Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
134 tokens/sec
GPT-4o
9 tokens/sec
Gemini 2.5 Pro Pro
47 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Evolution of waves in liquid films on moving substrates (2203.08201v5)

Published 15 Mar 2022 in physics.flu-dyn

Abstract: Accurate and computationally accessible models of liquid film flows allow for optimizing coating processes such as hot-dip galvanization and vertical slot-die coating. This paper extends the classic three-dimensional integral boundary layer (IBL) model for falling liquid films (FF) to account for a moving substrate (MS). We analyze the stability of the liquid films on vertically moving substrates in a linear and a nonlinear setting. In the linear analysis, we derive the dispersion relation and the temporal growth rates of an infinitesimal disturbance using normal modes and linearized governing equations. In the nonlinear analysis, we consider disturbances of finite size and numerically compute their evolution using the set of nonlinear equations in which surface tension has been removed. We present the region of (linear) stability of both FF and MS configurations, and we place the operating conditions of an industrial galvanizing line in these maps. A wide range of flow conditions was analyzed and shown to be stable according to linear and nonlinear stability analyses. Moreover, the nonlinear analysis, carried out in the absence of surface tension, reveals a nonlinear stabilizing mechanism for the interface dynamics of a liquid film dragged by an upward-moving substrate.

Summary

We haven't generated a summary for this paper yet.