EFFECT OF VISCOSITY ON THE LINEAR INSTABILITY OF A FLAT LIQUID SHEET

The mathematical investigation presented in this article with the beha vior of free viscous liquid sheets. The aim of this work is to show th e competition among the aerodynamic, surface tension, and viscous forc es in the disintegration process, and to deduce the situations in whic h the liquid viscosity introduces nonnegligible effects. The approach is based on linear theory considerations. The dispersion diagrams obta ined show that the viscosity may have a nonneligible effect on the gro wth of sinusoidal perturbations. However, it is seen that the viscosit y has no influence On the cutoff number of the dispersion diagram. The importance of the viscous effect is found to be strongly related to t he values of the other parameters. A detailed analysis yields that any liquid sheet may be considered as inviscid if M, defined by M = (mu(L ) rho(G)(2)U(3)h)/(rho(L) sigma(2)), is less than 0.001.