Evolution of waves in liquid films on moving substrates

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 conditions, i.e. FF and MS, and we place the operating conditions of an industrial galvanizing line in these maps. A wide range of flow conditions were analyzed and shown to be stable according to both linear and nonlinear stability analysis. Moreover, the nonlinear analysis, carried out in the absence of surface tension, reveals a nonlinear stabilizing mechanism for the interface dynamics of a liquid films dragged by an upward-moving substrate.

Automated summary

This study extends the classic three-dimensional integral boundary layer (IBL) model to consider the stability of liquid films on moving substrates. Through linear and nonlinear analysis, it is found that coating processes such as hot-dip galvanization and vertical slot-die coating are stable under various flow conditions.