(332g) Influence Of Evaporation On The Stability Of A Thin Liquid Film Flowing Over A Locally-Heated Surface

Tiwari, N., University of Massachusetts
Davis, J. M., University of Massachusetts, Amherst

Many aspects of micro-device operation and fabrication involve the flow of volatile liquids over non-isothermal surfaces. In this presentation, the dynamics and stability of a volatile liquid film flowing over a locally-heated surface are analyzed using a long-wave analysis. The film dynamics are governed by three dimensionless groups: a Marangoni number (M), which quantifies the gradient in surface tension induced by a temperature gradient at the free-surface; an equilibrium constant (K) that behaves as an inverse Biot number; and an evaporation number (E) that normalizes the energy flux by conduction across the film with that for phase change. The film profiles are computed and a linear stability analysis is performed for a range of the governing parameters to determine the effects of evaporation on the flow. The temperature gradient at the leading edge of the heater induces a gradient in surface tension (Marangoni stress) that opposes the gravitationally-driven flow and leads to the formation of a pronounced capillary ridge. Above a threshold Marangoni number this ridge is unstable to spanwise rivulet formation from the capillary ridge. Above a different threshold value of M, the film above the heater undergoes a thermocapillary instability modulated by evaporation. Depending on the values of E and K, either of these instabilities may be observed for sufficiently large M and can be distinguished by the structure of the corresponding eigenfunctions. A transient, non-modal analysis is used to determine the maximum amplification of perturbations to this non-normal system, and the optimal perturbations are computed to elucidate the most sensitive regions of the film. These structures differ significantly depending on the physical mechanism that governs the instability. The film ruptures near the heater for a range of E, M, and K, and simulations incorporating a disjoining pressure term are used to determine the subsequent evolution of the film, including rivulet instabilities that develop at the contact line. These simulations are also used to study the competition between and nonlinear evolution of the two different types of instabilities that develop for continuous films for different ranges of E and K.