PARTIAL WETTING EFFECTS IN THE FILM FLOW SOLVER REACTINGPARCELFILMFOAM

In this poster, we investigate the possibility to use the film flow solver reactingParcelFilmFoam to predict the breakup of a falling film into rivulets.

The film flow equations in the reactingParcelFilmFoam solver are based on the thin-film assumption, which states that the characteristic wavelength of the film interface deformations are large compared to its thickness [1]. This assumption allows integrating the transport equations across the film thickness, in the wall-normal direction. In isothermal conditions, we thus have an integral model with two equations: the continuity, and the conservation of momentum, which avoids the use of a local closure relation for the film mean velocity. The two unknowns are the film local thickness h and the mean film velocity U.

In order to account for partial wetting phenomena, the contact line, i.e. the triple line where the gas and liquid phases meet on the substrate, must be treated. For that, a surface-tangential force is defined in reactingParcelFilmFoam, which limits the spreading of the liquid, and which exists only for partially wetting fluids, i.e. liquids characterized by a positive contact angle. Combining the expression of the tangential surface force due to surface tension and Young's law, this force defined per unit width of contact line is a function of the characteristic static contact angle of the liquid on the substrate $\theta_0$, the liquid surface tension $\sigma$, the cell width at the contact line, and an empirical parameter, $\beta$. The contact angle force is thus accounted for through a phenomenological model that requires knowing the contact angle, and adjusting one empirical parameter. Partial wetting phenomena are reproduced by introducing random fluctuations of the contact angle on the substrate. The contact angle is chosen randomly within a normal distribution whose mean value and standard deviation are fixed by the user. The main weakness of the solver thus lies in the empirism of the contact line treatment.

In this poster, the predictions of the solver are confronted to experimental data for water [1] and water-glycerine films [2] falling on inclined planes. Beforehand, the sensitivity of the results to the mesh density and solver parameters is quantified: it is found that the location of rivulet transition is highly affected not only by the empirical parameters of the model (mean value and standard deviation of $\theta_0$, parameter $\beta$) but also by the mesh density (since the contact angle depends on the cell width). Moreover, the sequence of $\theta_0$ values along the mesh remains the same, whatever the mesh density, which makes it hard to conclude on the mesh independence. In order to get rid of its influence, we implemented new distributions of $\theta_0$, in which the value depend only on the spatial location on the substrate. Various types of distributions are tested, and their effect on the results quantified.

The empirism of the model can be lessened by introducing a disjoining pressure in the film equations, instead of the contact angle force described above. The disjoining pressure model, as introduced by Derjaguin [3], relates the observed static contact angle to the intermolecular forces that become important when the distance between the gas/liquid interface and the solid/liquid interface $\tilde{h}$ is sufficiently small. We use a disjoining pressure model inspired by the one of Thiele et al. [4], and its implementation is on going. Further results will be presented on the poster.

References

[1] K. Meredith, A. Heather, J. de Vries, Y. Xin, Y., “A numerical model for partially-wetted flow of thin liquid films”. Comp. Methods in Mult. Flows, IV:239–249, 2011 [2] M. F. G. Johnson, R. A. Schluter, M. J. Miksis, S. G. Bankoff, “Experimental study of rivulet formation on an inclined plate by fluorescent imaging”, J. Fluid Mech., 394:339–354, 1999 [3] B.V Derjaguin, N.V Churaev, “Structural component of disjoining pressure”, Journal of Colloid and Interface Science 49, 249-255, 1974 [4] U. Thiele, E. Knobloch, “On the depinning of a driven drop on a heterogeneous substrate”,New J. Phys. 8 313, 2006