Asymptotic and numerical analysis of vertical, planar liquid sheets subject to London‐van der Waals forces

Abstract

Asymptotic methods are employed to derive the long wave equations governing the fluid dynamics of thin, time‐dependent, incompressible, vertical, planar liquid sheets at low Reynolds numbers subjected to London‐van der Waals body forces and gravity. Analytical solutions for steady, viscous sheets in gravitational and zero‐gravity environments are obtained for large surface tension. Numerical studies of planar liquid sheets at low Reynolds numbers with no surface tension indicate that, for plane stagnation flows, the deceleration of the sheet as it approaches the solid wall decreases as the London‐van der Waals forces are increased, the effects of these body forces decrease as the Froude number is increased, and, for Reynolds‐to‐Froude numbers greater than one, the thickening of the sheet as it approaches the solid boundary increases as the Hamaker constant is increased. Numerical experiments of film casting processes with three different flow approximations which account for or neglect inertia and/or the gravitational pull have also been performed and indicate that for high take‐up speeds, a boundary layer is formed at the downstream boundary, the thickness of this layer decreases as the London‐van der Waals forces are increased, and, for Reynold‐to‐Froude numbers larger than one, the leading‐order thickness and axial velocity component are very sensitive to the value of the Hamaker constant.

Citation

Ramos, J.I. (1997), "Asymptotic and numerical analysis of vertical, planar liquid sheets subject to London‐van der Waals forces", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 7 No. 1, pp. 42-62. https://doi.org/10.1108/09615539710156192