A new model describing the dynamics of large-amplitude waves on laminar falling wavy films at high Reynolds numbers (Re≳300) is presented. The model is based on second-order boundary layer theory and includes the pressure variation across the film as well as higher-order viscous terms. The consistency and accuracy of the model is verified by comparing the linear stability results with Kapitza’s classical boundary layer model and Orr–Sommerfeld studies of the two-dimensional Navier–Stokes equations. Numerical integration of a traveling wave simplification of the model predicts the existence of chaotic large-amplitude, nonperiodic waves, as observed in the experiments. The computed wave statistics such as wave celerities, root-mean-square (RMS) values of film thickness, probability density function (PDF), and film thickness power spectrum using the present model are in reasonable agreement with those measured on naturally excited fully developed flows at Re≳300. The present model also overcomes the main deficiency of the classical boundary layer model (namely, negative wall shear stress) predicts large-amplitude waves (with peak to substrate ratios of 3 to 4) and gives better agreement with data.

Numerical simulations of mass transfer into falling liquid films, both through the wavy interface and from the wall, have been performed for experimentally measured large waves within which the flow fields have been computed. Experiments have shown that the occurrence of waves on free falling films causes dramatic increases in mass transfer into the film, even under laminar flow conditions. Wave effects have been modeled in several ways, none of which predicts the observed rate of enhancement. The present numerical procedure includes solving the convective-diffusion equation for wavy films by extending a technique developed for hydrodynamic simulation. The presence of waves is shown to cause significant velocities normal to each interface. In conjunction with recirculation within the large waves, these flow patterns produce transfer rates for large waves that are several times larger than predicted for quasiparallel velocity fields. Experimental wave structure data were used to define the dimensions and frequency of an average large wave and surrounding substrate. Computed transfer rates at both the gas-liquid interface and the wall for a film composed of a periodic sequence of average waves agree well with published data. These simulations confirm the inadequacy of parabolic, or Kapitza-type velocity profiles in formulating transport models.

Three isolated waves of differing amplitude and shape were selected from experimental measurements of a falling liquid film at Re = 880 for study using an algorithm developed for solution of the Navier-Stokes equations. The method computes the velocity and pressure fields as well as the velocity of the wave. The results show that large streamwise accelerations exist along with regions of recirculating flow in a moving coordinate system. These features can explain the enhanced rates of heat and mass transfer observed in wavy film flow. Computed wave velocities and wall shear stress were in reasonably good agreement with measurements. Wave velocity is shown to be sensitive to small variations in the wave shape and explains the apparent random variation of wave velocity with amplitude that has been observed experimentally. This numerical experiment points to the shortcomings of the many methods used to model large waves on falling films that have been based on parabolic velocity profiles.

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