Numerical study of a liquid drop on an inclined surface with solidification

Abstract

Drop deformation and solidification on an inclined surface appears in many engineered and industrial applications. In this paper, we thus present a front-tracking-based simulation of the deformation and solidification process of a liquid drop on a plate tilted at an angle ϕp in the range of 10°–80°. The plate temperature is kept fixed at a value below the liquid-solid phase change temperature of the drop liquid while the drop is assumed to stick to the surface. The drop experiences some oscillating deformation, and when it reaches almost a steady state shape the solidification process starts undergoing volume expansion (ρsl = 0.9). Increasing ϕp from 10° to 80° causes the liquid drop to experience more oscillations with larger amplitudes. The increase in ϕp makes the solidification process last longer and results in a more asymmetric solidified drop with an increase in the tip shift Δxt [i.e. Δxt/d = 0.1278(ϕp/ϕref) + 0.014 with d, apparent diameter of the liquid drop, and ϕref = 90°, reference angle]. However, varying ϕp in this range has a very minor effect on the height and the conical tip angle ϕt at the top of the solidified drop (i.e. Hs/d ≈ 0.784 and ϕt/ϕref ≈ 1.33). With the presence of the plate inclination (ϕp = 60°), the drop oscillates more strongly when increasing either the drop wetting angle ϕ0 (from 50° to 130°) or the Bond number Bo (from 0.1 to 3.2). These increases in ϕ0 and Bo also result in an increase in the solidification time τs and Δxt. In contrast, the tip angle is less affected by ϕ0 and Bo. Further investigations on ρsl and the growth angle ϕgr show that the solidified drop is more asymmetric with a decrease in ρsl from 1.0 to 0.8 while ϕgr varied from 0° to 28° induces no change in Δxt. Accordingly, the numerical results confirm that the plate angle and the initial liquid drop shape have strong impact on the asymmetry of the solidified drop, and volume expansion and the growth angle strongly affect the conical tip angle.