Dissolution-driven transport in a rotating horizontal cylinder

Abstract

We study the combined effects of natural convection and rotation on the dissolution of a solute in a solvent-filled circular cylinder. The density of the fluid increases with the increasing concentration of the dissolved solute, and we model this using the Oberbeck-Boussinesq approximation. The underlying moving-boundary problem has been modelled by combining the Navier-Stokes equations with the advection-diffusion equation and a Stefan condition for the evolving solute-fluid interface. We use highly resolved numerical simulations to investigate the flow regimes, dissolution rates, and mixing of the dissolved solute for $Sc = 1$, $Ra \in [10^5, 10^8]$ and $\Omega \in [0, 2.5]$. In the absence of rotation and buoyancy, the distance of the interface from its initial position follows a square root relationship with time ($r_d \propto \sqrt{t}$), which ceases to exist at a later time due to the finite-size effect of the liquid domain. We then explore the rotation parameter, considering a range of rotation frequency -- from smaller to larger, relative to the inverse of the buoyancy-induced timescale -- and Rayleigh number. We show that the area of the dissolved solute varies nonlinearly with time depending on $Ra$ and $\Omega$. The symmetry breaking of the interface is best described in terms of $Ra/\Omega^2$.