Capillary Driven Flows in Weakly 3-Dimensional Polygonal Containers

Weislogel, Mark; Jenson, Ryan; Bolleddula, Daniel

doi:10.2514/6.2007-748

Cited by 10 publications

(3 citation statements)

References 7 publications

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“…Experimental evidence continues to support the broadened application of the de Lazzer et al method for the flow phenomena of practical interest here; see Weislogel & Lichter (1998), Weislogel (2001), and Weislogel et al (2007). The method applied to the m = 1 section is sketched in figure 5(b) with relevant notation, from which the closed-form result is…”

Section: Notation and Known Height Boundary Condition Hmentioning

confidence: 86%

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

Weislogel

Baker²,

Jenson³

2011

J. Fluid Mech.

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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.

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Section: Notation and Known Height Boundary Condition Hmentioning

confidence: 86%

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

Weislogel

Baker²,

Jenson³

2011

J. Fluid Mech.

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“…Such compound flows require further study because the impact of the shifting bulk menisci changes the nature of the boundary condition imposed on the various edge flows. Some recent progress has been reported (Weislogel et al 2007) and there is no reason not to expect that simple bench-marked closed form equations will inevitably predict such 'compound' behavior for use in capillary fluidics systems design.…”

Section: Discussionmentioning

confidence: 98%

“…The constant height location is the z-location around which the interface appears to pivot-an apparent fixed point for the interface where h(0, t) = H. The successful analytical application of this boundary condition to flows of increased geometric complexity hinges on our ability to identify and track its location (e.g. Weislogel 2001; Weislogel and Collicott 2004;Weislogel et al 2007). …”

Section: Introductionmentioning

confidence: 98%

Compound Capillary Flows in Complex Containers: Drop Tower Test Results

Bolleddula

Chen

Semerjian

et al. 2010

Microgravity Sci. Technol.

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Drop towers continue to provide unique capabilities to investigate capillary flow phenomena relevant to terrestrial and space-based capillary fluidics applications. In this study certain 'capillary rise' flows and the value of drop tower experimental investigations are briefly reviewed. A new analytic solution for flows along planar interior edges is presented. A selection of test cell geometries are then discussed where compound capillary flows occur spontaneously and simultaneously over local and global length scales. Sample experimental results are provided. Tertiary experiments on a family of asymmetric geometries that isolate the global component of such flows are then presented along with a qualitative analysis that may be used to either avoid or exploit such flows. The latter may also serve as a design tool with which to assess the impact of inadvertent container asymmetry.

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