On the hydrodynamic interaction between a particle and a permeable surface

Ramon, Guy Z.; Huppert, Herbert E.; Lister, Joseph; Stone, Howard A.

doi:10.1063/1.4812832

Cited by 29 publications

(39 citation statements)

References 23 publications

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“…The permeation velocity through the membrane is V 0 and λ D is the Debye length. pressure within the thin fluid film, separating the droplet and the membrane, as 14,15…”

Section: Problem Formulation Geometry and Long-wave Approximationmentioning

confidence: 99%

Hydrodynamic–Colloidal Interactions of an Oil Droplet and a Membrane Surface

Galvagno

Ramon

2020

Langmuir

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Membranes have been shown to be exceptionally successfully in the challenging separation of stable oil-water emulsions, but suffer from severe fouling that limits their performance. Understanding the mechanisms leading to oil deposition on the membrane surface, as influenced by hydrodynamics and colloidal surface interactions is imperative for informing better engineered membrane surfaces and process conditions.Here, we study the the interactions between an oil droplet and a membrane surface.Hydrodynamics within the water film, confined between the droplet and the membrane, are captured within the framework of the lubrication approximation, coupled with the van der Waals (vdW) and electrostatic interactions through the droplet shape, which is governed by an augmented Young-Laplace equation. The model is used to calculate possible equilibrium positions, where the droplet is held at a finite distance from the membrane by a balance of the forces present. An equilibrium phase diagram is constructed as a function of various process parameters, and is shown in terms of the scaled permeation rate through the membrane. The phase diagram identifies the range of conditions leading to deposition, characterized by a 'critical' permeation rate, beyond which no equilibrium exists. When equilibrium positions are permitted, we find that these may be classified as stable/unstable, in the kinetic sense. Further, our arXiv:2003.10349v1 [physics.flu-dyn] 23 Mar 2020 results demonstrate the link between the deformation of the droplet and the stability of equilibria. An upward deflection of the droplet surface, owing to a dominant, long-range repulsion, has a stabilizing effect as it maintains the separation between droplet and membrane. Conversely, a downward deflection is de-stabilizing, due to the self-amplifying effect of strongly increasing attractive forces with separation distanceas the surfaces are pulled together due to deformation, the attractive force increases, causing further deformation. This is also manifested by a dependence of the bi-stable region on the deformability of the droplet, which is represented by a capillary number, modified so as to account for the effect of the permeable boundary. As the droplet becomes more easy to deform, the transition from an unconditionally stable region of the phase diagram, to a point beyond which there is no equilibrium (interpreted as deposition) becomes abrupt. These results provide valuable physical insight into the mechanisms that govern oil fouling of membrane surfaces.

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“…The permeation velocity through the membrane is V 0 and λ D is the Debye length. pressure within the thin fluid film, separating the droplet and the membrane, as 14,15…”

Section: Problem Formulation Geometry and Long-wave Approximationmentioning

confidence: 99%

Hydrodynamic–Colloidal Interactions of an Oil Droplet and a Membrane Surface

Galvagno

Ramon

2020

Langmuir

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“…The initial minimum fluid layer thickness is denoted by h min (0) = H f (> 0). Following Stone 10 , Skotheim and Mahadevan 17 and Ramon et al 15 , we consider smooth axisymmetric shapes of the form…”

Section: Model Formulationmentioning

confidence: 99%

“…Wu 11 (see also Prakash and Vij 12 and the review by Wu 4 ) considered squeeze-film flow between two annular discs, one of which is coated with a porous layer, and found that increasing the permeability of the layer reduces the normal force on the discs. Goren 13 and Nir 14 (see also the summary of previous work given in Table 1 in Ramon et al 15 ) calculated the force required to pull a sphere away from contact with a thin porous membrane at a constant velocity, and found that, unlike in the case of an impermeable membrane, the force is finite. In particular, Goren 13 found that the maximum value of the force does not occur when the sphere and the membrane are in contact.…”

