Laminar flow at the interface of two liquids

Abstract

The velocity distribution in the laminar boundary layers at the interface of two liquids in relative rectilinear motion, the thickness of the layers, and the stress at the interface are determined. Numerical results are given for nine cases of liquids in contact, including identical liquids and liquids with varying degrees of dissimilarity in characteristics. The evaluation of the desired quantities is based on Prandtl's boundary-layer t heory, and is carried out by a method of suc-cessive approximations. The numerical results are those given by the second approximation. CONTENTS Page I. Introduction ___ -_____ ______________________________ ___________ 303 II. Formulation of the problem ________________ ____ ____ _________ ___ _ 304 III. Prandtl's boundary-layer equation ___ ______ _____________ __ ____ ___ 305 IV. Approximate expressions for t he stream functions ______________ ____ 308 V. Evaluation of the constants ________ ___ ___________________ _______ 314 VI. First approximate solution for t he la.minar boundary Jayers _________ 317 VII. Second approximate solution for the laminar boundary layers _______ _ 318 VIII. Quality of the approximations ______ ____ ___________ ____ _________ _ 319 IX. Physically significa nt quantities of the layers _________ __ __ _________ 321 1. Local stress at the surface of separation __ __ __________ __ ____ __ 32l 2.