Laminar film flow down a wavy incline

Effect of inertia on electrified film flow over a wavy wall

“…Bontozoglou and Papapolymerou [31] identified a resonance effect in viscous film flow similar to that discovered for the complementary problem for inviscid flow. At resonance, the relative amplitude of the surface wave is significantly larger than the amplitude of the wall corrugations, meaning in the present context that |A 1 | is significantly larger than unity.…”

“…At resonance, the relative amplitude of the surface wave is significantly larger than the amplitude of the wall corrugations, meaning in the present context that |A 1 | is significantly larger than unity. Bontozoglou and Papapolymerou [31] performed calculations in which the surface wave amplitude was found to be around 2.5 times the amplitude of the wall corrugations. Similar calculations were presented by Wierschem et al [32], who provided evidence that the resonance is linked to an interaction between the falling film and gravity-capillary waves travelling in the opposite direction to the main flow.…”

Stability and nonlinear wavy regimes in downward film flows on a corrugated surface

“…A great number of studies involved linear and nonlinear analyses of wave formation in a downward film flow on a smooth surface [2][3][4][5][6][7]. The problem of nonlinear waves on a film falling down a smooth plate has much in common with the problem of a steady viscous flow over a corrugated surface [8][9][10][11][12][13][14][15]. In both cases, the equations are essentially nonlinear, the shape of the free surface is unknown beforehand, surface-tension forces play an important role, and there is a spatial period involved in the problem.…”

“…In both cases, the equations are essentially nonlinear, the shape of the free surface is unknown beforehand, surface-tension forces play an important role, and there is a spatial period involved in the problem. In spite of numerous applications of this problem to distillation processes and advanced heat exchangers [16], there are few experimental [8,17] and theoretical [9][10][11][12][13][14][15] studies of the film flow on a corrugated surface. For instance, the film flow down a sine-shaped surface with a small corrugation amplitude, as compared with the Nusselt thickness of the film, was examined with the perturbation technique by Wang [9].…”

“…The asymptotic approach was used by Shetty and Cerro [12] to examine a liquid flow down a corrugated surface with a corrugation amplitude much greater than the Nusselt film thickness H 0 . Treating corrugation in the linear approximation, Bontozoglou and Papapolymerou [13] examined resonant effects in the range of finite Reynolds numbers. The numerical solution of Navier-Stokes equations allowed the present author [14] to study the film flow in the range of finite Reynolds numbers for corrugation amplitudes commensurable with the Nusselt thickness.…”