Surface tension and wettability calculation using density gradient potential in a physically consistent particle method

Abstract A new surface tension model for particle methods using a density gradient potential was developed. The surface tension calculation is of importance for properly capturing free surface flows, and it is the case for particle methods. Since the presented model is a potential-based method, complex approximation for normal vector and curvature of the surface is not needed. The surface potential is formulated in combination with cohesive pressure potential and density gradient potential, and the interaction force with respect to surface tension is derived from the potential. It works mainly on the surface, and it also substitutes pressure force when the fluid is exposed on negative pressure. In addition, wettability is expressed by introducing an interaction ratio between fluid and wall, and the relation between the ratio and the contact angle is theoretically clarified. The surface tension and wettability models were verified via Laplace pressure calculation, droplet oscillation calculation, contact angle calculation, liquid bridge calculation and Plateau–Rayleigh instability calculation.