## Pre-Publicación 2024-09

## Fernando Betancourt, Raimund Bürger, Julio Careaga, Lucas Romero:

### Coupled finite volume methods for settling in inclined vessels with natural convection

### Abstract:

A widely applied technology of gravity-driven solid-liquid separation in mineral processing is the use of lamella settlers. These units are continuously operated tanks equipped with a number of parallel inclined plates immersed in the mixture to be separated. The inclination of the plates exploits the well-known Boycott effect that describes the enhancement of settling rates beneath inclined surfaces. This effect is usually attributed to a rapidly upward-streaming layer of clear liquid. The essence of this effect can be studied by examining gravity settling in an inclined tube or rectangular channel. The lower and upper surfaces of the channel represent the plate onto which the particles start to settle and below which the clarified liquid streams upward, respectively. In addition an increase of temperature in some part of the fluid causes a local change in the density of the fluid and circulation of the fluid within the vessel. It has been proposed to exploit this behaviour to accelerate the settling process by additional heating. To examine this hypothesis a model and corresponding numerical method to describe inclined settling enhanced by natural convection are formulated. The model consists in a two-dimensional scalar conservation law for the solids concentration coupled with a version of the Stokes system that accounts for density fluctuations in the mixture enhanced by a Boussinesq approximation of the effect of temperature. In addition a convection-diffusion equation describes heat transport and diffusion. The main outcome is a numerical method that allows one to simulate the effect of controllable parameters such as the initial concentration, difference of temperature, and angle of inclination on the progress of the solid-liquid separation. Numerical examples are presented. Results reconfirm that the enhancement of settling rates depends critically on the dimensions of the settling vessel, intensity of heating, and particle size, and is marginal for settling of relatively large particles and channels with a moderate length to width aspect ratio.