Various nonlinear wavy regimes of a viscous liquid film flowing down verticalwires and tubes were calculated using the integral method. The linear stability analysis of the trivial smooth solution was compared with the results published previously. In the region of linear instability, the competition among the gravity, viscous and capillary forces formed the steady-state traveling solutions of finite amplitudes. A t least two families of waves were shown to be parameterized by the wave number for given values of external parameters (Reynolds number, cylinder radius and physical characteristics of liquid). The basic waves characteristics depended on external parameters and on wave number. The intensity of wavy processes increased with decreasing cylinder radius. The calculations show the catastrophic growth of wave amplitude, when the system flows down a vertical tube of sufficiently small radius and moves into the linear, unstable region. (1974) for the case of the falling down of a vertical plane. Tougou (1 977) and Shlang and Sivashinsky (1 982) derived the nonlinear asymptotic equation for the surface elevation when the liquid film falling down a vertical cylinder with a small

No abstract

in Wiley InterScience (www.interscience.wiley.com).The article is devoted to a theoretical analysis of counter-current gas-liquid wavy film flow between vertical plates. We consider two-dimensional nonlinear waves on the interface over a wide variation of parameters. The main interest is to analyse the wave structure at the parameter values corresponding to the onset of flooding observed in experiments. We use the Navier-Stokes equations in their full statement to describe the liquid phase hydrodynamics. For the gas phase equations, we use two models: (1) the Navier-Stokes system and (2) the simplified Benjamin-Miles approach where the liquid phase is a small disturbance for the laminar or turbulent gas flow. With the superficial gas velocity increasing and starting from some value of the velocity, the waves demonstrate a rapid decreasing of both the minimal film thickness and the phase wave velocity. We obtain a region of the gas velocity where we have two solutions at one set of the problem parameters and where the flooding takes place. Both the phase wave velocity and the minimal film thickness are positive numbers at such values of the velocity. We calculate the flooding point dependences on the liquid Reynolds number for two different liquids. The wave regime corresponding to the flooding point demonstrates negative u-velocities in the neighbourhood of the interface near the film thickness maximum. At smaller values of the superficial gas velocity, the negative uvelocities take place in the neighbourhood of the film thickness minimumHere, Re ¼ 20 and k neut /L ¼ 0.25; (a) and (e) correspond to U GS ¼ 2.5 m/s; (b) and (f), U GS ¼ 7.0 m/s; (c) and (g) U GS ¼ 8.5 m/s; (d) and (h) U GS ¼ 9.07 m/s. Lines 1-3 correspond to water at k neut /L ¼ 0.25, 0.2, 0.15, respectively. Lines 4-6 correspond to 2.5% butanol at k neut /L ¼ 0.25, 0.2, 0.15, respectively.

No abstract

The paper is devoted to a theoretical analysis of nonlinear two-dimensional waves on the surface of a liquid film freely falling down a vertical plate. Using a model system of equations, steady-state travelling periodical wave regimes have been found numerically. It is shown that some of them agree quantitatively with experimental results. The question of the stability of various wave regimes with respect to two-dimensional infinitesimal disturbances is examined. The most-amplified disturbances are evaluated.