Scaling behavior for the onset of convection in a colloidal suspension

We investigate the early stages of mass convection in a colloidal suspension at high solutal Rayleigh number (Ra) over cap (s). From the time evolution of shadowgraph images and by assuming a diffusive growth of the boundary layers we obtain an indirect measurement of the concentration boundary layer thickness delta(*) at the onset of convection. We show that the dimensionless boundary layer thickness delta = delta(*)/d scales as Ra-s(-p), where Ra-s = (Ra) over cap (s)delta is a modified solutal Rayleigh number for convection which accounts for the actual density unbalance and d is the thickness of the sample layer. This scaling behavior is analogous to that reported at steady state for turbulent convection in simple fluids. We find p = 0.35, a value compatible with the exponent 1/3, reported for turbulent heat convection in simple fluids at steady state.