Session RM: Free Surface Flows: Interfacial Phenomena

Transition between a film flowing down a slope and a liquid sheet floating on a denser fluid: where is the grounding line?

We have investigated experimentaly and with analytical calculations, the flow of a viscous liquid down a incline entering suddenly a liquid bath of higher density. This leads to the formation of a liquid sheet floating on the bath, the line of intersection of the substrate and liquid/liquid interface being called the grounding line in litterature relative to ice field formation. At long enough time, and for small enough substrate inclination, the position of the grounding line and the angle of detachment of the flow are given by very simple expressions, that are in good agreement with our experiments. This angle of detachment depends only on the substrate inclination and on the relative density mismatch, while the distance between the grounding line and the initial shore position is proportional to the inverse of the inclination angle.   

Formation of dynamic coherent structures by an ensemble of rigid particles

We report numerical studies of the surprising effect of formation of coherent particulate structures in the thermocapillary liquid bridge flow. The studied regimes of the flow are characterized by a hydrothermal wave travelling in the azimuthal direction. Although formation of those structures was discovered experimentally more than a decade ago, until now it has remained unexplained and was not reproduced numerically in physically realistic regimes. The particles are small (with Stokes number of the order of 10-6) and non-obtrusive. Usually such particles are expected to follow the flow. However, under certain conditions they create stable coherent structures. Those structures are dynamic and rotate azimuthally together with the travelling wave. The results reported are counterparts of our theoretical study of the physical mechanism leading to the formation of particulate coherent structures.   

Transition from Selective Withdrawal to Light Layer Entrainment in an Oil-Water System

Selective withdrawal refers to the selective removal of fluid of one density without entraining an adjacent fluid layer of a different density. Most prior literature has examined removal of the lower density fluid and the transition to entraining the higher density fluid. In the present experiments, a higher density liquid is removed through a tube that extends just below its interface with a lower density fluid. The critical depth for a given flow rate at which the liquid-liquid interface transitions to entrain the lighter fluid was measured. Experiments were performed for a range of different light layer silicone oils and heavy layer water or brine, covering a range of density and viscosity ratios. Applications include density-stratified reservoirs and brine removal from oil storage caverns. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.   

The effect of spreading on vertically directed jet impinging a sharp density interface

A large existing body of literature categorizes the flow behavior of negatively buoyant jets and fountains and characterizes their flow structure into distinct regimes and their maximum penetration depth predominately as a function of the Richardson number. In the present study, similar flow regimes have been identified and determined to be a function of Richardson number based on jet properties at the interface. This ``interface Richardson number'' increases as the jet is separated from the interface based on a jet spreading factor. The study uses immiscible fluids (silicone oil and a glycerin water mixture) with matched indices of refraction.   

Drop orbiting in a circular hydraulic jump

In our experiment, a circular hydraulic jump is formed by a viscous jet impacting a horizontal or slightly tilted glass disk. A drop of the same liquid, deposited in the jump does not coalesce, and remains trapped at its periphery, because of the air entrainment linked to the high drop rotation speed. In this strange state of non-wetting, a gyroscopic instability occurs that tends to induce orbital motions of the drop around the jump perimeter. For a slightly inclined substrate, the drop oscillates around the lowest equilibrium position, while for a rigorously horizontal disk, the drop exhibits two distinct motions depending on the ratio between drop and jump radius: (1) a orbital motion at constant speed, and (2) a irregular (chaotic?) motion involving random inversions of the velocity. A simple model in which the drop is treated as a rigid sphere sliding on the free surface of the liquid allows us to recover the orbital motion, but not the irregular phase, that seems to involve distorsions of the jump shape.   

Application of geometric shock dynamics to a circular hydraulic jump

When a vertical jet of fluid strikes a horizontal plate, a circular hydraulic jump is often observed. Despite its apparent simplicity, the hydraulic jump exhibits features which are still poorly understood, the most striking of which is the instability of the circular shape with the resultant formation of stationary or spinning polygonal jumps. Here we investigate the phenomenon within the framework of shallow-water approximation by means of the geometric shock dynamics approach of Whitham. The theoretical predictions will be related with the available experimental observations.   

Experimental results on evaporation waves

A liquid contained in a vertical glass tube is suddenly depressurized from a high initial pressure down to one for which the stable state is vapour, so vaporization sets off at the free surface. For large enough evaporation rates, the planar vapour-liquid interface is Darrieus-Landau unstable [1], leading to the interface surface rippling close to the instability threshold. Further increasing the initial to final pressure ratio brings about evaporation waves [2,3], in which a highly corrugated front propagates downwards into the liquid. A new experimental method is presented as well as some experimental results obtained by tracking the evolution of the front with a high speed camera. In addition, a number of new phenomena related to the dynamics of bubbles growth at the walls has been uncovered. In particular, a new mode of propagation of the evaporation front is found. In this mode the front originates from below the interface, so the propagation is upwards against gravity with a curved but smooth front.\\[4pt] [1] F. J. Higuera, Phys. Fluids, V. 30, 679 (1987).\\[0pt] [2] J.E.Shepherd and B.Sturtevant, J.Fluid Mech., V.121,379 (1982).\\[0pt] [3] P.Reinke and G.Yadigaroglu, Int.J.Multiph. Flow, V.27,1487 (2001).   

Effective Free Surfaces

In this investigation we introduce the concept of an ``effective free surface'' arising as a solution of time--averaged equations in the presence of free boundaries. This work is motivated by applications of optimization theory to problems involving free surfaces, such as droplets impinging on the weld pool surface in welding processes. In such problems the time--dependent governing equations lead to technical difficulties, many of which are alleviated when methods of optimization are applied to a steady problem with effective free surfaces. The corresponding equations are obtained by performing the Reynolds decomposition and averaging of the time--dependent free--boundary equations based on the volume--of--fluid (VoF) formalism. We identify the terms representing the average effect of fluctuating free boundaries which, in analogy with the Reynolds stresses in classical turbulence models, need to be modelled and propose some simple algebraic closures for these terms. We argue that effective free boundaries can be computed using methods of shape optimization and present some results.