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Thermocapillary effects on eccentric compound drops in Poiseuille flows

We analytically study the motion and deformation of an eccentric compound drop subject to an externally imposed temperature gradient and suspended in a Poiseuille flow, using a bispherical coordinate system. The temperature gradient alters surface tensions at the drop interfaces and triggers strong Marangoni flows, altering the drop dynamics. While a positive temperature gradient speeds up both drops, a negative gradient can potentially lead to a stable equilibrium where both drops move with the same velocity. The Marangoni effect also enhances deformation, particularly in the inner drop, which may take either a prolate or an oblate shape.