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Particle-laden slurries are pervasive in both natural and industrial settings, whenever particles are suspended or transported in a fluid. Previous literature has investigated the case of a single species of negatively buoyant particles suspended in a viscous fluid. On an incline, three distinct regimes emerge depending on the particle concentration and inclination angle: settled (where particles settle and there is a pure fluid front), well-mixed (where particle concentration is constant throughout), and ridged (where a particle-rich ridge leads the flow). Recently, the same three regimes were also found for constant volume two species bidensity slurries. We extend the literature on bidensity slurries by presenting results on constant volume and a new type of initial condition: constant flux, where slurry is pumped onto the incline at a constant rate. We present front positions of the slurries and compare them to theoretical predictions. In addition, height profiles (film thicknesses) are also presented for the constant flux case, showing the distinct behavior of the ridged regime. We find that for constant flux conditions the settled regime forms for small particle volume fractions and inclination angles while the ridged regime forms for large corresponding values. Intermediate values of these two parameters are shown to produce a well-mixed regime.KEYWORDS: Thin Films; Particle-Laden Flow; Multiphase Fluids; Interfacial Flows; Particle Segregation
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This content will become publicly available on February 1, 2026
Equilibrium theory of bidensity particle-laden suspensions in thin-film flow down a spiral separator
Spiral gravity separators are designed to separate multi-species slurry components based on differences in density and size. Previous studies [S. Lee et al., Phys. Fluids 26, 043302 (2014); D. Arnold et al., Phys. Fluids 31, 073305 (2019)] have investigated steady-state solutions for mixtures of liquids and single particle species in thin-film flows. However, these models are constrained to single-species systems and cannot describe the dynamics of multi-species separation. In contrast, our analysis extends to mixtures containing two particle species of differing densities, revealing that they undergo radial separation—an essential mechanism for practical applications in separating particles of varying densities. This work models gravity-driven bidensity slurries in a spiral trough by incorporating particle interactions, using empirically derived formulas for particle fluxes from previous bidensity studies on inclined planes [J. T. Wong and A. L. Bertozzi, Phys. D 330, 47–57 (2016)]. Specifically, we study a thin-film bidensity slurry flowing down a rectangular channel helically wound around a vertical axis. Through a thin-film approximation, we derive equilibrium profiles for the concentration of each particle species and the fluid depth. Additionally, we analyze the influence of key design parameters, such as spiral radius and channel width, on particle concentration profiles. Our findings provide valuable insights into optimizing spiral separator designs for enhanced applicability and adaptability.
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- Award ID(s):
- 2407006
- PAR ID:
- 10575425
- Publisher / Repository:
- AIP Publishing
- Date Published:
- Journal Name:
- Physics of Fluids
- Volume:
- 37
- Issue:
- 2
- ISSN:
- 1070-6631
- Page Range / eLocation ID:
- 023397
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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