Hydrodynamic meniscus profiles in creeping flow

Many industrial coating processes involve drawing a thin strip or wire thro ugh a coating bath. A knowledge of the fluid dynamics,at the entry is impor tant for understanding the coating mechanism. In this note the fluid flow a nd meniscus profile generated by a strip being drawn vertically through a l iquid 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 micr oscopic length scale, and predicts a constant free surface velocity somewha t 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 solu tions of the creeping flow equations exist in which the free surface veloci ty decays to zero far from the contact line. The resulting normal stresses are then balanced against surface tension forces to determine the dynamic m eniscus profile. Although the change of the dynamic contact angle with cont act line speed remains the single biggest influence on the resulting menisc us, the normal stresses induced by the flow are a significant:factor in det ermining the meniscus shape. (C) 1998 Elsevier Science Ltd. All rights rese rved.