Experimental and theoretical investigation of the effects of pressure on the hydrodynamically driven droplet spreading

Abstract

The dynamics of the hydrodynamically driven droplet are studied on four different substrates at surrounding gauge pressures ranging from 0 to 20 MPa. By combining the extended Overall Energy Balance (OEB) approach, the Lucas empirical model for estimating drop viscosity at elevated pressures, the advancement of a droplet on a solid substrate is modeled as it undergoes constant mass flux addition while maintaining a spherical cap. The theoretical governing equation, which incorporates two different modeling methods of viscous dissipation: lubrication approximation and boundary layer approximation, is validated with an experimental investigation involving hydrodynamically driven water droplets. The results show that an increase in surrounding pressure lowers the spreading radius and simultaneously increases the advancing contact angle. In addition, the minimum spreading ratio falls, and the average Reynolds number decreases in a monotone fashion while the Weber and Capillary numbers rapidly increase with increasing pressure.