Separation of bidensity suspensions in gravity-driven thin-film flow in helical channels

Spiral gravity separators are devices designed to separate slurry components based on density. While previous modeling focused solely on mixtures of liquids and a single particle species [Lee, Stokes, and Bertozzi, "Behaviour of a particle-laden flow in a spiral channel," Phys. Fluids 26, 043302 (2014)], this study extends the theory to account for the influence of density differences among different species on particle segregation. We implement our model to analyze gravity-driven bidensity slurries on an incline by considering particle interactions using empirically obtained formulas. In this investigation, we examine a thin film bidensity particle slurry down a rectangular channel helically wound around a vertical axis. By applying a thin-film approximation, we derive an equilibrium profile for the concentration of each particle species and fluid depth. Our research identifies the dependence of particle concentration distribution on various parameters and reveals the optimal conditions that enhance particle separation, providing valuable insights into designing the spiral separator.