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Quasi-steady capillarity-driven flows in slender containers with interior edges

Published online by Cambridge University Press:  23 September 2011

Mark M. Weislogel ,
J. Alex Baker  and
Ryan M. Jenson
Mark M. Weislogel*
Affiliation:
Department of Mechanical and Materials Engineering, Portland State University, PO Box 751, Portland, OR 97207, USA
J. Alex Baker
Affiliation:
Department of Mechanical and Materials Engineering, Portland State University, PO Box 751, Portland, OR 97207, USA
Ryan M. Jenson
Affiliation:
Department of Mechanical and Materials Engineering, Portland State University, PO Box 751, Portland, OR 97207, USA
*
†Email address for correspondence: [email protected]
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Abstract

In the absence of significant body forces the passive manipulation of fluid interfacial flows is naturally achieved by control of the specific geometry and wetting properties of the system. Numerous ‘microfluidic’ systems on Earth and ‘macrofluidic’ systems aboard spacecraft routinely exploit such methods and the term ‘capillary fluidics’ is used to describe both length-scale limits. In this work a collection of analytic solutions is offered for passive and weakly forced flows where a bulk capillary liquid is slowly drained or supplied by a faster capillary flow along at least one interior edge of the container. The solutions are enabled by an assumed known pressure (or known height) dynamical boundary condition. Following a series of assumptions this boundary condition can be in part determined a priori from the container dimensions and further quantitative experimental evidence, but not proof, is provided in support of its expanded use herein. In general, a small parameter arises in the scaling of the problems permitting a decoupling of the edge flow from the global bulk meniscus flow. The quasi-steady asymptotic system of equations that results may then be easily solved in closed form for a useful variety of geometries including uniform and tapered sections possessing at least one critically wetted interior edge. Draining, filling, bubble displacement and other imbibing flows are studied. Cursory terrestrial and drop tower experiments agree well with the solutions. The solutions are valued for the facility they provide in computing designs for selected capillary fluidics problems by way of passive transport rates and meniscus displacement. Because geometric permutations of any given design are myriad, such analytic tools are capable of efficiently identifying and comparing critical design criteria (i.e. shape and size) and the impact of various wetting conditions resulting from the fluid properties and surface conditions. Sample optimizations are performed to demonstrate the utility of the method.

JFM classification

Interfacial Flows (free surface): Capillary flows Low-Reynolds-number flows: Lubrication theory Micro-/Nano-fluid dynamics: Microfluidics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 685 , 25 October 2011 , pp. 271 - 305
Copyright
Copyright © Cambridge University Press 2011

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