Modeling of early stage droplet spreading based on numerical simulations

The initial spreading dynamics of a droplet has been studied for decades, however, the mechanism of such phenomenon is still not well known and an efficient prediction model considering combined effects of each influence factor for this process is absent. In present study, numerical simulations for the early stage droplet spreading are carried out based on a modified MPS method with up-to-date viscosity model, pressure Poisson equation, pressure gradient model as well as improved boundary conditions. Influences of the contact angle, viscosity and surface tension force are individually investigated, and their effects are properly characterized by dimensionless contact angle Θ, Reynolds number Re and Bound number Bo. Results show that the droplet spreading radius can be modeled as r/R₀ = β(t*)^α, where α and β are functions of dimensionless numbers above. Parameters α and β of the contact radius’ power-law growth in all simulations are adopted as inputs to determine coefficients in droplet spreading correlation. The proposed correlation generates pretty close predicted results whose relative errors are less than 5% comparing with experimental values. Present research provides a picture on how the initial contact between the liquid drop and solid surface develops, and it could be a fundamental research for more complicated droplet behaviors e.g. the droplet impact and collision.