Empirical Formula for Mass Transfer across the Boundary between Convections in a Two-layer System

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Abstract
When a two-layer system which consists of water (upper layer) and an aqueous solution (lower layer) is heated from one side and cooled from the opposite side, a convection starts in each layer and a sharp horizontal boundary is formed by the two flows in opposite directions. The empirical formula for the transfer of a solute across the boundary was obtained by measuring the change in the concentration of a solute in the upper layer. The flux, WA, of a solute, A, was expressed by W A=a3(Δρ1–Δρ0)D0.5(ΔcI⁄Δρ2). Here, a3 is the mass-transfer coefficient; Δρ1, the density difference between the liquid on the heated wall and that on the cooled wall; Δρ0, the value of Δρ1 at which the convections start; D, the diffusion coefficient of a solute; and ΔcI and Δρ2, the concentration difference and the density difference, respectively, between the solution of the upper layer and that of the lower layer.