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On a Hele--Shaw-Type Domain Evolution with Convected Surface Energy Density

Matthias Günther, Georg Prokert
2005 SIAM Journal on Mathematical Analysis  
Interest is directed to a moving boundary problem with a gradient flow structure which generalizes surface-tension driven Hele-Shaw flow to the case of nonconstant surface tension coefficient taken along  ...  The problem is reformulated as a vector-valued, degenerate parabolic Cauchy problem. To solve this, we prove and apply an abstract result on Galerkin approximations with variable bilinear forms.  ...  Introduction Various experimental studies investigate the influence of spatial variations of the surface energy density (corresponding to the surface tension coefficient γ) on surface tension driven Hele-Shaw  ... 
doi:10.1137/s0036141004444846 fatcat:p3he53jtfrcvnnncbiqkuy2es4

On a Hele–Shaw Type Domain Evolution with Convected Surface Energy Density: The Third‐Order Problem

Matthias Günther, Georg Prokert
2006 SIAM Journal on Mathematical Analysis  
We investigate a moving boundary problem with a gradient flow structure which generalizes Hele-Shaw flow driven solely by surface tension to the case of nonconstant surface tension coefficient taken along  ...  The resulting evolution problem is first order in time, contains a third-order nonlinear pseudodifferential operator and is degenerate parabolic.  ...  It is the aim of the present paper to consider the generalization of the well-investigated Hele-Shaw flow problem to the case of nonconstant surface tension coefficient (or surface energy density).  ... 
doi:10.1137/050626995 fatcat:kmy65ot7kvepjakc5yywu6vblq

Adaptive Micromixer Based on the Solutocapillary Marangoni Effect in a Continuous-Flow Microreactor

Dmitry Bratsun, Konstantin Kostarev, Alexey Mizev, Sebastian Aland, Marcel Mokbel, Karin Schwarzenberger, Kerstin Eckert
2018 Micromachines  
We propose a new type of micromixer based on the intensive relaxation oscillations induced by a fundamental effect discovered recently.  ...  Microreactors of this type have a special vessel, in which the convective vortices are organized to mix the reagents to increase the product output.  ...  Due to its higher density, water is filled as the lower layer and paraffin oil with isopropyl alcohol forms the upper layer in the vertically oriented Hele-Shaw cell.  ... 
doi:10.3390/mi9110600 pmid:30453467 pmcid:PMC6266721 fatcat:5lzxopqxe5bsdhs2snjyhiktsa

Page 612 of Mathematical Reviews Vol. , Issue 97A [page]

1997 Mathematical Reviews  
Summary: “Marangoni-Bénard convection is the process by which oscillatory waves are generated on an interface due to a change in surface tension.  ...  The focus is on local behavior in three settings: (1) Hele-Shaw flows in which the interface is initially nonanalytic; (2) power-law Hele- Shaw flows in which the interface contains a corner; and (3) Stefan  ... 

The formation and evolution of layered structures in porous media: effects of porosity and mechanical dispersion

Stan Schoofs, Ron A. Trompert, Ulrich Hansen
2000 Physics of the Earth and Planetary Interiors  
Growth of a convective layer through convective entrainment, the formation of a stable density interface on top of the layer and destabilization of the next layer are intimately Ž . Ž . linked.  ...  This force balance also indicates whether a density interface keeps intact, migrates upwards or breaks down during the further evolution of the layered sequence.  ...  Another specific feature of low-porosity flow is that fluid exchange occurs on small lateral scales, compared with Hele-Shaw flow.  ... 
doi:10.1016/s0031-9201(99)00148-x fatcat:n7yel5fafrhghoxlyu2ypb26mq

Numerical Analysis of Density-Driven Reactive Flows in Hele-Shaw Cell Geometry

S. Bekkouche, M. Kadja
2020 Zenodo  
which is called an Hele-Shaw cell, vertically oriented, with an expected neutralization reaction between an acid and a base in the lower layer, under the action of gravity, is studied.  ...  Attention is given on the general behavior of the complete temporal pattern evolution (velocity, temperature, and concentration profiles) and the identification of the exothermic reaction's role in giving  ...  MATHEMATICAL FORMULATION AND COMPUTATION PROCEDURE A. Physical Domain Our study is based on the experimental work of [10] in a Hele-Shaw cell.  ... 
doi:10.5281/zenodo.3748334 fatcat:tngb6pda5vd2leicrh5zm4rfay

Plume dynamics in quasi-2D turbulent convection

C. Bizon, J. Werne, A. A. Predtechensky, K. Julien, W. D. McCormick, J. B. Swift, Harry L. Swinney
1997 Chaos  
We have studied turbulent convection in a vertical thin ͑Hele-Shaw͒ cell at very high Rayleigh numbers ͑up to 7ϫ10 4 times the value for convective onset͒ through experiment, simulation, and analysis.  ...  We construct scaling arguments for the average momentum and buoyant scalar fluxes based on an analysis of the plume motion and of the boundary layers at the top and bottom surfaces of the convection cell  ...  convection, but not for Hele-Shaw convection.  ... 
doi:10.1063/1.166243 pmid:12779641 fatcat:bcktyopv3ffbpolajantscvp4u

Page 7872 of Mathematical Reviews Vol. , Issue 2004j [page]

2004 Mathematical Reviews  
Summary: “We consider two-dimensional Hele-Shaw corner flows without effect of the surface tension and with an interface extend- ing to the infinity along one of the walls.  ...  To prove this, the evolution problem is reformulated in a fixed domain by means of the Hanzawa transformation (as in the case of the Stefan problem).  ... 

