Bulge formation of liquid film at the trailing edge: Scaling laws and particle removal assessment

Abstract

We present numerical simulations of bulge formation at the trailing edge of an inclined surface and its inhibitory effect on particle removal during surface cleaning. We investigate the spatial variations in liquid films near the trailing edge and find that the Weber number can be used as a dominant parameter to determine bulge occurrence over the trailing edge. We divide the film region near the trailing edge at which the bulge occurs into two: the region where the surface linearly grows and the surface tension is negligible, and the region where the surface tension force becomes dominant and the film surface is curved. In the investigated cases in which the Reynolds number is $O(10)$ or greater, the viscous forces is negligible, which allows for the derivation of the scaling laws for the length of the two regions according to the condition that the bulge height scales with the capillary length.In the resulting scaling law, the length scales depend on the Froude number and the inclination angle. The proposed scaling law allows for the prediction of the bulge shape and the prediction agrees with the simulation results, particularly at low Weber numbers (i.e, We < 0.5$). Moreover, we construct a particle removability map to assess the removal of particles of different sizes at specific locations on the substrate. The map reveals the reduced of the removability for small-size particles or particles located in the bulge.