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