Page 5139 of Mathematical Reviews Vol. , Issue 93i [page]

1993 Mathematical Reviews  
in Hele-Shaw cells.  ...  Fluids A 4 (1992), no. 12, 2641-2650. This paper concerns a theoretical treatment of thermal growth of an ascending plume in a Hele-Shaw cell.  ... 

Effect of solid–liquid density change on dendrite tip velocity and shape selection

Y. Sun, C. Beckermann
2009 Journal of Crystal Growth  
The dendrite is assumed to grow two-dimensionally inside a Hele-Shaw cell.  ...  The predicted dependence of the dendrite tip growth P eclet number on the relative density change is compared with an available analytical solution and good agreement is obtained.  ...  The dendritic growth is assumed to be two-dimensional and inside of a Hele-Shaw cell.  ... 
doi:10.1016/j.jcrysgro.2009.07.031 fatcat:ve3j3pkfybcsvnvpwgoevjeinq

From the Hele-Shaw Experiment to Integrable Systems: A Historical Overview

Alexander Vasil'ev
2008 Complex Analysis and Operator Theory  
This paper is a historical overview of the development of the topic now commonly known as Laplacian Growth, from the original Hele-Shaw experiment to the modern treatment based on integrable systems.  ...  A trivial circular solution on the plane becomes an evolution of highly non-trivial Hele-Shaw disks on a surface. Hele-Shaw flows on curved surfaces were discussed also in [106] .  ...  In the Hele-Shaw context it means sweeping the Dirac measure out in evolution with the prescribed density function (see, [30; 33] ).  ... 
doi:10.1007/s11785-008-0104-8 fatcat:4rf3px3gszf75kq2mz35al22ly

Solutal convection in porous media: Comparison between boundary conditions of constant concentration and constant flux

Mohammad Amin Amooie, Mohamad Reza Soltanian, Joachim Moortgat
2018 Physical review. E  
The latter model is found to involve a nonlinear evolution of CO2 composition and associated aqueous-phase density, which depend on the formation permeability.  ...  Dissolution is associated with slow diffusion of free-phase CO2 into the underlying aqueous phase followed by density-driven convective mixing of CO2 throughout the water-saturated layer.  ...  Department of Energy's (DOE) Office of Fossil Energy funding to Oak Ridge National Laboratory (ORNL) under project  ... 
doi:10.1103/physreve.98.033118 fatcat:jqwjhci5tjh7lcdn6fpbjafd4e

Vigorous convection in porous media

D. R. Hewitt
2020 Proceedings of the Royal Society A  
The problem of convection in a fluid-saturated porous medium is reviewed with a focus on 'vigorous' convective flow, when the driving buoyancy forces are large relative to any dissipative forces in the  ...  detailed examination of convective dynamics and fluxes; the latter involves convection from one boundary only, which evolves in time through a series of regimes.  ...  I am grateful to three anonymous referees for their constructive comments on an earlier draft of this review, and particularly for providing them in the midst of the troubled times of the COVID-19 global  ... 
doi:10.1098/rspa.2020.0111 pmid:32821241 pmcid:PMC7426043 fatcat:tbfyosirtzatjpzrdp23yipow4

Spatiotemporal behavior of convective Turing patterns in porous media

Matthew Marlow, Yuji Sasaki, Desiderio A. Vasquez
1997 Journal of Chemical Physics  
In larger domains, we find that convection leads to an oscillatory state which becomes steady for large density gradients.  ...  We investigate the effects of convection on Turing patterns in porous media. We show that convectionless patterns can only exist confined to small domains.  ...  ACKNOWLEDGMENTS The authors thank Joseph Wilder for many discussions and for a critical reading of the manuscript. This research was supported by an award from Research Corporation.  ... 
doi:10.1063/1.474883 fatcat:zpry3bbctvguberyinn5qqyzsu

Removing the stiffness from interfacial flows with surface tension

Thomas Y. Hou, John S. Lowengrub, Michael J. Shelley
1994 Journal of Computational Physics  
A second computation shows the formation of a very ramified interface through the interaction of surface tension with an unstable density stratification.  ...  Here they are applied to computing with high resolution the motion of interfaces in Hele-Shaw flows and the motion of free surfaces in inviscid flows governed by the Euler equations.  ...  The first of these is the motion of Hele-Shaw interfaces, which evolve by a competition of surface tension and unstable density stratification.  ... 
doi:10.1006/jcph.1994.1170 fatcat:vso3bx7hovep5dlyhlqnc3uqre
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