Wicking flow in irregular capillaries

Staples, Thomas L.; Shaffer, Donna G

doi:10.1016/s0927-7757(01)01138-4

Cited by 66 publications

(62 citation statements)

References 9 publications

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“…Previously, a similar expression for the 'effective' radius in a non-uniform capillary under wetting conditions has been reported 19 and good agreement has been found for radii ratio (r max /r min ) up to 10:1. Although such an expression gives values matching the experimental results, they are physically unsound as the area ratio term is neglected.…”

Section: Origin Of 'Effective' Dimension Of Non-uniform Capillarysupporting

confidence: 65%

“…An incompressible, laminar flow is assumed. 6,16,17,19 A simple extension of Hagen-Poiseuille's law for steady-state flow is adopted for the present geometry. Equations describing the velocity of the meniscus as it rises in the capillary are derived.…”

Section: Modeling Fluid Flow In Model Porous Mediamentioning

confidence: 99%

“…Based on the two-segment repeating unit, Einset 6 explained infiltration rates of silicon into porous carbon. Sinusoidal capillary 18,19 models with converging-diverging sections have been developed as more realistic representation of flow paths in porous bodies. The effect of multidimensional flow in porous media has been addressed by incorporating a tortuosity factor of 3 (for random network structure comprised of one-dimensional (1D) non-uniform capillaries) and network theory.…”

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confidence: 99%

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Flow Kinetics in Porous Ceramics: Understanding with Non‐Uniform Capillary Models

Patro

Bhattacharyya

Jayaram

2007

Journal of the American Ceramic Society

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The present work describes the development of a two-parameter non-uniform capillary model to describe kinetics of flow in porous solids with complex tortuous varying paths. Experimentally, the rate of fluid flow in such a non-uniform capillary is found to be orders of magnitude slower compared with a corresponding average uniform capillary. This slow rate is explained in terms of an extremely small 'effective' hydrodynamic radius. The origin of such an 'unphysical' radius is rationalized based on geometrical considerations and effective driving forces for flow through a stepped capillary. Infiltration rate parameters are derived from the geometry of the porous medium for both wetting and non-wetting conditions.

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Section: Origin Of 'Effective' Dimension Of Non-uniform Capillarysupporting

confidence: 65%

Section: Modeling Fluid Flow In Model Porous Mediamentioning

confidence: 99%

mentioning

confidence: 99%

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Flow Kinetics in Porous Ceramics: Understanding with Non‐Uniform Capillary Models

Patro

Bhattacharyya

Jayaram

2007

Journal of the American Ceramic Society

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“…Yang et al, 2011) and nanofluidic capillaries widths of a few tens of nm (Han et al, 2006) or with depths as small as 6 nm (Oh et al, 2009). Whilst non-constant channel cross sections have been a focus of study experimentally and theoretically (Legait, 1983;Staples andShaffer, 2002, Reysatt et al, 2008;Liou et al, 2009), increased solid-liquid contact area, and hence increased capillary pull can be achieved using a range of in-channel structures. In a series of studies, Bico and co-workers studied imbibition using hemi-wicking, which amplifies the capillary pull using wall roughness (Bico 2000Bico and Quéré, 2003;Ishino et al, 2007); ideas recently applied to rough Cu 6 Sn 5 /Cu intermetallic surfaces (Liu et al, 2011).…”

Section: Introductionmentioning

confidence: 99%

Wetting considerations in capillary rise and imbibition in closed square tubes and open rectangular cross-section channels

Ouali

McHale

Javed

et al. 2013

Microfluid Nanofluid

149

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The spontaneous capillary-driven filling of microchannels is important for a wide range of applications. These channels are often rectangular in cross-section, can be closed or open, and horizontal or vertically orientated. In this work, we develop the theory for capillary imbibition and rise in channels of rectangular cross-section, taking into account rigidified and non-rigidified boundary conditions for the liquid-air interfaces and the effects of surface topography assuming Wenzel or Cassie-Baxter states. We provide simple interpolation formulae for the viscous friction associated with flow through rectangular cross-section channels as a function of aspect ratio. We derive a dimensionless cross-over time, T c , below which the exact numerical solution can be approximated by the Bousanquet solution and above which by the visco-gravitational solution. For capillary rise heights significantly below the equilibrium height, this cross-over time is T c  (3X e /2) 2/3 and has an associated dimensionless crossover rise height X c  (3X e /2) 1/3 , where X e =1/G is the dimensionless equilibrium rise height and G is a dimensionless form of the acceleration due to gravity. We also show from wetting considerations that for rectangular channels, fingers of a wetting liquid can be expected to imbibe in advance of the main meniscus along the corners of the channel walls. We test the theory via capillary rise experiments using polydimethylsiloxane oils of viscosity 96.0, 48.0, 19.2 and 4.8 mPa s within a range of closed square tubes and open rectangular cross-section channels with SU-8 walls. We show that the capillary rise heights can be fitted using the exact numerical solution and that these are similar to fits using the analytical visco-gravitational solution. The viscous friction contribution was found to be slightly higher than predicted by theory assuming a non-rigidified liquid-air boundary, but far below that for a rigidified boundary, which was recently reported for imbibition into horizontally mounted open microchannels. In these experiments we also observed fingers of liquid spreading along the internal edges of the channels in advance of the main body of liquid consistent with wetting expectations. We briefly discuss the implications of these observations for the design of microfluidic systems.

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“…The simplest theoretical description of the wetting front motion in dry porous medium under capillary force is based on the Poiseuille-Hagen description of the viscous flow in circular capillary tube of radius r supplemented with gravitational force [17][18][19][20][21][22][23]. Starting with those simplistic assumptions, forming the basis of the Washburn-Bosanquet approach [17][18][19], it can be shown that the time evolution of the distance l of the meniscus from the liquid supplied end of the vertical capillary can be described by the equation…”

Section: Discussionmentioning

confidence: 99%

Effect of Gravitation on Water Migration in Granular Media

et al. 2008

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The results of the experiments on water migration in unsaturated granular media performed with dynamic neutron radiography technique are presented. It was found that the porosity of the medium did not determine the kinetics of the process in a marked way. The influence of gravity was found to be considerable for media like coarse sand and gravel, consisting of large grains. No effect of gravitation on the water migration in clay beds was observed. The results are discussed in terms of the classical WashburnBosanquet theory of adhesion driven motion of the liquid in a straight circular capillary under gravity. It was found that this theory provides only qualitative description of the water migration within granular media, and the viscous dissipation effects are greatly underestimated.

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Wicking flow in irregular capillaries

Cited by 66 publications

References 9 publications

Flow Kinetics in Porous Ceramics: Understanding with Non‐Uniform Capillary Models

Flow Kinetics in Porous Ceramics: Understanding with Non‐Uniform Capillary Models

Wetting considerations in capillary rise and imbibition in closed square tubes and open rectangular cross-section channels

Effect of Gravitation on Water Migration in Granular Media

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