A conservation law model for bidensity suspensions on an incline

Wong, Jeffrey; Bertozzi, Andrea L.

doi:10.1016/j.physd.2016.05.002

Cited by 2 publications

(5 citation statements)

References 17 publications

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“…One question that might arise here is whether particle accumulation at the front can grow to an extent that causes pinch-off. In fact, by looking closely into the experiments of Zhou et al Wong & Bertozzi (2016) for particle-laden film flow down an incline, there is no evidence that such accumulation may lead to pinch-off. Also note that our computational code fails when particle enrichment approaches the jamming limit (µ → ∞ as φ → φ j ).…”

Section: 2mentioning

confidence: 99%

“…In this appendix we would like to verify the conditions under which such an assumption is valid. The particle transport equation for particle-laden film flows is given by Murisic et al (2013) and Wong & Bertozzi (2016) as…”

Section: Appendix a Shear-induced Migration Effectsmentioning

confidence: 99%

“…The settling and migration flux components can be expressed as the following (Murisic et al 2013;Wong & Bertozzi 2016):…”

Section: Appendix a Shear-induced Migration Effectsmentioning

confidence: 99%

“…The constants K c ≈ 0.41 and K v ≈ 0.62 correspond to shear-induced particle flux due to gradients in the particle volume fraction and effective viscosity of the suspension, which are determined empirically (Phillips et al 1992;Wong & Bertozzi 2016). From the velocity expression (3.15), it can be found that u y ∼ Re; see also appendix C for the coefficients.…”

Section: Appendix a Shear-induced Migration Effectsmentioning

confidence: 99%

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Monodisperse particle-laden exchange flows in a vertical duct

Mirzaeian

Alba

2018

J. Fluid Mech.

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We study buoyancy-driven exchange flow of two mixtures in a vertical narrow duct (two-dimensional channel as well as pipe) theoretically. While the light mixture is assumed always to be a pure fluid, the heavy mixture can be selected as either a pure or a particle-laden fluid. A small width-to-length ratio considered for the duct ($\unicode[STIX]{x1D6FF}\ll 1$) has been used as the perturbation parameter in developing a lubrication model (negligible inertia). In particular, we have adopted the methodology of Zhou et al. (Phys. Rev. Lett., vol. 94, 2005, 117803) for free-surface particle-laden film flows and extended it to a lock exchange system in confined geometry under the Boussinesq approximation. The resulting model is in the form of the classical Riemann problem and has been solved numerically using a robust total variation diminishing finite difference scheme. Both pure and particle-laden cases are investigated in detail. It is observed that the interface between the two fluids takes a self-similar shape at long times. In the case that both heavy and light fluids are pure, the dynamics of the flow is governed by two dimensionless quantities, namely the Reynolds number, $Re$, and the viscosity ratio, $\unicode[STIX]{x1D705}$, of the light and heavy fluids. The interpenetration of the heavy and light layers increases with $Re$ but decreases with $\unicode[STIX]{x1D705}$. Also, the heights of the heavy and light fronts change with $\unicode[STIX]{x1D705}$ but remain unchanged with $Re$. In the case of the particle-laden flow, however, four additional dimensionless parameters emerge, namely the initial volume fraction of particles, $\unicode[STIX]{x1D719}_{0}$, the ratio of particle diameter to duct width, $r_{p}$, and the density ratios of particles to carrying fluid, $\unicode[STIX]{x1D709}$, and of light fluid to carrying fluid, $\unicode[STIX]{x1D702}$. The effect of these parameters on the dynamics of the flow has been quantified through a systematic approach. In the presence of solid particles, the interface between the heavy and light layers becomes more curved compared to the case of pure fluids. This modification occurs due to the change of heavy mixture viscosity alongside the duct. Novel particle-rich zones are further discovered in the vicinity of the advancing heavy and light fronts. These zones are associated with different transport rates of the fluid and solid particles. The degree of particle enrichment remains the same with $Re$, is enhanced by $\unicode[STIX]{x1D705}$, $r_{p}$ and $\unicode[STIX]{x1D702}$, and is slightly diminished with $\unicode[STIX]{x1D719}_{0}$ and $\unicode[STIX]{x1D709}$. On the other hand, the stretched exchange zone between the heavy and light fronts grows with $r_{p}$, $\unicode[STIX]{x1D702}$ and $Re$, but decays with $\unicode[STIX]{x1D719}_{0}$, $\unicode[STIX]{x1D705}$ and $\unicode[STIX]{x1D709}$.

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Section: 2mentioning

confidence: 99%

Section: Appendix a Shear-induced Migration Effectsmentioning

confidence: 99%

“…The settling and migration flux components can be expressed as the following (Murisic et al 2013;Wong & Bertozzi 2016):…”

Section: Appendix a Shear-induced Migration Effectsmentioning

confidence: 99%

Section: Appendix a Shear-induced Migration Effectsmentioning

confidence: 99%

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Monodisperse particle-laden exchange flows in a vertical duct

Mirzaeian

Alba

2018

J. Fluid Mech.

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“…Models for flows of slurries consisting of two or more species of particles are less well understood than monodisperse slurries, and there is significant scope to improve modelling of such complex mixtures. Combining a recent model for bidensity suspensions 41 with our equations for the helical geometry is seen as a useful next step towards understanding particle separation in curved channels.…”

Section: Discussionmentioning

confidence: 99%

Particle-laden thin-film flow in helical channels with arbitrary shallow cross-sectional shape

2019

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Particle-laden flows in helical channels are of interest for their applications in spiral particle separators used in the mining and mineral processing industries. In this paper, we extend the previous work of Lee et al. 20 by studying thin-film flows of mono-disperse particle-laden fluid in helicallywound channels of arbitrary centreline curvature and torsion, and arbitrary cross-sectional shape. In the case where the particles are uniformly distributed through the depth of the film, significant analytic progress can be made: the governing equations reduce to a single nonlinear ordinary differential equation, which is readily integrated numerically to obtain the solution subject to appropriate boundary conditions. Motivated by possible application to the design of spiral separators, we consider the effects of changing the channel centreline geometry, the cross-sectional shape and the particle density on the resulting flows and the radial distribution of particles. Our results support the findings in Arnold et al. 2 regarding the effect of channel centreline geometry and cross-sectional shape on flows in particle-free regions. In particle-rich regions, similar effects are seen, although the primary velocity is lower due to increased effective mixture viscosity. Of key interest, is the effect of channel geometry on the focusing of the particles, for given fluxes of fluid and particles. We find that introducing a trench into the channel cross-section, a feature often used in commercial spiral particle separators, leads to smaller radial width of the particle-rich region, i.e. sharper focusing of the particles, which is consistent with experiments showing that channel geometry influences particle separation in a spiral separator.

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A conservation law model for bidensity suspensions on an incline

Cited by 2 publications

References 17 publications

Monodisperse particle-laden exchange flows in a vertical duct

Monodisperse particle-laden exchange flows in a vertical duct

Particle-laden thin-film flow in helical channels with arbitrary shallow cross-sectional shape

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