Two-Fluid Marangoni–Bénard Convection with a Deformable Interface

Tavener, Simon; Cliffe, K. A.

doi:10.1006/jcph.2002.7167

Cited by 17 publications

(7 citation statements)

References 28 publications

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“…The relative size of these two effects depended on the fluid layer depth, with thermocapillary forces dominating in sufficiently thin layers [24].…”

Section: Formation Mechanism Analysis Of Micro-structured Surfacementioning

confidence: 44%

Fabrication of a micro-structured surface based on interfacial convection for drag reduction

et al. 2011

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Based on interfacial convection in the presence of solvent evaporation, a novel method for the fabrication of a micro-structured surface is proposed to facilitate drag reduction. A mixture was coated on a substrate through a specially developed spray-painting system. Micron scale pits formed spontaneously in the coated surface because of interfacial convection and deformation driven by the gradient of the interfacial tension. Experimental results indicated that particles in the mixture played a crucial role in pit formation, and with a suitable selection of particle size and dosage, the characteristic parameters of the pitting could be controlled. The drag reduction experiments were first performed in a water tunnel, and the results showed that the micro-structured surface had a remarkable drag reduction performance over a great range of flow speeds. micro-structured surface, particle, pit, interfacial convection, drag reduction Citation:Dou Z L, Wang J D, Yu F, et al. Fabrication of a micro-structured surface based on interfacial convection for drag reduction.

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“…The relative size of these two effects depended on the fluid layer depth, with thermocapillary forces dominating in sufficiently thin layers [24].…”

Section: Formation Mechanism Analysis Of Micro-structured Surfacementioning

confidence: 44%

Fabrication of a micro-structured surface based on interfacial convection for drag reduction

et al. 2011

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“…Zhang and Alexander [8] have addressed the simpler computational problem of flows with curved deformable surfaces in liquid-bridge related problems. Cliffe and Tavener [9] employed an orthogonal mapping technique to solve the location of the deformable interface. However, to avoid the complex issues surrounding moving contact lines and time-dependent interfaces, they limited their studies to steady solutions.…”

Section: Introductionmentioning

confidence: 49%

Application of the lattice Boltzmann method to two-phase Rayleigh–Benard convection with a deformable interface

Chang

Alexander

2006

Journal of Computational Physics

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“…Zeren & Reynolds (1972) presented a linear stability analysis for the analogous thermocapillary problem, which also included the effect of buoyancy, but which assumed that the deformation of the interface was negligible. Interfacial deformation has been accounted for in more recent work by Tavener & Cliffe (2002) using a finite-element method. In this work, three distinct cases were studied, and we summarize these below.…”

Section: Conclusion and Further Workmentioning

confidence: 99%

Incipient mixing by Marangoni effects in slow viscous flow of two immiscible fluid layers

Rickett¹,

Penfold²,

Blyth³

et al. 2015

IMA J Appl Math

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Ignoring inertia, a deformable interface separating two fluid films is considered, subject to non-uniform tension driven by the solutal Marangoni effect in the presence of a scalar concentration field. Detailed description of adsorption kinetics is abrogated by a simple ansatz directly relating interfacial tension and bulk solute concentration. Consequently, the formal mathematical treatment and some of the results share features in common with the Rayleigh-Bénard-Marangoni thermocapillary problem. Normal mode perturbation analysis in the limit of small interface deformations establishes the existence of an unstable response for low wavenumber excitation. In the classification of Cross & Hohenberg (1993, Pattern formation outside of equilibrium. Rev. Mod. Phys., 65, 851-1112), both type I and type II behaviour are observed. By considering the zero wavenumber situation exactly, it is proved that all eigenvalues are purely imaginary with non-positive imaginary part; hence, a type III instability is not possible. For characteristic timescales of mass diffusion much shorter than the relaxation time of interfacial fluctuations (infinite crispation number): the response growth rate is obtained explicitly; only a single excitation mode is available, and a complete stability diagram is constructed in terms of the relevant control parameters. Otherwise, from a quiescent base state, an infinite discrete spectrum of modes is observed that exhibit avoided crossing and switching phenomena, as well as exceptional points where stationary state pairs coalesce into a single oscillatory standing wave pattern. A base state plane Poiseuille flow, driven by an external pressure gradient, generally exaggerates the response: growth rates of instabilities are enhanced, and stable decay is further suppressed with increasing base flow speed, but the inherent symmetry breaking destroys stationary and standing wave response. Results are obtained in this most general situation by implementing a numerical Chebyshev collocation scheme. The model was motivated by hydrodynamic processes supposed to be involved in gastric digestion of humans.

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Two-Fluid Marangoni–Bénard Convection with a Deformable Interface

Cited by 17 publications

References 28 publications

Fabrication of a micro-structured surface based on interfacial convection for drag reduction

Fabrication of a micro-structured surface based on interfacial convection for drag reduction

Application of the lattice Boltzmann method to two-phase Rayleigh–Benard convection with a deformable interface

Incipient mixing by Marangoni effects in slow viscous flow of two immiscible fluid layers

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