We develop a general methodology for the inclusion of variable surface
tension into a Volume-of-Fluid based Navier-Stokes solver. This new numerical
model provides a robust and accurate method for computing the surface gradients
directly by finding the tangent directions on the interface using height
functions. The implementation is applicable to both temperature and
concentration dependent surface tension, along with the setups involving a
large jump in the temperature between the fluid and its surrounding, as well as
the situations where the concentration should be strictly confined to the fluid
domain, such as the mixing of fluids with different surface tension
coefficients. We demonstrate the applicability of our method to thermocapillary
migration of bubbles and coalescence of drops characterized by different
surface tension
