Centrifugal Convection due to Mass Transfer Near a Rotating Disk at High Schmidt Number

Abstract

The centrifugally-driven flow due to a density gradient between the surface of an infinite disk and the ambient fluid in a rotating system with mass transfer is studied for the case of high Schmidt number. Under certain assumptions the velocity and density fields exhibit a similarity like the classical von Karman disk flow, and the governing equations reduce to a nonlinear system of ordinary differential equations. These equations are solved by boundary layer technique or numerically, for high Schmidt number σ = v/D and finite or small density difference ερ = (ρd - ρ∞ )/ρ∞ . In the latter case it is shown that the major scaling parameter is the product σερ . For σρ ≫ 1 the flow field consists of a constant density (ρ∞ ), linear Ekman layer driven by a buoyancy sublayer of relative thickness (σερ )-1/4 in which ρ varies from ρd to ρ∞ . The representative Rossby number of the buoyancy driven flow is (σερ )-1/2 . The general case ερ = O(1), σ ≫ 1 shows similar trends, i.e., a σ-1/4 sublayer. The case of simultaneous driving by density difference and angular velocity difference εv = (Ωd - Ω∞ )/Ω∞ is also discussed.