SPATIAL INSTABILITY OF A VISCOUS-LIQUID SHEET

The spatial instability theory is used to study the evolution of symme trical and antisymmetrical disturbances of a moving viscous liquid she et in an inviscid gas medium. The similarities and dissimilarities bet ween spatial and temporal instabilities are delineated. Effects of pro perties such as viscosity, density, and surface tension on instability are examined. It is found that liquid viscosity always reduces the gr owth rate and dominant wave number for symmetrical disturbances. For a ntisymmetrical disturbances, liquid viscosity reduces the growth rate and dominant wave number at large Weber number, whereas liquid viscosi ty enhances instability at low Weber number. An increase in the gas-to -liquid density ratio always raises the growth rate of symmetrical dis turbances. The growth rate of antisymmetrical disturbances initially i ncreases with the density ratio, and then decreases when the density r atio exceeds Weber number. Surface tension always opposes the developm ent of instability. Symmetrical disturbances control the instability f or small Weber number, whereas antisymmetrical disturbances dominate f or large Weber number. The dominant wave numbers associated with symme trical disturbances are always greater than those of antisymmetrical d isturbances.