Theoretical model of maximum spreading diameter on superhydrophilic surfaces

Abstract

Liquid droplets impacting on the solid surface is an ubiquitous phenomenon in natural, agricultural, and industrial processes. The maximum spreading diameter of a liquid droplet impacting on a solid surface is a significant parameter in the industrial applications such as inkjet printing, spray coating, and spray cooling. However, former models cannot accurately predict the maximum spreading diameter on a superhydrophilic surface, especially under low Weber number (<i>We</i>). In this work, the spreading characteristics of a water droplet impacting on a superhydrophilic surface are explored by high-speed technique. The spherical cap of the spreading droplet, gravitational potential energy, and auxiliary dissipation are introduced into the modified theoretical model based on the energy balance. The model includes two viscous dissipation terms: the viscous dissipation of the initial kinetic energy and the auxiliary dissipation in spontaneous spreading. The energy component analysis in the spreading process shows that the kinetic energy, surface energy, and gravitational potential energy are all transformed into the viscous dissipation on the superhydrophilic surface. The transformation of surface energy into viscous dissipation is dominant at lower <i>We</i> while the transformation of kinetic energy into viscous dissipation is dominant at higher <i>We</i>. It is found that the gravitational potential energy and auxiliary dissipation play a significant role in spreading performance at low <i>We</i> according to the energy component analysis. Moreover, the energy components predicted by the modified model accord well with the experimental data. As a result, the proposed model can predict the maximum spreading diameter of a droplet impacting on the superhydrophilic surface accurately. Furthermore, the model proposed in this work can predict the maximum spreading diameter of the droplet impacting on the hydrophilic surface and hydrophobic surface. The results of this work are of great significance for controlling droplet spreading diameter in spray cooling and falling film evaporation.