TIME-DEPENDENT EQUATIONS GOVERNING THE SHAPE OF A 2-DIMENSIONAL LIQUID CURTAIN .1. THEORY

Approximate equations have been derived that govern the time-dependent response of a two-dimensional liquid curtain falling under the influe nce of gravity and subjected to ambient pressure disturbances. Startin g with the assumptions of potential flow and constant surface tension, and using the approximation that the curtain is long and thin, a stea dy-state base flow is first determined. In agreement with previous lit erature results, the analysis reveals that the curtain flow is essenti ally in free fall, where the velocity profile is only slightly curved across the curtain thickness. Then, by assuming that the disturbances to the curtain are small, the time-dependent equations are linearized about the approximated base flow. The approximate nature of the base f low necessitates a careful ordering of terms to assure that the linear ization is valid. Two equations governing the curtain shape are derive d: the first governs the deflection of the curtain centerline, and no the second governs the thickness variations. Previous literature resul ts regarding wave propagation and steady curtain deflections can be pr edicted via the derived equations. It is also found that to lowest ord er, pressure disturbances induce a deflection of the curtain centerlin e while preserving the local thickness associated with the undisturbed curtain. (C) 1997 American Institute of Physics. [S1070-6631(97)02412 -4].