Fragmentation (computing)

2014-01-27T07:58:56Z

173.75.247.232: Numerous additions, clarifications, and a few corrections.

In [[fluid statics]], '''capillary pressure''' is the difference in [[pressure]] across the interface between two [[immiscible]] fluids, and thus defined as
:<math>p_c=p_{\text{non-wetting phase}}-p_{\text{wetting phase}}</math>
In oil-water systems, water is typically the [[wetting]] phase, while for gas-oil systems, oil is typically the wetting phase.

The [[Young–Laplace equation]] states that this pressure difference is proportional to the [[interfacial tension]], <math>\gamma</math>, and inversely proportional to the effective radius, <math>r</math>, of the interface, it also depends on the [[contact angle|wetting angle]], <math>\theta</math>, of the liquid on the surface of the capillary.
:<math>p_c=\frac{2\gamma \cos \theta}{r}</math>

The equation for capillary pressure is only valid under capillary equilibrium, which means that there can not be any flowing phases.

== In porous media==
In [[porous media]], capillary pressure is the force necessary to squeeze a hydrocarbon droplet through a pore throat (works against the interfacial tension between oil and water phases) and is higher for smaller pore diameter. The expression for the capillary pressure remains as before, ''i.e.,''
<math>p_c=p_{\text{non-wetting phase}}-p_{\text{wetting phase.}}</math>
However, the quantities <math>p_c</math>, <math>p_{\text{non-wetting phase}}</math> and <math>p_{\text{wetting phase}}</math> are quantities that are obtained by averaging these quantities within the pore space of porous media either statistically or using the volume averaging method.<ref>Jacob Bear: “Dynamics of Fluids in Porous Media,” Dover Publications, 1972.</ref>

The Brooks-Corey correlation<ref>Brooks, R.H. and Corey, A.T.: “Hydraulic properties of porous
media,” Hydraulic paper no. 3, Colorado State University, 1964.</ref> for capillary pressure reads
:<math>p_c = cS_w^{-a}</math>
where <math>c</math> is the entry capillary pressure, <math>1/a</math> is the pore-size distribution index and <math>S_w</math> is the normalized water saturation (see [[Relative permeability]])

==See also==
* [[Capillary action]]
* [[Capillary number]]
* [[Disjoining pressure]]
* [[Leverett J-function]]
* [[Young–Laplace equation]]
* [[Amott test]]
* [[Laplace pressure]]

==References==
* Kim Kinoshita, Electrochemical Oxygen Technology p139, John Wiley & Sons, Inc. 1992.
* [http://www.articleworld.org/index.php/Capillary_pressure Capillary pressure equations]
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[[Category:Fluid dynamics]]

{{fluiddynamics-stub}}

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