Dynamic meniscus profiles in free coating III predictions based on two‐dimensional flow fields

Abstract

AbstractOne challenging problem in liquid‐gas, interfacial phenomena is the prediction of the size and location of a flowing meniscus because it involves surfaces which are highly curved. The paper presents one aspect of this problem. A numerical method is presented for predicting the dynamic meniscus profiles–specifically these distorted considerably by flow. The geometry considered to provide those free (liquid‐gas) surfaces is coating of a moving sheet by upward withdrawal from a finite bath. The predicted profiles agree with data taken with a glycerine‐water solution and with viscous oils.The method predicts the three parameters (coating thickness and two others) which are the minimum number of parameters necessary to describe the dynamic‐meniscus profiles for this geometry. The numerical method is iterative, it simultaneously predicts the flow field in the bath, and it is based on the two‐dimensional Navier‐Stokes equations and appropriate boundary conditions. The interfacial boundary condition used for iteration is the normal stress condition which is composed of pressure, surface tension, and viscous terms.