Disintegration of macroscopic fluid sheets on substrates: a singular perturbation approach

Abstract

A thin liquid film supported on a horizontal solid surface recedes spontaneously when holes larger than a critical size are created in the film by external means (e.g., disturbances, trapped bubbles, etc.). Alternatively, for a given hole size, a critical film thickness can be identified such that all films thinner than the critical thickness are rendered unstable due to spontaneous growth of the hole. Films thicker than the critical film heal and thus maintain their continuity when challenged by transient holes. The critical condition for the film breakup is identified to be the emergence of a smooth, energetically unstable solution of the Young-Laplace equation for the hole-profile. An explicit analytical expression is obtained for conditions of film breakup by matched asymptotic expansions, which makes the dependence of the critical thickness on the hole-radius and on physical properties to be physically transparent. The procedure obviates the need for tedious trial-and-error type numerical solutions of stiff Young-Laplace equation. Results are applicable to axisymmetric, unbounded menisci in solid-liquid-fluid systems. The analytical results are shown to be in very good agreement with numerical solutions for thin films, and they also correlate well with the available data on the critical thicknesses of several liquid-solid systems. Applications of the theory are in stability of solid-fluid-fluid dispersions (e.g., flotation), in elimination and stabilization of thin films on substrates, and in coating of thin wires and fibers.