Film condensation in porous media

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Film condensation occurs when the temperature of a vertical, impermeable, and wettable wall next to a porous medium saturated with vapor falls below saturation temperature (Fig. 8.29). In addition to gravity-driven downward liquid flow, the liquid also infiltrates the vapor region due to capillary force. The latter will create a two-phase region between the liquid film and the vapor region, where both condensate and vapor are present. It is assumed that the vapor  temperature is equal to the saturation temperature, i.e., there is no superheat in the vapor phase. [[Image:Chapter7 (17).jpg|thumb|400 px|alt=Film condensation in a porous medium. | Figure 8.29 Film condensation in a porous medium. ]]The temperature in the liquid region is below saturation temperature, while the temperature in the two-phase region is at saturation temperature. The discussion in this section is limited to the case where the thickness of the liquid film is much greater than the diameter of the pore size. This is referred to as a thick-film region, and the local volume average is applicable [[#References|(Kaviany, 1995)]]. If the liquid film thickness is less than or comparable to the pore size, the local volume average will no longer be applicable and a direct simulation at the pore level must be performed.
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[[Image:Condensation_in_porous_media.png|thumb|300 px|alt=Film condensation in a porous medium. |Film condensation in a porous medium. ]]
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Film condensation occurs when the temperature of a vertical, impermeable, and wettable wall next to a porous medium saturated with vapor falls below saturation temperature (see figure). In addition to gravity-driven downward liquid flow, the liquid also infiltrates the vapor region due to capillary force. The latter will create a two-phase region between the liquid film and the vapor region, where both condensate and vapor are present. It is assumed that the vapor  temperature is equal to the saturation temperature, i.e., there is no superheat in the vapor phase. The temperature in the liquid region is below saturation temperature, while the temperature in the two-phase region is at saturation temperature. The discussion in this section is limited to the case where the thickness of the liquid film is much greater than the diameter of the pore size. This is referred to as a thick-film region, and the local volume average is applicable [[#References|(Kaviany, 1995)]]. If the liquid film thickness is less than or comparable to the pore size, the local volume average will no longer be applicable and a direct simulation at the pore level must be performed.
The dominant forces in the condensation process are gravitational and capillary forces, and the latter dictates the thickness of the two-phase region, <math>{{\text{ }\!\!\delta\!\!\text{ }}_{\ell v}}</math>. The ratio of gravity and capillary forces is measured by Bond number:  
The dominant forces in the condensation process are gravitational and capillary forces, and the latter dictates the thickness of the two-phase region, <math>{{\text{ }\!\!\delta\!\!\text{ }}_{\ell v}}</math>. The ratio of gravity and capillary forces is measured by Bond number:  
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In the following two subsections, an analysis of gravity-dominated condensation will be discussed first, followed by a discussion of the effect of surface tension on the condensation process.  
In the following two subsections, an analysis of gravity-dominated condensation will be discussed first, followed by a discussion of the effect of surface tension on the condensation process.  
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==Film Condensation on an Inclined Wall==
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==Gravity dominated film-condensation in a porous medium==
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''See Main Article'' [[Film Condensation on an Inclined Wall]] <br>
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When condensation is dominated by gravity, the effect of surface tension is negligible, and consequently, no two-phase region exists. A porous medium saturated with dry vapor at its saturation temperature, T<sub>sat</sub>, is bounded by an inclined impermeable wall with a temperature T<sub>w</sub> (<math>{{T}_{w}}<{{T}_{sat}}</math>). Since the wall temperature is below saturation temperature, film condensation occurs on the inclined wall and the condensate flows downward due to gravity. It is assumed that the condensation is gravity-dominated and, therefore, that the liquid and vapor are separated by a sharp interface, not a two-phase region.
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''See Main Article'' [[Gravity dominated film-condensation in a porous medium]]. <br>
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==Effect of Surface Tension on Condensation in Porous Media==
==Effect of Surface Tension on Condensation in Porous Media==
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''See Main Article'' [[Effect of Surface Tension on Condensation in Porous Media]] <br>
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The analysis in the [[gravity dominated film-condensation in a porous medium]] is valid for <math>\text{Bo}\gg 1</math>. When the condensation is gravity-capillary forces dominated (<math>\text{Bo}\sim 1</math>) or capillary force dominated (<math>\text{Bo}\ll 1</math>), there will be a two-phase region that is saturated by a mixture of liquid and vapor.
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''See Main Article'' [[Effect of surface tension on condensation in porous media]] <br>
==References==
==References==
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Faghri, A., and Zhang, Y., 2006, ''Transport Phenomena in Multiphase Systems'', Elsevier, Burlington, MA

Revision as of 08:35, 26 July 2010

Film condensation in a porous medium.
Film condensation in a porous medium.

Film condensation occurs when the temperature of a vertical, impermeable, and wettable wall next to a porous medium saturated with vapor falls below saturation temperature (see figure). In addition to gravity-driven downward liquid flow, the liquid also infiltrates the vapor region due to capillary force. The latter will create a two-phase region between the liquid film and the vapor region, where both condensate and vapor are present. It is assumed that the vapor temperature is equal to the saturation temperature, i.e., there is no superheat in the vapor phase. The temperature in the liquid region is below saturation temperature, while the temperature in the two-phase region is at saturation temperature. The discussion in this section is limited to the case where the thickness of the liquid film is much greater than the diameter of the pore size. This is referred to as a thick-film region, and the local volume average is applicable (Kaviany, 1995). If the liquid film thickness is less than or comparable to the pore size, the local volume average will no longer be applicable and a direct simulation at the pore level must be performed.

The dominant forces in the condensation process are gravitational and capillary forces, and the latter dictates the thickness of the two-phase region, {{\text{ }\!\!\delta\!\!\text{ }}_{\ell v}}. The ratio of gravity and capillary forces is measured by Bond number:

\text{Bo}=\frac{g({{\rho }_{\ell }}-{{\rho }_{v}})K/\varepsilon }{\sigma }
(1)

where K and ε are, respectively, permeability and porosity. When \text{Bo}\simeq 1, condensation in a porous medium is dominated by both gravitational and capillary force. The condensation is dominated by capillary force when Bo < 1. When gravity dominates, Bond number will be greater than 1, and there will be no two-phase region, in which case the analysis will be significantly simplified.

In the following two subsections, an analysis of gravity-dominated condensation will be discussed first, followed by a discussion of the effect of surface tension on the condensation process.

Gravity dominated film-condensation in a porous medium

When condensation is dominated by gravity, the effect of surface tension is negligible, and consequently, no two-phase region exists. A porous medium saturated with dry vapor at its saturation temperature, Tsat, is bounded by an inclined impermeable wall with a temperature Tw (Tw < Tsat). Since the wall temperature is below saturation temperature, film condensation occurs on the inclined wall and the condensate flows downward due to gravity. It is assumed that the condensation is gravity-dominated and, therefore, that the liquid and vapor are separated by a sharp interface, not a two-phase region.

See Main Article Gravity dominated film-condensation in a porous medium.

Effect of Surface Tension on Condensation in Porous Media

The analysis in the gravity dominated film-condensation in a porous medium is valid for \text{Bo}\gg 1. When the condensation is gravity-capillary forces dominated (Bo˜1) or capillary force dominated (\text{Bo}\ll 1), there will be a two-phase region that is saturated by a mixture of liquid and vapor.

See Main Article Effect of surface tension on condensation in porous media

References

Faghri, A., and Zhang, Y., 2006, Transport Phenomena in Multiphase Systems, Elsevier, Burlington, MA