Shearing of a stratified layer of amphiphilic (bio)molecules

Davoust, Laurent; Huang, Yong-Heng; Chang, Shuo-Hung

doi:10.1016/j.susc.2009.07.019

Cited by 7 publications

(3 citation statements)

References 16 publications

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“…Due to corner singularities for velocity at the edges of the rotating disk, related to the nonphysical jump in the Dirichlet boundary conditions for the velocity, the series solution needs to be approximated with a truncation number near the floor much larger than that required for finding the velocity along the liquid surface [21]. Corner singularities stand as a topic extensively addressed by many authors in the literature devoted to numerical issues (see, e.g., Refs.…”

Section: A Azimuthal Flow Fieldmentioning

confidence: 99%

“…Most existing studies on annular channel flows have been performed numerically or experimentally [13,[15][16][17], quite often with the aim of investigating the impact of physicochemical contamination along the upper liquid surface. To our knowledge, except for the recent analytical modeling performed by Shtern [18,19] for an annular cavity considered as semi-infinite along the vertical direction, all existing analytical studies devoted to this configuration only focus on the azimuthal flow either when the liquid surface is free of contamination [20] or when it is contaminated [21,22],…”

Section: Introductionmentioning

confidence: 99%

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Low-to-moderate Reynolds number swirling flow in an annular channel with a rotating end wall

2015

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This paper presents a new method for solving analytically the axisymmetric swirling flow generated in a finite annular channel from a rotating end wall, with no-slip boundary conditions along stationary side walls and a slip condition along the free surface opposite the rotating floor. In this case, the end-driven swirling flow can be described from the coupling between an azimuthal shear flow and a two-dimensional meridional flow driven by the centrifugal force along the rotating floor. A regular asymptotic expansion based on a small but finite Reynolds number is used to calculate centrifugation-induced first-order correction to the azimuthal Stokes flow obtained as the solution at leading order. For solving the first-order problem, the use of an integral boundary condition for the vorticity is found to be a convenient way to attribute boundary conditions in excess for the stream function to the vorticity. The annular geometry is characterized by both vertical and horizontal aspect ratios, whose respective influences on flow patterns are investigated. The vertical aspect ratio is found to involve nontrivial changes in flow patterns essentially due to the role of corner eddies located on the left and right sides of the rotating floor. The present analytical method can be ultimately extended to cylindrical geometries, irrespective of the surface opposite the rotating floor: a wall or a free surface. It can also serve as an analytical tool for monitoring confined rotating flows in applications related to surface viscosimetry or crystal growth from the melt.

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Section: A Azimuthal Flow Fieldmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Low-to-moderate Reynolds number swirling flow in an annular channel with a rotating end wall

2015

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“…There are numerous interest in this configuration, which is inspired by the deep channel viscometer [12][13][14][15]. First, the electroconductive rotating fluid subjected to an outer magnetic field constitutes a MHD liquid/gas stratified flow, which is a basic study case in view of the description of different MHD two-phase flow regimes.…”

Section: Introductionmentioning

confidence: 99%

Surface viscometry in a uniform magnetic field

Delacroix

Davoust

2016

Mechanics & Industry

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This paper addresses an original numerical coupling between surface mechanics of a gradually oxidizing liquid metal surface, and a supporting annular MHD flow, in the general layout of the classical annular viscometer, originally developed by Mannheimer et al. [J. Colloid Interface Sci. 32 (1970) 195-211]. A purely hydrodynamic interplay between a main azimuthal flow (induced by a rotating floor) and a secondary overturning flow generated by centrifugation is found to be strongly affected by both surface viscous shear and surface viscous dilatation. When centrifugation competes with electromagnetic effects, advection of the main flow by the secondary flow is proved to affect significantly the core MHD flow, leading to original MHD flow patterns. The latter phenomenology reveals to be relevant to characterise the surface viscosities of a gradually oxidising liquid metal surface.

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Electrical activity of the Hartmann layers relative to surface viscous shearing in an annular magnetohydrodynamic flow

Delacroix

Davoust

2014

Physics of Fluids

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As a first step towards two-phase magnetohydrodynamics (MHD), this paper addresses an original analytical coupling between surface rheology, e.g., a gradually oxidizing liquid metal surface, ruled by the Boussinesq number Bo, and a supporting annular MHD flow, ruled by the Hartmann number Ha, in the general layout of a classical annular deep-channel viscometer, as developed by Mannheimer and Schechter [J. Colloid Interface Sci. 32, 195–211 (1970)]. Using a matched asymptotic expansion based on the small parameter 1/Ha, we can express the surface velocity as a coupling variable in the jump momentum balance at the liquid surface. By solving the latter through the determination of the Green's function, the whole flow can be analytically calculated. A modified Boussinesq number, \documentclass[12pt]{minimal}\begin{document}$\tilde{B_o}$\end{document}Bõ, is produced as a new non-dimensional parameter that provides the balance between surface viscous shearing and the Lorentz force. It is shown that the \documentclass[12pt]{minimal}\begin{document}$\tilde{B_o}$\end{document}Bõ number drives the electrical activation of the Hartmann layers, heavily modifying the MHD flow topology and leading to the emergence of the Lorentz force, for which interaction with the flow is not classical. Finally, the evolution laws given in this study allow the determination of scaling laws for an original experimental protocol, which would make it possible to accurately determine the surface shear viscosity of a liquid metal with respect to the quality of the ambient atmosphere.

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Shearing of a stratified layer of amphiphilic (bio)molecules

Cited by 7 publications

References 16 publications

Low-to-moderate Reynolds number swirling flow in an annular channel with a rotating end wall

Low-to-moderate Reynolds number swirling flow in an annular channel with a rotating end wall

Surface viscometry in a uniform magnetic field

Electrical activity of the Hartmann layers relative to surface viscous shearing in an annular magnetohydrodynamic flow

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