In this work, the issue is studied in a broader perspective with the aim to investigate the stability of thin film flows in the most general framework. In addition, the study of this work may help researchers who pursue analytic work in this subject to improve the assumptions made in their models.
For this purpose, the transient 2D Navier Stokes equations are solved with Galerkin finite elements in a computational domain that resembles an actual laboratory set up. A slit is introduced upstream the free surface flow and the perturbation of the free surface is achieved by periodically changing the flow rate at the entrance of the slit. In this way, any artificial velocity profiles are alleviated at the inlet of the free surface flow, because the velocity at that point is computed directly form the Navier Stokes equations. Additionally, bigger perturbations are allowed in this way, so that it takes faster for the waves in the free surface to develop.
Vertical films have been studied, in order to investigate if this phenomenon occurs for this case as well. First the laboratory experiments of Alekseenko et al (1994) are compared with our computational results. Agreement between both works is found in the regions where the self-similar parabolic velocity profile is valid. Agreement is also found in the observations of Alekseenko et al that the biggest changes both in the velocity profiles and the shear stress occur at the minimum of the waves. However, we were able to determine the velocity profiles and shear stress there and we found flow reversal with subsequent eddy formation in the case of the soliton like profile of their original work.
This finding encouraged us to continue the investigation in the whole spectrum of Kapitza numbers in the visco-capillary regime (Weber number greater than 1). We found that this phenomenon of flow reversal and eddy formation is a common situation in thin film flows. Actually, we found conditions under which multiple eddies exist. The eddies in vertical flows become so big that they reach the free surface, so that positions in the films exist where the streamwise velocity is negative at the free surface (that is the fluid moves upwards), although the whole flow is directed in the opposite direction (downwards).
There are many experiments and simulations published in the literature where the flows take place in the visco-capillary regime. These cases belong to the regime where we predict flow reversal. From the many cases, we picked one that has historical value, in order to verify our predictions. This is one of the original Kapitza's experiments (1949) which has been simulated by Gao et al (2003). By taking the conditions of Gao's work (2003) we were able to calculate flow reversal even for Kapitza's experiments. We calculated the variation of shear rate at a given position at the wall as a function of time. It is shown that the shear rate becomes negative when the vortex passes through that point. Since the minimum of the wave for this case is not constant, the negative value of the shear rate varies as a function of the strength of the vortex.
The velocity component vertical to the flow direction is positive in the region of the eddy in both the vertical and the inclined case near the wall. This finding is in accordance with experimental observations that the wavy structure of the film enhances heat and mass transfer. However, the detailed computations of this work show that it is the eddies that are formed right upstream the main hump of the wave that are responsible for this enhancement. This conclusion of the computations is the main new message of the present study.
Partial finacial support for this work for N.A.Malamataris has been granted by the Greek Ministry of Education through programme ARCHIMEDES I.
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