Thin film dynamics in coating problems using Onsager principle

摘要

A new variational method is proposed to investigate the dynamics of the thin film in a coating flow where a liquid is delivered through a fixed slot gap onto a moving substrate.A simplified ODE system has also been derived for the evolution of the thin film whose thickness hf is asymptotically constant behind the coating front.We calculate the phase diagram as well as the film profiles and approximate the film thickness theoretically,and agreement with the well-known scaling law as Ca2/3 is found.