Abstract
The Rayleigh-Taylor instability of viscous liquid film under a temperature-modulated inclined substrate is studied. Long wave approximation and weighted residual model are used respectively to derive the nonlinear evolution equations of liquid film, and it is shown that the two evolution equations by the above two approaches are equivalent. The recurrence relation and damped Mathieu equation are obtained by employing Floquet theory and linear analysis, respectively. When amplitude a and oscillation frequency ω of the temperature exceed critical values, the film surface loses its stability. The stability diagram is obtained by linear analysis based on Floquet theory. Moreover, based upon the line approach, the nonlinear evolution equation is numerically simulated to give the spatiotemporal evolution of the free surface. Heated capillary tension might accelerate the production of suspended droplets due to the appearing of Marangoni number Ma produced by heating inclined wall. The results reveal that the larger Reynolds number Re, Marangoni number Ma and Biot number Bi will result in the instability of free surface. Moreover, the liquid film becomes more unstable at the smaller Froude number Fr and Weber number We.
Published Version
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