Dissolution-driven transport in a rotating horizontal cylinder

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 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 $\varOmega \in [0, 2.5]$ . 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 time scale – and Rayleigh number. We show that the area of the dissolved solute varies nonlinearly with time depending on $Ra$ and $\varOmega$ . The symmetry breaking of the interface is best described in terms of $Ra/\varOmega ^2$ .