Three-phase solidification of a liquid compound droplet on a curved surface

Abstract

A compound droplet solidifying on a cold curved surface in a gaseous environment is numerically studied by an axisymmetric three-phase front tracking method. The compound droplet containing an inner core of gas is initially assumed to be part of a sphere, and the curved surface is maintained at temperature below the solidification point of the shell liquid. The effects of the radius of the cold surface, volume change (in terms of the solid-to-liquid density ratio ρsl), supercooling degree (in terms of the Stefan number St), growth angle ϕgr and shell liquid thickness on the solidified droplet shape, the solidification rate and the solidification times are under consideration. Volume expansion (ρsl < 1.0) induces an apex, and volume shrinkage (ρsl > 1.0) results in a cavity on top of the outer surface while volume change has a minor effect on the inner surface of the solidified droplet. A more convex surface causes the solidification process to finish earlier, whereas a more concave surface prolongs the entire solidification time. However, the mean solidification rate, the tip angle at the droplet top and the additional height are not affected by the radius of the curved surface. The tip angle is also slightly affected by the outer shape of the initial droplet, the shell thickness and St while these parameters strongly affect the rate of solidification. It is found that the completion of solidification around the inner core is not affected by the growth angle, while it takes longer when increasing ρsl, the size of the inner core or decreasing the Stefan number.