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| Using long-wave theory and direct numerical simulations (DNS) of the Navier-Stokes and energy equations, we investigate the nonlinear dynamics of a bilayer system consisting of a thin liquid film and an overlying gas layer driven by the Marangoni instability. The bottom solid substrate is heated in the form of periodical thermal waves propagating along the substrate with a constant frequency $\omega$.In the case of a stationary thermal wave, $\omega=0$,the liquid film rupture takes place with a flattish wide trough when both Marangoni number and the amplitude of the thermal wave are sufficiently large. Regimes in which the film forms a train of localized drops traveling along the substrate arise for sufficiently small, but non-zero $\omega$, In this case, localized traveling drops are interconnected by thin liquid bridges with negligible small flow velocities.With an increase of $\omega$ the interfacial profiles represent traveling waves with less localized shapes. We show that the liquid is trapped inside the drops during the drop train motion, and the total flow rate is linearly proportional to $\omega$.When the minimal thickness of the bridges between consecutive drops is increased, a faster flow rate can be achieved than in the localized drop-train configuration. In this case, however, fluid in the bridges has the negative (backward) velocity and can migrate from one drop to another, thereby leading to a gradual exchange of the content of drops in the train. |
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