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

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.

[1]  Werner Lehnert,et al.  Investigation of water droplet kinetics and optimization of channel geometry for PEM fuel cell cathodes , 2009 .

[2]  S. Watson,et al.  Fluid flow and heat transfer in a dual-wet micro heat pipe , 2007, Journal of Fluid Mechanics.

[3]  Uwe Rosendahl,et al.  Choked flows in open capillary channels: theory, experiment and computations , 2004, Journal of Fluid Mechanics.

[4]  Yongkang Chen,et al.  A better nondimensionalization scheme for slender laminar flows: The Laplacian operator scaling method , 2008 .

[5]  Balram Suman,et al.  An analytical model for fluid flow and heat transfer in a micro-heat pipe of polygonal shape , 2005 .

[6]  C. Radke,et al.  Kinetics of liquid/liquid capillary rise: I. Experimental observations , 1986 .

[7]  Mark M. Weislogel Capillary Flow in Containers of Polygonal Section , 2001 .

[8]  S. Lichter,et al.  Capillary flow in an interior corner , 1998, Journal of Fluid Mechanics.

[9]  Mark M. Weislogel,et al.  Measurement of critical contact angle in a microgravity space experiment , 2000 .

[10]  Ioannis Chatzis,et al.  The Imbibition and Flow of a Wetting Liquid along the Corners of a Square Capillary Tube , 1995 .

[11]  G. Gerard,et al.  Optimum structural design concepts for aerospace vehicles. , 1966 .

[12]  P. Concus,et al.  Correction for Concus and Finn, On the behavior of a capillary surface in a wedge , 1969, Proceedings of the National Academy of Sciences.

[13]  M. Weislogel,et al.  Capillary driven flow along interior corners formed by planar walls of varying wettability , 2005 .

[15]  Louis A. Romero,et al.  Flow in an open channel capillary , 1996, Journal of Fluid Mechanics.

[16]  S. Herminghaus,et al.  Dewetting of liquid filaments in wedge-shaped grooves. , 2007, Langmuir : the ACS journal of surfaces and colloids.

[17]  Robert Finn,et al.  Singular solutions of the capillary problem , 1999 .

[18]  Yongkang Chen,et al.  The Capillary Flow Experiments Aboard the International Space Station: Increments 9-15 , 2009 .

[19]  Anthony R. Kovscek,et al.  Gas bubble snap-off under pressure-driven flow in constricted noncircular capillaries , 1996 .

[20]  Mark M. Weislogel,et al.  Capillary Driven Flows in Weakly 3 -Dimensional Polygonal Containers , 2007 .

[21]  Yongkang Chen,et al.  More Handheld Fluid Interface Experiments for the International Space Station (CFE-2) , 2009 .

[22]  Mark M. Weislogel,et al.  Capillary Rewetting of Vaned Containers: Spacecraft Tank Rewetting Following Thrust Resettling , 2004 .

[23]  Mark M. Weislogel,et al.  Capillary-driven flows along rounded interior corners , 2005, Journal of Fluid Mechanics.

[24]  Mark M. Weislogel,et al.  Some analytical tools for fluids management in space: Isothermal capillary flows along interior corners , 2003 .

[25]  Portonovo S. Ayyaswamy,et al.  Capillary Flow in Triangular Grooves , 1974 .

[26]  Mark M. Weislogel,et al.  A Novel Device Addressing Design Challenges for Passive Fluid Phase Separations Aboard Spacecraft , 2009 .

[27]  P. Griffith,et al.  THE ROLE OF SURFACE CONDITIONS IN NUCLEATE BOILING. Technical Report No. 14 , 1958 .

[28]  D. Quéré,et al.  Rise of liquids and bubbles in angular capillary tubes. , 2002, Journal of colloid and interface science.

[29]  Clayton J. Radke,et al.  Laminar flow of a wetting liquid along the corners of a predominantly gas-occupied noncircular pore , 1988 .

[30]  David J. Chato,et al.  Cryogenic Fluid Transfer for Exploration , 2008 .

[31]  Christophe Clanet,et al.  A universal law for capillary rise in corners , 2011, Journal of Fluid Mechanics.

[32]  H. Wong,et al.  Theory of slope-dependent disjoining pressure with application to Lennard-Jones liquid films. , 2005, Journal of colloid and interface science.

[33]  Mark M. Weislogel,et al.  Computing Existence and Stability of Capillary Surfaces Using Surface Evolver , 2004 .

[34]  G. P. Peterson,et al.  A review and comparative study of the investigations on micro heat pipes , 2007 .

[35]  S. Bankoff Ebullition From Solid Surfaces in the Absence of a Pre-Existing Gaseous Phase , 1957, Journal of Fluids Engineering.

[36]  Mark M. Weislogel,et al.  A Fast Numerical Procedure for Steady Capillary Flow in Open Capillary Channels , 2008 .

[37]  E. Ramé,et al.  Gravity effects on capillary flows in sharp corners , 2009 .

[38]  David J. Chato,et al.  Vented Tank Resupply Experiment: Flight Test Results , 2006 .

[39]  Kinetics of liquid/liquid capillary rise , 1986 .

[40]  Mark M. Weislogel,et al.  A fast numerical procedure for steady capillary flow in open channels , 2008 .