Analytical Consideration for the Maximum Spreading Factor of Liquid Droplet Impact on a Smooth Solid Surface

Based on the energy conservation approach, this study develops a universal model to predict the maximum spreading factor of liquid droplet impact on a smooth solid surface. Validated with the present simulations and experiments in the literature, this model effectively overcomes the limitation of previous models in the viscous regime and greatly reduces the computing errors from over 30% to below 6%. It is demonstrated that the underestimated maximum spreading factor by previous models results from the overestimation of viscous dissipation. By replacing the conventional model of spreading time, tm = 8D0/3U0, with a more precise one, tm = 1.47τiWe–0.44, the formulation to compute the viscous dissipation of entire spreading is improved. Finally, we examine the applicability of present model in the capillary regime and good performance is also shown.