Force Balance on a Differential Surface Element

We wish to perform a force balance on a differential surface element like the one shown in figure 2. There are four types of forces on this differential surface element:

1. Surface tension forces - depend on local curvature. It only act normal to the surface.
2. Pressure forces - depend on the flow fields on each side of the surface. Also act normal to the surface.
3. Viscous stress - also depend on the flow fields on each side of the surface. Viscous stress have both normal and tangential components.
4. Electric forces - this depends on the shape of the object and the imposed electric field. Generally has components normal and tangential to the surface.

 
Figure 2: Differential surface element pointing from fluid 2 to fluid 1.

The force balance is then:

 

• Surface Tension
• Pressure
• Viscous Stress
• Electrical Forces
• Normal and Tangential Components