NUMERICAL STUDY OF TRANSPORT PHENOMENA IN SESSILE DROPLETS DURING INTERNAL SOLIDIFICATION

Abstract

A unified equation is derived, which describes transport phenomena induced by thermocapillary effects in a sessile drop with internal solidification, by means of a point cooling at the center of the drop base. The effect of the buoyancy force is taken into account. Based on experimental observation, the entire solidification process is divided into the early solidification stage, where the solid phase grows in a hemispherical form until its front reaches the top of the drop, and the late solidification stage, with the solidification front propagating in a cylindrical form until the completion of solidification. Two mathematical models are developed: one for the early-stage solidification, with a vorticity - stream function scheme in a spherical coordinate system, and the other for the late-stage solidification, with a pressure-velocity component scheme in a cylindrical coordinate system. A finite volume technique is employed to solve the early-stage model using an alternating-direction implicit method and late-stage model using a modified SIMPLER procedure. Numerical results are obtained for the distribution of surface temperature and velocity, isotherms, streamlines, and velocity vectors. They are in qualitative agreement with the existing experiments on a p-xylene drop. The effects of thermocapillary forces, gravitational acceleration, cooling strength, ambient heat transfer, and aspect ratio on the transport phenomena and solidification are also determined.