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.
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 (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 }

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.