Theoretical Model of Droplets Motions on Solid Surface With Radial Wettable and Evaporation Rate Gradients

Wettability gradient in radial direction and evaporation rate gradient can cause droplet motion on a solid surface. Here a theoretical model is proposed. Besides, an equation of droplet velocity is derived on a solid surface. We consider the wettability and evaporation rate gradients are mainly caused by the chemical composition and surface roughness, only along the radial direction. Surface tension at the liquid-vapor interface is constant as it is assumed that the temperature does not change during the whole process. Thus, Marangoni effect induced by the liquid-vapor surface tension gradient is neglected. Besides, as droplet size is set as less than the capillary length (⁠$l=γ/ρg$⁠), the gravity effect is ignored as well. The velocity at the droplet center on a gradient surface along the radial direction is half of that along the x-direction. With the simulation of water droplet, the center velocity decreases with time and the droplet radius increases at the beginning part and then decreases.