Chemical Engineering Science, Vol.53, No.24, 4129-4133, 1998
Hydrodynamic meniscus profiles in creeping flow
Many industrial coating processes involve drawing a thin strip or wire through a coating bath. A knowledge of the fluid dynamics,at the entry is important for understanding the coating mechanism. In this note the fluid flow and meniscus profile generated by a strip being drawn vertically through a liquid surface are investigated under the assumption of creeping flow. It is known that the assumption of normal or shear stresses at the free surface and no-slip at the plate gives solutions with a force singularity on a microscopic length scale, and predicts a constant free surface velocity somewhat less than the strip velocity. It is shown that if the condition that the flow generates no normal stresses at the free surface is relaxed, then solutions of the creeping flow equations exist in which the free surface velocity decays to zero far from the contact line. The resulting normal stresses are then balanced against surface tension forces to determine the dynamic meniscus profile. Although the change of the dynamic contact angle with contact line speed remains the single biggest influence on the resulting meniscus, the normal stresses induced by the flow are a significant:factor in determining the meniscus shape.