Thermocapillary motion of three-dimensional deformable bubbles in zero gravity and shear flow is investigated by direct numerical simulations. The governing equations are solved by a front tracking/finite difference technique that accounts for viscous forces and inertia effects. The effect of shear rate on the migration velocity of a single bubble is studied and it is found that compared to a quiescent flow, the migration velocity may increase or decrease depending on the shear rate. Similar comparison is made between the average migration velocity of a freely evolvingarray of eight bubbles rising in a shear and in a quiescent flow and it is shown that the average rise velocity of the former is higher.
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