Power laws for sizes and growth times of double-diffusive convection cells

We perform quantitative investigations of double-diffusive convection in a setup that is extremely easy to implement and to observe. In this setup, a drop (containing a surfactant, as destabilizing substance, and glycerine, as stabilizing substance, stirred in water) is injected at the bottom of a dish filled with water. After a few minutes, surfactant cells are formed. Later, fingers transporting surfactant grow upwards at the vertices of these cells. The size λ of the cells and their growth time Tem are observed with a light microscope; also, these quantities are estimated analytically and determined from PDE simulations. We obtain power laws for the dependence of λ and Tem on the initial concentration of the stabilizing substance; the exponents in these laws are widely independent of the experimental conditions and on the model assumptions.