Numerical simulations of thermal capillary migration of a droplet on a temperature gradient wall with smoothed particle hydrodynamics method

Abstract

Thermal capillary migration is a phenomenon due to the Marangoni effect, which refers to the spontaneous motion of a liquid on a non-isothermal surface. Numerical simulation of thermal capillary migration of a droplet is extremely difficult due to the multi-physics field coupling and the violent motion of the droplet surface. In this paper, an improved smooth particle hydrodynamics (SPH) method is developed for simulating thermal capillary migration of a droplet driven by thermal gradient. In improved SPH model, an improved continuous surface force model is proposed to enhance the accuracy and stability of surface tension force calculation by introducing an improved surface tangential force. The contact angle model is utilized to model the surface wettability. The SPH method for simulating the thermal fluid flow is developed based on the continuum, momentum, and energy equations. In addition, kernel gradient correction and particle shifting technique are utilized to improve the accuracy and stability of the SPH method. The correctness and effectiveness of the improved SPH method are verified by numerical examples. Moreover, the motions of a droplet driven by thermal gradient under different conditions are investigated. Comparing with the results obtained by experiments and other resources, we can conclude that the improved SPH model is effective in modeling the thermal capillary migration of a droplet.