Asymptotic solution to the problem of drag of a fluid by a moving plate

An analogy is established between the formulations of the problem of the drag of a fluid by a moving plate 1–3] and the problem of propagation of a stationary flame 4, 5]. The theory of singular perturbations is used to a find a two-term asymptotic expression for the film thickness h₀. The expansion parameter is the Bond number Bo 1. The limited applicability of the well-known formula of 1, 2] is estimated quantitatively. Such an estimate has been obtained earlier experimentally 3]. The approach used in the present paper should also be fruitful for the solution of other problems in capillary hydrodynamics.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 52–56, November–December, 1980.