Surface Tension

One of the earliest physics models added to FLOW-3D was for surface tension. This model has been widely used over the years for many different kinds of applications, e.g., inkjets, liquid fuel behavior in zero-gravity environments and a variety of MEMS (micro-electronic-mechanical-system) devices. Many user requests for improvements and extensions of the model have been addressed, but these never quite resolved all issues dealing with stability and accuracy.

To get a better grip on surface tension a new model has been developed for code Version 11 of FLOW-3D. This model improves the accuracy of all computed surface tension forces, as well as the accuracy of adhesion forces gripping solid surfaces of arbitrary shape. Additionally, the new model has in its grip capillary pressures in porous materials and tangential surface tension forces arising from non-uniform surface tension.

To grasp the improvements available in the new model consider the simple problem of wetting the wall of a circular contained in zero gravity. Fig. 1a shows the case of a 0.25m diameter cylinder 75% filled with water that has a zero degree contact angle with the cylinder. This is to be contrasted with a similar simulation using the previous surface tension model shown in Fig.1b. The previous model has trouble wetting the entire wall surface because the contact line has gotten stuck on the wall and even with a zero contact angle is unable to pull the water smoothly around the cylinder. In both cases the times are 0.0, 2.5, 5.0 and 10.0s.

Surface tension model in FLOW-3D

Figure 1a. Fluid (red) wetting surface of cylinder with zero contact angle in zero gravity. Simulation using new surface tension model.

Old surface tension model in FLOW-3D

Figure 1b. Fluid (red) wetting surface of cylinder with zero contact angle in zero gravity. Simulation using previous surface tension model.

A similar comparison between the previous and new models is shown in Figs. 2a and 2b, where two initially spherical drops of differing density (indicated by color in the plots) are moving downward toward a solid wall. The times in the plots are 0.0, 0.01, 0.02 and 0.03s.  The drops have a diameter of 0.0017m, different densities, but the same surface tension coefficient of 1.872 newton/m. Even before encountering the wall, the drops simulated with the previous model have developed large surface distortions that eventually cause them to merge.  This does not happen with the new model because more accuracy has been obtained in the computation of surface curvatures over the entire surface of the drops.

Simulating spherical drops with the new surface tension model

Figure 2a. Spherical drops moving toward a plate; simulated with new surface tension model. Color indicates density.


Simulating spherical drops with FLOW-3D's old surface tension model

Figure 2b. Spherical drops moving toward a plate, simulation with previous surface tension model. Color indicates density.

These examples clearly show the improvements that have been made in modeling surface tension by getting a better grasp on the physical problem through adhesion to more accurate numerical approximations.

For more information about this model, download the Flow Science Report on Surface Tension.