Surface Tension

At the interface between a fluid film and the gas phase, surface tension is caused by the greater attraction of fluid molecules to each other than to the gas molecules. The net effect is an inward force at the interface that causes the fluid film to behave as if its surface were covered with a stretched elastic membrane: that is, the surface is under tension. This tension is expressed using the experimentally determined surface tension coefficient $\sigma$ .

Following [593], the surface tension can be written in terms of its normal and tangential components as:

where $p_{\sigma }$ is the capillary pressure and ${\tau }_{\sigma }$ is the contact line force. For surfaces with slight curvature, the capillary pressure can be expressed as [592]:

where:

• $\sigma$ is the surface tension coefficient.
• ${\nabla }_s^2{h}_f$ approximates the curvature of the liquid surface with $h_f$ being the fluid film thickness.
• $a$ is a non-dimensional scale factor.

The contact line force can be expressed as:

where:

• $\theta$ describes the contact angle as a fundamental parameter of the wetting behavior of the film.
• $w$ is defined as 1 wherever $h_f>h_{f,\min }$ (a user-specified minimum value) and 0 elsewhere.
• $b$ is an empirical parameter that is used to calibrate the model with respect to experimental results.

Eqn. (2729) contributes to the film momentum equation Eqn. (2722).