(535i) Theory for Thin-Film Evolution Between a Sphere and a Planar Free Surface

The spatiotemporal evolution of thin liquid films is ubiquitous in the mechanics of emulsions. The so-called "thin film equations," i.e. the Navier-Stokes equations simplified in the thin-film limit, have been applied in numerous technological problems in order to explain the detailed flow physics within a liquid with one or more free surfaces. It is well known that excess interfacial stresses at one or more free surfaces, due to the presence of surface-active species, can have a major influence on the dynamics of thin films. Recent interferometry experiments involving a bubble being pressed against a flat interface have shown that 1) the temporal scaling law for thin-film drainage can have a different exponent depending on the type of surfactant used, and 2) an interesting flow instability can occur in a thin film squeezed between two fluid-fluid interfaces when surfactant is present.

In this talk, the theoretical problem of a sphere passing through an initially planar, fluid-fluid interface is discussed, with the particular aim of explaining observations 1 and 2 above. The theory is built up under the auspice of the thin-film approximation, with suitable homage paid to prior theoretical descriptions. The deformation is computed for axisymmetric films for all time. The importance of three length scales in the problem, namely the capillary length, the sphere radius, and the characteristic thickness of the film, are illuminated in light of the new theory. Four regimes of the motion are characterized, namely the approach, penetration, drainage, and eventual rupture of the thin film. The implications for the mechanics of concentrated emulsions and foams are discussed.