h hi& hm 4 L N P P p1 Q Qm t T U 2, V Y X = layer thickness, m = values of h for Q < Qm, m = maximum value of h, m = discrete values of h, m = length scale in y-direction, m = number of discrete points, dimensionless = fluid pressure, N-m-2 = jet pressure, N.m-2 = scaled maximum pressure gradient, dimensionless = volume flux per unit span, m2.s-1 = maximum value of Q, m2.s-1 = time, s = tangential stress in jet, N.m-2 = horizontal fluid velocity, m-s-1 = vertical fluid velocity, m-s-1 = upward speed of sheet, ms-1 = horizontal coordinate, m = vertical coordinates, m Greek Letters E P = fluid viscosity, N-m-2-s-1 V = PIP P = fluid density, kg-m-3 U = surface tension coefficient, N-m-' r 1 = normal stress, N.m-2 7 1 1 = tangential stress, N-m-2 7 = u~~/~V 1/2p-3/2g-3/2L-3, dimensionless = measure of surface slope h/L, dimensionless LITERATURE CITED Atherton, R. W., and G. M. Homsy, "On the Derivation of Evolution Equations For Interfacial Waves," Chem. Eng. Comm., 2,57 (1976). Cameron, A., Principles of Lubrication, Longmans, London (1966). Deryaguin, B. V., "On The Thickness of the Liquid Film Adhering to the Walls of a Vessel after Emptying," Acta Pkyssiochtmicu U.R.S.S., 20, 349 (1945). 2 000 3000 4 000 5000 T e m p e r a t u r e , K Figure 2. Equilibrium composition of the C-0 system. C O = 19.