Formation of the Capillary Ridge on the Free Surface Dynamics of Second-Grade Fluid Over an Inclined Locally Heated Plate

Abstract

Abstract The formation of capillary ridges is the typical features of thin viscous or viscoelastic fluids over a locally heated plate. This ridge leads to the nonuniformity in the thin film coating. In this work, the formation of capillary ridges on the free surface of thin second-grade non-Newtonian fluid flowing over an inclined heated plate is discussed. The flow is modelled by two-dimensional laws of conservation of mass, momentum, and energy with corresponding boundary conditions at the plate and the free surface. An evolution equation for the description of the liquid thin film height is derived from the two-dimensional balance equations using the long-wave approximation. The resulting nonlinear dynamic equation is discretised implicitly on a uniform grid using the finite volume method. The obtained results on the capillary ridge in the free surface are discussed for the different flow parameters. It is noted that the capillary ridge height is higher for the second-grade viscoelastic fluid in comparison to the Newtonian one. This study can be a starting point to investigate the influence of second-grade viscoelastic parameter on the free surface instability and other phenomena of interest.