### 7.18.4. Surface Tension

#### 7.18.4.1. Background

Surface tension is the force that holds the interface together. If an interface is cut, the magnitude of the surface tension force per unit length is called the surface tension coefficient, . Surface tension has a number of important physical effects, including:

- If the interface is curved, it induces a force normal to the interface. For a droplet at rest, this induces a pressure rise within the droplet of , where is the droplet curvature. The effect of this normal force is to smooth regions of high curvature; it tends to reduce the surface area of droplets.

- When the surface tension coefficient is not constant, the surface tension force has a tangential component that tends to move fluid along the interface toward regions of high surface tension coefficient. This is often called Marangoni convection.

- When the free surface interface touches a wall, the wall may attract the liquid (wetting wall) or repel the liquid (non-wetting wall). In a static situation, the wall contact angle may be measured. This phenomenon, known as wall adhesion, gives rise to effects such as the meniscus and capillary rise in tubes.

For free surface flows, you have the option of including surface tension effects. When it is enabled, a surface tension coefficient must be specified. If the surface tension coefficient is variable, the Marangoni force is automatically included. If the surface tension model is activated, using double precision is often required to avoid roundoff errors in the curvature calculation.

Additional information on the surface tension implementation in ANSYS CFX is available in Surface Tension in the CFX-Solver Theory Guide.

#### 7.18.4.2. Discretization Options

##### 7.18.4.2.1. Volume Fraction Smoothing Type

When evaluating the interface normal vector for the curvature and surface tension force, it is usually beneficial to take the gradient of a smoothed volume fraction field. The volume fraction smoothing method may be optionally set in CFX-Pre. The options are `None`, `Laplacian`, and `Volume-Weighted`. `Volume-Weighted` is the default. `Laplacian` is slightly more accurate, but also slightly more expensive, than `Volume-Weighted`. Occasionally, when the surface tension force is driven only by wall adhesion and there is no interior curvature, it may be beneficial to choose `None`.

##### 7.18.4.2.2. Curvature Under-Relaxation Factor

This is used for underrelaxing the curvature. The default value is 1 (unity), but for flows strongly driven by surface tension, it may be useful to use a smaller value (for example, 0.25).

#### 7.18.4.3. Initial Conditions

When setting initial conditions for surface tension calculations, it may also be beneficial to assign a smeared volume fraction rather than a discontinuous one. The hyperbolic tangent function (available in CEL) is useful for this purpose. For example, the following expressions defined a smeared droplet of radius 0.3 m centered at (x,y) = (0.5 [m], 0.5 [m]):

`rdrop = 0.3 [m]`

`dist = rdrop -sqrt((x - 0.5[m])^2 + (y - 0.5[m]^2)`

`delta = 0.01 [m]`

`drop = 0.5*tanh(dist/delta)+0.5`

These expressions represent:

`rdrop` - droplet radius

`dist` - signed distance to the droplet interface

`delta` - smearing distance

`drop` - the smeared volume fraction field: 1 inside the droplet, 0 outside, and smoothly varying between 0 and 1 over a range of about 3*delta on each side of the interface.

#### 7.18.4.4. Wall Adhesion

To account for wall adhesion, you should specify a contact angle when setting wall boundary conditions. This is the angle the interface makes with the wall through the Primary Fluid that is prescribed on the Fluid Pairs tab of the Domain details view when the Surface Tension Coefficient is set. If the Primary Fluid is a liquid and the secondary fluid is a gas then, for non-wetting walls, the contact angle is greater than 90 degrees, while for wetting walls the contact angle is less than 90 degrees.

Release 18.2 - © ANSYS, Inc. All rights reserved.