Modeling Surface Tension

Consider the wetting and spreading phenomena of droplets impacting on a substrate. Inertial, viscous, capillary, and contact-line forces govern the contact line (triple line) dynamics at the free surface between two fluids and a solid ([607]). The surface tension coefficient $\sigma$ is defined as the amount of work necessary to create a unit area of free surface.

The contact angle $\theta$ describes the influence of a solid wall on the free surface. The magnitude of the contact angle for a phase interaction depends on the pair of fluids and the solid that are in contact and on the temperature. The contact angle is measured at the triple line, which is the line where the wall and both fluid phases are in mutual contact. It is assumed that the specified value is with respect to the primary phase of the phase interaction. Values of contact angle smaller than $90°$ mean that the phase is wetting the wall, as illustrated in part (a) of the following figure:

In order to comply with the usual convention on contact angle values, as shown above, define a liquid phase as the primary phase of the interaction.

By default, the Surface Tension Force model uses a static contact angle to calculate the free surface curvature in the vicinity of the triple line. However, the use of a static contact angle does not satisfy the dynamics of many flows and causes unrealistic free surface shapes in many applications. For these applications, you can define a dynamic contact angle.

In practice, the contact angle is considered a function of the triple line velocity. The triple line is the line where the wall and both fluid phases are in mutual contact. Some simple models are based on a step function that uses a single advancing and receding angle, while other models use a smoothed step function. These models work well for inertia-dominated flows because the dynamic contact angle does not depend strongly on the velocity.

Other models, such as the Kistler correlation, work well for capillary-dominated flows. Capillarity is a phenomenon in which the free surface is observed to be elevated or depressed when it comes into contact with a solid wall. Capillarity can be explained by considering the effects of adhesion (the attractive or repulsive force between the fluid and solid wall molecules) and cohesion (the attractive force between the fluid molecules). These models attempt to account for the dependency of the advancing and receding contact angles on the triple line velocity. Both static advancing and receding contact angles have been found to increase or decrease further during spreading and recession, respectively. In most cases, the static advancing and receding contact angles can be determined from the contact angle hysteresis: the minimum and maximum contact angle that is measured for a stationary triple line.

Consider the following recommendations and limitations when you model surface tension:

• Calculation of the free surface curvature is sensitive to mesh quality. Therefore, to get good results even on coarse grids, the use of Cartesian meshes is recommended.

• The Kistler correlation is suitable for both inertia- and capillary-dominated flows. However, you cannot use a Capillary number-driven dynamic contact angle method at slip walls. The triple line velocity is always evaluated to be 0 at slip walls, and therefore there is no variation in the contact angle.

• In some scenarios, oscillations can develop in the interfacial flow field for capillary-dominated flows. These oscillations can be damped or eliminated if a blending function is used in the dynamic contact angle specification. The Blended Kistler method uses a blending function, see Eqn. (2618). In addition, you are recommended to activate the Interface Momentum Dissipation model in combination with a dynamic contact angle method in order to remove the parasitic currents at the interface. Specify a value of Interface Artificial Viscosity large enough to reduce parasitic currents, but keep the value as small as possible to avoid affecting the simulation results.

• If the interface shows much smearing, and other treatments (such as reducing the time-step size) do not improve the results, you can adjust the Sharpening Factor setting in the Volume of Fluid (VOF) model. Increasing this value from its default of 0 reduces the numerical diffusion at the interface. For surface-tension dominated flows, setting a higher value can improve the resolution of the interface. Raising the sharpening factor increases the runtime necessary to preserve volume conservation.

To model surface tension: