Physics

Nanotechnology

Coating

Mathematics

Mechanics

Limit (mathematics)

Mathematical analysis

Materials science

Flow (mathematics)

AIChE Journal

The region of acceptable quality in the space of operating parameters of a coating process is called coating window. Their limits are set by coating defects. For the slot‐coating process the low‐flow limit is important. It corresponds to the maximum web speed at a given film thickness, or the minimum film thickness at a given web speed, at which the coating bead remains stable. The available viscocapillary model is based on the Landau‐Levich equation, which is limited to small Capillary and Reynolds numbers. Under these conditions, the minimum film thickness that can be coated decreases with decreasing coating speed, but many coating processes do not occur at low Capillary numbers. It is important to determine the range of validity of the viscocapillary model and find the low‐flow limit outside this range. The low‐flow limit was determined here theoretically and experimentally. The 2‐D Navier‐Stokes equations with free surfaces describe liquid flow in the coating bead. Theoretical approaches solve the Navier‐Stokes system by either using Galerkin's method with finite‐element basis functions or applying a long‐wave expansion. The minimum layer thickness at a set of parameters was determined by the turning point on the solution path as the thickness was diminished. The minimum film thickness was measured experimentally by determining the flow rate at which the coating bead breaks, leading to stripes of coated and uncoated web. Results show that the low‐flow limit of the coating bead at large Capillary and Reynolds numbers fundamentally differs from that at their low numbers. At large Capillary and Reynolds numbers, the minimum film thickness that can be coated decreases with increasing coating speed. The coating window of the process is much larger than that in the literature, broadening the applicability of this coating method.

Low‐flow limit in slot coating: Theory and experiments