Here we present an unsteady two-dimensional numerical study on drops migrating in a matrix fluid. A computer code is developed to simulate the temperature distribution and velocity field both inside and outside drops. The governing momentum and energy equations are solved by finite-difference method and the deformable interface of drops is captured by front-tracking technique. The moving interface advection in front-tracking method is improved and mass conservation is maintained during the entire course of drop migration. Simulation results show that our improved model is consistent with previous numerical work on this subject. With the numerical model, two-dimensional thermocapillary motion of drops is studied.

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