Analytical, asymptotic and numerical studies of liquid curtains and comparisons with experimental data

Abstract

A mathematical model of liquid curtains falling under gravity is used to determine the liquid curtain geometry analytically, asymptotically, and numerically. The model accounts for gravity, surface tension, and pressure differences across the liquid curtain. The domain of validity of the analytical solution is determined as a function of the convergence parameter and Froude number. The convergence length is determined asymptotically for large and small values of the convergence parameter. An explicit fourth-order accurate Runge-Kutta method and a Newton-Raphson algorithm are used to solve the nonlinear equations governing the fluid dynamics of liquid curtains. The analytical, asymptotic, and numerical solutions are compared with four sets of experimental data. Good agreement between the solutions presented in this paper and experimental data is obtained for long curtains. For short curtains the discrepancies between the model predictions and experimental data are attributed to the meniscus and the adverse axial pressure gradient that develops near the liquid curtain convergence.