Forced spreading of films and droplets of colloidal suspensions

Espín, Leonardo; Kumar, Satish

doi:10.1017/jfm.2014.27

Cited by 25 publications

(90 citation statements)

References 39 publications

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“…The solid particles, which are considered to be heavier than the carrying fluid (negatively buoyant), have radiusâ and densitŷ ρ p . In particular, we are interested in non-Brownian suspensions, i.e.â > 1 µm (Espín & Kumar 2014). The Newtonian carrying fluid in the heavy solution has densityρ f ,H and viscosityμ f ,H .…”

Section: Dimensional and Dimensionless Governing Parametersmentioning

confidence: 99%

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: Dimensional and Dimensionless Governing Parametersmentioning

confidence: 99%

Monodisperse particle-laden exchange flows in a vertical duct

Mirzaeian

Alba

2018

J. Fluid Mech.

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“…Analytical models for viscosity were formulated by Einstein (1906) for dilute suspensions and later extended by Batchelor & Green (1972), incorporating two-body interactions. However, empirical models are preferred for higher concentrations -the Krieger-Dougherty correlation being one of the widely used models (Phillips et al 1992;Merhi et al 2005;Murisic et al 2013;Espin & Kumar 2014). Suspension physics, beyond viscosity modification, can be classified broadly based on three non-dimensional numbers.…”

Section: Introductionmentioning

confidence: 99%

“…Such shallow granular flows have been studied extensively in the literature (Pouliquen 1999;Forterre & Pouliquen 2003;Gray & Edwards 2014;Kumaran 2014;Baker, Johnson & Gray 2016). In the opposite limit of St = 0, Pe p = 0 exist colloidal particles (< 1 μm) which undergo diffusive motion due to thermal effects (Espin & Kumar 2014) characterised by the Einstein diffusivity D 0 . In the context of a spreading film, Espin & Kumar (2014) studied the role of colloidal particles on the advancing contact line of a spreading film.…”

Section: Introductionmentioning

confidence: 99%

Stability of gravity-driven particle-laden flows – roles of shear-induced migration and normal stresses

Roy²

2022

J. Fluid Mech.

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In this paper, we study the role of shear-induced migration and particle-induced normal stresses in the formation and stability of a particle-laden, gravity-driven shallow flow. We first examine the modification of the base-state Nusselt flow due to the underlying microstructure, how shear-induced migration leads to viscosity stratification. We inspect the development of the base state via the boundary layer formation in the ‘shallow’ limit and find a reduction in entrance length with increasing bulk particle concentration and an increase in entrance length with increasing Péclet number ( $Pe_p = \dot {\gamma } a^2 / D_0$ , where $\dot{\gamma}$ is the average shear rate, a is the particle size and $D_0$ is the single particle diffusivity). A linear stability analysis is then performed on the fully developed state to identify two modes of instability typically found in gravity-driven falling films – the long-wave surface and the short-wave shear modes. We find that when the associated Péclet number is $Pe_p \ll 1$ , increasing bulk particle volume fraction delays the onset of instability for both the surface mode and shear mode. However, with $Pe_p = {O}(1)$ , we find an enhancement in both modes of instability. We also find that, beyond a critical Péclet number, for a fixed particle volume fraction, the surface mode is unstable even in the absence of fluid inertia. The enhanced destabilisation is attributed to the combined effects of base-state viscosity stratification and momentum forcing via particle concentration perturbations. We also show that the physics behind the enhancement of instability is independent of the choice of the constitutive model used to describe the dynamics of the particle phase, provided the chosen model has elements of shear-induced migration.

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“…Beyond the φ dependence of the effective viscosity, neutrally buoyant suspensions have been shown to highlight non-Newtonian behaviour such as shear-thickening/thinning, yield stress, normal stress differences, etc. in many configurations (Gadala-Maria & Acrivos 1980;Leighton & Acrivos 1987;Lyon & Leal 1998;Snabre & Pouligny 2008;Fall et al 2009Fall et al , 2010Ancey et al 2013a;Andreini, Ancey & Epely-Chauvin 2013;Espín & Kumar 2014a). Even if the origin of these mechanisms is not always obvious, it is clear that migration processes of the solid phase can play a significant role in the apparent behaviour of the suspension at the scale of the considered system, as the material becomes heterogeneous.…”

Section: Introductionmentioning

confidence: 99%

Collapse of a neutrally buoyant suspension column: from Newtonian to apparent non-Newtonian flow regimes

2017

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Experiments on the collapse of non-colloidal and neutrally buoyant particles suspended in a Newtonian fluid column are presented, in which the initial volume fraction of the suspension $\unicode[STIX]{x1D719}$, the viscosity of the interstitial fluid $\unicode[STIX]{x1D707}_{f}$, the diameter of the particles $d$ and the mixing protocol, i.e. the initial preparation of the suspension, are varied. The temporal evolution of the slumping current highlights two main regimes: (i) an inertial-dominated regime followed by (ii) a viscous-dominated regime. The inertial regime is characterized by a constant-speed slumping which is shown to scale as in the case of a classical inertial dam-break. The viscous-dominated regime is observed as a decreasing-speed phase of the front evolution. Lubrication models for Newtonian and power-law fluids describe most of situations encountered in this regime, which strongly depends on the suspension parameters. The temporal evolution of the propagating front is used to extract the rheological parameters of the fluid models. At the early stages of the viscous-dominated regime, a constant effective shear viscosity, referred to as an apparent Newtonian viscous regime, is found to depend only on $\unicode[STIX]{x1D719}$ and $\unicode[STIX]{x1D707}_{f}$ for each mixing protocol. The obtained values are shown to be well fitted by the Krieger–Dougherty model whose parameters involved, say a critical volume fraction $\unicode[STIX]{x1D719}_{m}$ and the exponent of divergence, depend on the mixing protocol, i.e. the microscale interaction between particles. On a longer time scale which depends on $\unicode[STIX]{x1D719}$, the front evolution is shown to slightly deviate from the apparent Newtonian model. In this apparent non-Newtonian viscous regime, the power-law model, indicating both shear-thinning and shear-thickening behaviours, is shown to be more appropriate to describe the front evolution. The present experiments indicate that the mixing protocol plays a crucial role in the selection of a shear-thinning or shear-thickening type of collapse, while the particle diameter $d$ and volume fraction $\unicode[STIX]{x1D719}$ play a significant role in the shear-thickening case. In all cases, the normalized effective consistency of the power-law fluid model is found to be a unique function of $\unicode[STIX]{x1D719}$. Finally, an apparent viscoplastic regime, characterized by a finite length spreading reached at finite time, is observed at high $\unicode[STIX]{x1D719}$. This regime is mostly observed for volume fractions larger than $\unicode[STIX]{x1D719}_{m}$ and up to a volume fraction $\unicode[STIX]{x1D719}_{M}$ close to the random close packing fraction at which the initial column remains undeformed on opening the gate.

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Forced spreading of films and droplets of colloidal suspensions

Cited by 25 publications

References 39 publications

Monodisperse particle-laden exchange flows in a vertical duct

Monodisperse particle-laden exchange flows in a vertical duct

Stability of gravity-driven particle-laden flows – roles of shear-induced migration and normal stresses

Collapse of a neutrally buoyant suspension column: from Newtonian to apparent non-Newtonian flow regimes

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