A generalized scaling theory for spontaneous spreading of Newtonian fluids on solid substrates

There exists a generalized solution for the spontaneous spreading dynamics of droplets taking into account the influence of interfacial tension and gravity.

This work presents a generalized scaling theory for the problem of spontaneous dynamic spreading of Newtonian fluids on a flat substrate using experimental analysis and numerical simulations. More specifically, we first validate and modify a dynamic contact angle model to accurately describe the dependency of contact angle on the contact line velocity, which is generalized by the capillary number. The dynamic contact model is implemented into a two-phase moving mesh computational fluid dynamics (CFD) model, which is validated using experimental results.

We show that the spreading process is governed by three important parameters: the Bo number, viscous timescale τ_viscous, and static advancing contact angle, θ_s. More specifically, there exists a master spreading curve for a specific Bo and θ_s by scaling the spreading time with the τ_viscous. Moreover, we developed a correlation for prediction of the equilibrium shape of the droplets as a function of both Bo and θ_s. The results of this study can be used in a wide range of applications to predict both dynamic and equilibrium shape of droplets, such as in droplet-based additive manufacturing.