Stagnation Point and Meniscus of Low Inertia Free Drag-Out of Liquid by Thin Strip

Abstract

The time-averaged film thickness of the coating on a smooth strip from a bath can be predicted by the Landau-Levich (LL), and Derjaguin theory for low inertia and low Capillary number, Ca. Using the smoothed particle hydrodynamics (SPH) method incorporating adhesion force of the liquid to the strip surface, cohesion between liquid particles, and robustly tuned artificial viscosity, the flow and the evolution of meniscus of liquid drag-out within Ca range 0.06≤Ca≤0.25 and fluid Property number P0=0.1 is studied to characterize the stagnation point locations and the meniscus shape. The predicted time-averaged film thicknesses match closely with the LL prediction and previously published experimental data and other theoretical models. The distances of the stagnation points from the strip Xstg are within (2.5±0.3)h∞ and insensitive to Ca. These stagnation points are always on the meniscus air–liquid interface. However, the stagnation point elevation from the bath liquid level, Ystg increase with Ca.