CONVECTION ONSET FOR A BINARY MIXTURE IN A POROUS-MEDIUM AND IN A NARROW CELL - A COMPARISON

The hydrodynamic equations describing the fluid motion in a narrow cell and in a porous medium become identical in the limit of infinite height-to-width ratio (Hele-Shaw limit) in the first and zero permeability in the second case. The properties of the convection onset are, however, indistinguishable from an experimental point of view away from these limits. For realistic (rigid, impermeable) boundary conditions the critical Rayleigh number, the critical wavenumber and in the case of a Hopf bifurcation additionally the critical frequency are derived in both cases for a binary fluid mixture. For the porous medium the assumption of zero permeability is usually a very good approximation. The critical values for the porous medium are compared to those of the narrow cell for different height-to-width ratios and the connection with experiments is discussed.