The modeling of surface tension forces is computationally difficult because it requires the evaluation of surface curvatures, i.e., second derivatives of the surface location. This is particularly true in ** FLOW-3D **since it uses a rectangular grid that does not conform to surface shapes. Although this simple grid structure makes it more difficult to evaluate surface slopes and curvatures, it is this feature that also gives the strength needed to simulate coalescence and breakup of fluids.

A new update to the surface tension model introduced in ** FLOW-3D**, Version 11, greatly improves the accuracy of the model with regard to the computation of curvatures as well as improving the application of wall adhesion forces. Additionally, the new model fully integrates thermocapillary forces, i.e., tangential surface forces, into the basic model without the need for a separate model routine.

Briefly, the evaluation of surface slope and curvature in ** FLOW-3D** is done by first determining for each computational cell that contains a surface the coordinate direction that is closest to the outward normal vector to the surface. Following this, cell columns containing 3 cells that are associated with the surface cell and its four principal neighbors (i.e., those located perpendicular to the principal surface normal) have their fluid fraction values summed up in the direction of the normal. This effectively gives a discrete representation of the surface heights in five columns surrounding the surface cell, which can then be used to compute slopes and curvatures at the surface. These heights are also used to compute the surface normal and area for the cell.

To compute the forces of adhesion between a fluid surface and a solid it is necessary to determine the location and extent of the contact line where the fluid and solid surfaces intersect. In the newly updated model this determination is done separately at each side of a surface cell, i.e., those sides whose normals are perpendicular to the principal surface-normal direction. Associated with each element side, the orientation of the solid surface and its specified contact angle are evaluated and used to compute the proper adhesion force components. These forces replace the fluid-to-fluid values that may have been computed in the basic surface tension force computation, or at least those forces for the portion of the side area that is blocked by the solid.

### CITATION

C.W. Hirt, “Modeling Surface Tension,” Flow Science Report 01-14, January 2014, Copyright Flow Science