Confined thermocapillary motion of a three-dimensional deformable drop

In this paper, simulations are performed of the thermocapillary motion of three-dimensional and axisymmetric drops in a confined apparatus. The refined level-set grid method is used to track the interface and resolve very small deformations. We compare our results to theoretically predicted thermocapillary migration velocities of drops and to experimentally measured migration velocities in microgravity experiments. The motivation of the present work is to address four important questions surrounding thermocapillary migration. These are as follows. (1) What is the impact of initial conditions on both the initial transient and steady state drop behavior? (2) What is the impact of the domain geometry on drop behavior? (3) Do drops deform for intermediate Marangoni numbers and are those deformations axisymmetric? (4) Can the assumption of constant temperature fluid properties be used when simulating physical experiments? To answer the first question, we explore the parameter space of initial drop temperature distribution and drop holding time. We find that in lower Marangoni number regimes, the drop rapidly settles to a quasisteady state. For larger Marangoni numbers, the initial conditions dominate the drop behavior. To address the second and third questions, we look at the spatial distribution of tangential temperature gradients on the surface of the drop as well as drop deformations and migration velocities. The domain geometry induces nonaxisymmetric deformations and temperature distributions. The results of several axisymmetric runs with realistic physical properties are examined to answer the fourth question. It is found that the variation of material properties influences the drop migration behavior in a nontrivial way.