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Analysis of film break-up and dry patch stability de Rodriguez, Sara Gersberg


The stability of stationary dry patches in a thin, heated liquid film was analyzed according to previous models and compared with recent experimental data. Previous analysis indicate that dry patch stability is expressed in terms of a balance of forces at the upstream edge of the dry patch: a pressure force tends to rewet the dry patch, and the surface tension and thermocapillary forces causes the dry patch to spread. Roughly, the models are reduced to two types, the first evaluates pressure force applying a Bernoulli-type equation to the center-streamlines, the second uses the control-volume approach. The former method gives half the pressure force predicted by the second model; in both analyses the flow is considered one-dimensional. In the present study the contradiction was clarified by applying the control volume technique to a two-dimensional flow. Both methods give equivalent results for the limiting case of control volume coinciding with the center streamline. When experimental data are used the model that proposes a Bernoulli-type equation to find pressure force best describes the balance of forces, specially for low Reynolds numbers. For high Reynolds numbers pressure forces depart significantly from surface forces. In the present study the force balance criterion for stability of dry patches was extended to the case of a wavy film. Kapitza's analysis for surface waves on thin film was used and the bi-dimensional character of the flow was considered through the introduction of a coefficient whose value was assumed equal to the steady case. Results show that a body force must be included together with pressure force to balance surface tension force. A better description of the flow field is needed since Kapitza's analysis is not valid near the dry patch. A further model is presented by means of which film profiles and pressure forces can be evaluated. The goal was to describe flow behaviour of a thin heated film around a dry patch. Due to the complexity of the problem different assumptions at various stages were made. The problem was divided into two regions, similar to a boundary layer method. In the outer region surface tension effects were neglected and the patch acts like a solid object for the flow. Increases in stagnation pressure are balanced by changes in hydrostatic pressure. In the inner region surface tension effects predominate over inertial effects. The free surface profiles, valid for a narrow range of low Reynolds numbers, are wedge-shaped and different from measured profiles. In future work surface tension effects in the outer region must be included and the solution extended to a larger range of Reynolds numbers.

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