Fernando A. Saita

THE AXISYMMETRIC AND PLANE CASES OF A GAS PHASE STEADILY DISPLACING A NEWTONIAN LIQUID : A SIMULTANEOUS SOLUTION OF THE GOVERNING EQUATIONS

The flow induced by a long bubble steadily displacing a liquid confined by two closely located parallel plates or by a cylindrical tube of small diameter is numerically analyzed. The technique employed solves the complete set of governing equations simultaneously. The present analysis encompasses, and also extends, the whole range of Capillary values previously studied with various numerical techniques. The results shown uncover a type of recirculating flow pattern that appears to have been overlooked before. The effects of the inertial forces on the liquid flow rate are also assessed.

The rear meniscus of a long bubble steadily displacing a Newtonian liquid in a capillary tube

In this work the interfacial shapes and the flow occurring at the trailing meniscus of a long bubble is numerically analyzed. The technique employed solves the complete set of governing equations simultaneously. The numerical results reported complete previous descriptions of the creeping flow regime; the influence of the inertia forces on the free surface shapes, interfacial undulations, and flow patterns is also analyzed.

Numerical prediction of the film thickening due to surfactants in the Landau–Levich problem

In this work numerical solutions of the dip coating problem in the presence of a soluble surfactant are shown. Predictions of film thickening as well as thickening factors are in very good agreement with published experimental data, showing that pure hydrodynamic modeling suffices to mimic the process. Our numerical solutions provide a wealth of information on the functioning of the dip coating system; they show the appearance of a second stagnation point located in the bulk phase near the dynamic meniscus and they give clues about how the flow patterns might change as the surfactant becomes less soluble.

A numerical analysis of the influence of the liquid depth on two-dimensional Faraday waves

In this work a numerical analysis of two-dimensional Faraday waves is presented. This study is based on direct numerical simulation of Navier–Stokes and continuity equations with appropriate boundary conditions. Stability maps on the (F-α) plane for viscous liquid layers with equilibrium depths between 5×10−5 m and 10−5 m are presented; comparisons are made with the linear stability predictions obtained with Benjamin and Ursell’s model for an inviscid fluid and with Kumar and Tuckerman’s model for a viscous fluid. Regions in which time-periodic solutions are no longer obtained and nonlinear effects are relevant, and are also delimited and analyzed: in these zones the disintegration of the free surface into drops may take place.

Numerical analysis of the Rayleigh instability in capillary tubes: The influence of surfactant solubility

A two-dimensional (2D) free surface flow model already used to study the Rayleigh instability of thin films lining the interior of capillary tubes under the presence of insoluble surfactants [D. M. Campana, J. Di Paolo, and F. A. Saita, “A 2-D model of Rayleigh instability in capillary tubes. Surfactant effects,” Int. J. Multiphase Flow 30, 431 (2004)] is extended here to deal with soluble solutes. This new version that accounts for the mass transfer of surfactant in the bulk phase, as well as for its interfacial adsorption/desorption, is employed in this work to assess the influence of surfactant solubility on the unstable evolution. We confirm previously reported findings: surfactants do not affect the system stability but the growth rate of the instability [D. R. Otis, M. Johnson, T. J. Pedley, and R. D. Kamm, “The role of pulmonary surfactant in airway closure,” J. Appl. Physiol. 59, 1323 (1993)] and they do not change the successive shapes adopted by the liquid film as the instability develops [S. Kw...

A deeper insight into the dip coating process in the presence of insoluble surfactants: A numerical analysis

A numerical investigation is carried out to study the effects of an insoluble surfactant on the dip coating of a flat substrate. Predictions of both the film thickness and the concentration of surfactant in the film as a function of the capillary number compare well with the solutions of a simpler asymptotic model based on the lubrication approximation. Streamline patterns confirm the existence of a stagnation point located in the bulk phase in the region of the dynamic meniscus—a conjecture postulated forty years ago. The evolution of the flow patterns and the interfacial variables shows how the classical result of Landau and Levich is recovered as the coating speed is augmented. Finally, we show that the effect of inertia forces cannot be neglected when the viscosity of the coating liquid is low.

A gas phase displacing a liquid with soluble surfactants out of a small conduit: The plane case

In this work we report the actions of soluble surfactants when a liquid contained between parallel plates is being displaced by a steadily moving gas phase. For that purpose the full Navier–Stokes equations are solved together with surfactant mass balances at the interface, as well as in the liquid phase. The influence of the different relevant dimensionless parameters is described and analyzed for capillary numbers within the range 10−4–1; these results proved to be in good agreement with those obtained by Ratulowski and Chang for very low values of the capillary number. Besides, the bulk and interfacial distribution of surfactants along with the corresponding flow fields are shown for several values of the elasticity and Peclet numbers.

Elastic effects of an insoluble surfactant on the onset of two-dimensional Faraday waves: a numerical experiment

The elastic effects of an insoluble surfactant on the formation and evolution of two-dimensional Faraday waves is investigated numerically. We analyse the influence of the elasticity of the surface-active agent on the amplitude of the vertical vibration needed to excite two-dimensional standing waves on the free surface. The numerical solutions show that the interface is always subharmonically excited at the onset and that the presence of the surfactant requires a higher external force to induce standing waves. They also show that the magnitude of the external amplitude is related to the temporal phase shift that exists between the evolution of the surfactant concentration and the free-surface shape. A detailed description of the time-varying velocity fields and interfacial distribution of surfactants helps to provide insight into the mechanisms ruling the phenomenon.

Simplified models of flexible blade coating

Abstract Two closed-form models of flexible blade coating, named “A” and “B”, are presented; they derive from a more realistic one which requires numerical solution and which is used here as standard. The governing equations of the models are simply nonlinear algebraic expressions, yet they exhibit the elastohydrodynamic quality of the system. Both models approach the standard one in the limit of small blade deformation and, at low values of the loading, they provide an upper and a lower bound on the results from the standard model. Model “B” reproduces the general behavior of blade coating systems; it also predicts quite well—at least for the results presented here—the thinnest film deposited by the blade.

The influence of inertia and contact angle on the instability of partially wetting liquid strips: A numerical analysis study

The stability of a thread of fluid deposited on a flat solid substrate is studied numerically by means of the Finite Element Method in combination with an Arbitrary Lagrangian-Eulerian technique. A good agreement is observed when our results are compared with predictions of linear stability analysis obtained by other authors. Moreover, we also analysed the influence of inertia for different contact angles and found that inertia strongly affects the growth rate of the instability when contact angles are large. By contrast, the wave number of the fastest growing mode does not show important variations with inertia. The numerical technique allows us to follow the evolution of the free surface instability until comparatively late stages, where the filament begins to break into droplets. The rupture pattern observed for several cases shows that the number of principal droplets agrees reasonably well with an estimation based on the fastest growing modes.