Effect of Normal Body Force on Fingering Instability of a Liquid Sheet Driven by Shear Stress or Gravity

A thin liquid sheet driven by either gravity or shear force along a flat plate exhibits a long-wave fingering instability at the liquid front that leads to development of small rivulets of liquid penetrating into the unwetted part of the plate. Rivulet formation causes uneven surface wetting and degrades coating efficiency of the liquid film. The fingering instability occurs because thicker regions of the liquid sheet experience less resistance from the solid surface, and can hence move forward at a faster rate, than thinner regions of the sheet. As this process proceeds, mass conservation acts to make the thin regions of the sheet thinner in order to supply fluid for the thicker regions of the sheet to move forward. The current paper examines the effect on the fingering instability of a body force, such as gravity or centrifugal acceleration, oriented normal to the plate. The presence of a normal body force gives rise to a normal pressure gradient within the liquid sheet. When one region of the sheet becomes thinner than a neighboring region, the normal body force leads to a pressure force acting parallel to the plate that pushes fluid from the thick regions toward the thin regions of the sheet, thus inhibiting the fingering instability. The paper reports both a linear stability analysis of the fingering instability in the presence of a normal body force and a computational study of the effect of normal body force on rivulet development.