On the development of rational approximations incorporating inertial effects in coating and rimming flows: A multiple-scales approach

Abstract

Analysis of thin-film rimming and coating flows is extended to create a more general model, which can be identified as a new distinguished limit that has the work of certain previous studies as specific limiting cases. Specifically, three-dimensional flows under the influence of gravity are considered in which the Reynolds number is large enough to necessitate consideration of both inertial and centrifugal effects, along with those of viscous, gravitational and surface-tension forces. Reduction of dimensionality is shown to be attainable within a systematic (multiple-timescale) asymptotic framework that encompasses all these effects, leading to a two-dimensional formulation that not only is more general than many of the existing ones but also represents a rational approximation in the sense that, in particular, the sizes of the dimensionless physical parameters to which it corresponds, together with the orders of magnitude of the errors resulting from the reduction, can be precisely characterized. © 2006 Oxford University Press.