes. We suggest that a non-linear analysis would show convection produces no new instabilities, as a linear analysis of inhomogeneous non-convecting stationary states shows that reaction-diffusion growth rates are reduced by convection at long wavelengths and are otherwise unchanged. For applications in embryology, numerical estimates suggest that convection can be ignored in reaction-diffusion mechanisms for pattern formation, and this conclusion is supported by a dimensional analysis.