Session FF: Drops and Bubbles IV

Viscous effects in drop impact

We investigate the onset of splash for a viscous drop impacting a solid surface. The simulation is based on the volume-of-fluid methods of Popinet and Zaleski [Int.\ J.\ Numer.\ Meth.\ Fluids \textbf{30}, 775-793 (1999)] and tracks the interface evolution explicitly. The qualitative shape evolution and the quantitative spreading dynamics are examined and compared against available experimental results.   

Drop Impact of a Shear-Thinning Fluid

The impact of a liquid drop onto a solid surface is an event ubiquitous in a wide range of natural and industrial processes, and thus has been extensively studied. While nearly all research has focused on characterizing the impact of a Newtonian fluid drop, recent experimental work has demonstrated that non-Newtonian effects, and in particular elasticity, can dramatically affect drop impact behaviour. In this work, we take a first step towards characterizing non-Newtonian drop impact, by examining the spread of a drop of shear-thinning fluid. The approach is computational: we have developed an axisymmetric VOF model of drop impact, that incorporates recently developed approaches to interface reconstruction and the modeling of surface tension, and includes a Cross model of shear-thinning behaviour. A series of drop impact simulations were run, systematically varying each of the three parameters of the Cross model to examine the influence of shear-thinning on the overall behaviour of the droplet during spread. The results were then fit to a Newtonian correlation for maximum spread (a function of the Reynolds and Weber numbers), by modifying the Reynolds number by introducing a viscosity calculated from a characteristic shear rate.   

Drop-interface partial coalescence in polymeric fluids

A drop falling onto a fluid-fluid interface may not merge with it at once but undergo a so-called partial coalescence cascade. We will discuss recent experimental observations and numerical simulations of this phenomenon for Newtonian as well as polymeric fluids. In Newtonian fluids, the partial coalescence takes place for an intermediate range of drop sizes and consists of viscous, inertio-capillary and gravity regimes. Viscoelasticity in either the drop or the ambient fluid tends to delay the pinch-off of the secondary drop, and may even suppress partial coalescence altogether. The underlying mechanism is large tensile polymer stresses resisting the stretching and thinning of the fluid neck. The numerical results are in qualitative, and in some cases quantitative, agreement with experiments.   

Motion of a Drop above an Evaporating Liquid-Gas Interface

Motion of a drop above a planar evaporating liquid-gas interface is consedered. Thermal gradients in the gas and liquid phases result in Marangoni flows that govern the drop motion. Using bi-spherical coordinates, the equations of motion and diffusion of vapor and heat are solved in the Stokes and zero Peclet number approximations, respectively, and the drop velocity is found as a function of the separation distance from the planar interface. It is shown that, in the absence of gravity, there is a critical distance below which the drop moves towards the interface and above which it moves away from it. In the presence of gravity, there can be two critical distances, the smaller stable and the larger unstable, the latter corresponding to a drop levitating above the planar interface in a state when the gravity, Marangoni and lubrication forces are balanced. These results can explain some experimental observations of microscopic water drops condensing above the surface of evaporating liquid films.   

Bouncing droplets on a vibrated liquid/gaz interface

The coalescence of a droplet onto a planar liquid/air interface can be delayed by vertically vibrating the bath. Mechanisms that make the droplet bounce on the interface are investigated experimentally, by observing vertical trajectories of the droplet and interference fringes due to the air film between the droplet and the bath. A finite lifetime is generally observed. A dynamical model based on surface deformations and viscous dissipations is proposed. It is able to reproduce the main features of droplet bouncing, and states when coalescence can be significantly delayed or not.   

A deeper analysis of the partial coalescence of a droplet onto a planar interface

The partial coalescence of a droplet onto a planar liquid/liquid interface is investigated theoretically by using a dimensional analysis. Three dimensionless parameters seem to play an important part: the Bond number, and the Ohnesorge numbers in both fluids. The impact of these parameters is assessed by the way of an experimental work on 2000 coalescence events. Global quantities such as the available surface energy has been measured. According to the experimental results, the viscosity does not dissipate energy in the same way in both fluids. The different dissipation mechanisms are discussed. Simple theoretical models are able to predict when partial coalescence has to occur. Finally, the maximum number of steps in the cascade is investigated. It seems that the biggest number of successive partial coalescences is about eleven. Possible applications of the partial coalescence in microfluidics are discussed.   

Model and experimental vizualisation of a bubble interacting with an inclined wall

We describe the motion of an air bubble rising through water as it interacts with a wall of variable inclination. The bubble diameter varies about O(1) mm. We use lubrication theory to determine the modification of the bubble interface and compute the hydrodynamic force exerted by the wall. The present work is an extension of Moraga et al's model [Computers and Fluids 2006], which was devised for a horizontal wall. The predictions of the model are checked against experimental visualizations. The influence of the Weber number, Reynolds number and wall inclination is examined   

Bubble impacts with microcantilevers.

In the current study, we investigate bubbles in laminar channel flows impacting microcantilever obstacles. Static and resonating cantilevers instrumented with integrated strain gages are mounted perpendicular to the mean flow in a vertically-oriented channel with thickness 2mm, span 10mm, and length 585 mm. Steady, fully-developed upward flows with channel Reynolds numbers based on mean fluid velocity and hydraulic diameter of 0-2500 are considered. Bubbles of diameter 200-1000$\mu $m are introduced upstream of the test section, and impacts are observed using a microscope equipped with a high frame rate camera. Observations are made along the length of cantilevers backlit with white light. Strain gage signals are monitored and correlated to impact events. The effect of obstacles on bubble motion and deformation as well as the effect of bubble impacts on the cantilever will be discussed. The flow studies are part of a larger research program examining reliability and performance of vibrating microbeams.