Section: Introductionmentioning

confidence: 99%

“…In particular, Goren 13 found that the maximum value of the force does not occur when the sphere and the membrane are in contact. More recently, Ramon et al 15 studied a particle with a more general shape approaching a thin porous membrane. They showed that the particle attains a finite non-zero velocity as it sediments under gravity towards the membrane, and hence that it comes into contact with the membrane in a finite time.…”

Section: Introductionmentioning

confidence: 99%

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Squeeze-film flow between a curved impermeable bearing and a flat porous bed

et al. 2017

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This version is available at https://strathprints.strath.ac.uk/59331/ Strathprints is designed to allow users to access the research output of the University of Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Please check the manuscript for details of any other licences that may have been applied. You may not engage in further distribution of the material for any profitmaking activities or any commercial gain. You may freely distribute both the url (https://strathprints.strath.ac.uk/) and the content of this paper for research or private study, educational, or not-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to the Strathprints administrator: strathprints@strath.ac.ukThe Strathprints institutional repository (https://strathprints.strath.ac.uk) is a digital archive of University of Strathclyde research outputs. It has been developed to disseminate open access research outputs, expose data about those outputs, and enable the management and persistent access to Strathclyde's intellectual output. Axisymmetric squeeze-film flow in the thin gap between a stationary flat thin porous bed and a curved impermeable bearing moving under a prescribed constant load is analysed. The unsteady Reynolds equation is formulated and solved for the fluid pressure. This solution is used to obtain the time for the minimum fluid layer thickness to reduce to a given value, and, in particular, the finite time for the bearing and the bed to come into contact. The effect of varying the shape of the bearing and the permeability of the layer is investigated, and, in particular, it is found that both the contact time and the fluid pressure behave qualitatively differently for beds with small and large permeabilities. In addition, the paths of fluid particles initially situated in both the fluid layer and the porous bed are calculated. In particular, it is shown that, unlike in the case of a flat bearing, for a curved bearing there are fluid particles, initially situated in the fluid layer, that flow from the fluid layer into the porous bed and then re-emerge into the fluid layer, and the region in which these fluid particles are initially situated is determined.

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“…23,24 On the other hand, the velocity slip also occurs in porous media such as the brine water and supercritical CO 2 flow in nanopores of sandstone rocks, and it is necessary to consider the SBC for the fluid flow in microporous media. [25][26][27][28][29][30][31] In addition, we compare the fluid flow past the porous wall with the one past a rough wall. Much work has been done to study the influence of wall roughness on the channel flows, including the rectangular, sinusoidal, triangular [32][33][34] and topological surfaces.…”

Section: Introductionmentioning

confidence: 99%

Nanochannel flow past permeable walls via molecular dynamics

Xie

Cao

2016

AIP Advances

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The nanochannel flow past permeable walls with nanopores is investigated by molecular dynamics (MD) simulations, including the density distribution, velocity field, molecular penetration mechanism and surface friction coefficient. A low density distribution has been found at the gas-wall interface demonstrating the low pressure region. In addition, there exists a jump of the gas density on the permeable surface, which indicates the discontinuity of the density distribution across the permeable surface. On the other hand, the nanoscale vortices are observed in nanopores of the permeable wall, and the reduced mass flux of the flow in nanopores results in a shifted hydrodynamic boundary above the permeable surface. Particularly the slip length of the gas flow on the permeable surface is pronounced a non-linear function of the molecular mean free path, which produces a large value of the tangential momentum accommodation coefficient (TMAC) and a big portion of the diffusive refection. Moreover, the gas-gas interaction and multi-collision among gas molecules may take place in nanopores, which contribute to large values of TMAC. Consequently the boundary friction coefficient on the permeable surface is increased because of the energy dissipation consumed by the nanoscale vortices in nanopores. The molecular boundary condition provides us with a new picture of the nanochannel flow past the permeable wall with nanopores.

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On the hydrodynamic interaction between a particle and a permeable surface

Cited by 29 publications

References 23 publications

Hydrodynamic–Colloidal Interactions of an Oil Droplet and a Membrane Surface

Hydrodynamic–Colloidal Interactions of an Oil Droplet and a Membrane Surface

Squeeze-film flow between a curved impermeable bearing and a flat porous bed

Nanochannel flow past permeable walls via molecular dynamics

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