Session HQ: Instability: Interfacial and Thin-Film V

Drop formation from an unstable partially wetting fluid rivulet

We consider the formation of drops by the spontaneous breakup of an unstable liquid rivulet on a horizontal substrate under partial wetting conditions. We describe the dynamics by means of a model within the lubrication approximation that includes capillarity, van der Waals forces, and gravity. We focus on gravity effects for macroscopic rivulets, and on intermolecular forces for the nanoscopic case. We find the scaling law of the emerging distance between drops (formed after the breakup process) as a function of the rivulet cross-section area. Unlike the case of thin films, the numerical results for finite length rivulets show that there is no nucleation regime, and only spinodal instability develops. Finally, we apply this model to the study of a metalic rivulet of nanometric thickness, melted via pulsed laser radiation.   

Droplet deformation in a channel: viscoelastic effects

In this work, the influence of viscoelasticity on the deformation of a sessile droplet subjected to a pressure-driven flow in a channel is investigated experimentally. The droplet's response is examined using flow visualisation as a function of initial droplet volume, flow rate and elasticity. The results of our experiments are used to identify various flow regimes. These include low flow rate regimes wherein the droplets optimise their shapes in response to the flow before reaching a steady state. With increasing flow rate, droplets exhibit ``sliding'', ``crawling'', and detachment regimes. In the latter case, and due to large elastic contributions, droplets develop very long necks, which pinch off and recoil to join the remnants of the mother droplet. By plotting a ``flow map'' in the space of the Ohnesorge and Deborah numbers, transitions between each regime of deformation are identified.   

Surfactant-enhanced rapid spreading of drops on solid surfaces

We consider the surfactant-enhanced rapid spreading of drops on solid substrates. This work is conducted in connection with the ability of aqueous trisiloxane solutions to wet effectively highly hydrophobic substrates. We use lubrication theory to derive coupled advective-diffusion equations for surfactant transport to an interface equation. This model accounts for Marangoni stresses, diffusion, intermolecular forces, basal surfactant transport, micelle formation and break-up in the bulk, and sorptive fluxes at both the gas-liquid and liquid- solid interfaces; the model also employs appropriate surfactant equations of state. Our numerical results show the effect of basal adsorption and the mass of deposited surfactant on the deformation of the droplet and its spreading rate. We demonstrate that this rate is maximised for intermediate rates of basal adsorption and total surfactant mass. We also show that for a certain range of parameter values, the spreading is accompanied by pronounced rim formation, as previously observed experimentally. The stability of this rim to transverse disturbances is briefly explored.   

Dynamics of surfactants spreading on gel layers

Gel-like materials are of central importance to a large number of engineering, biological, biomedical and day-life applications. This work attempts to investigate the spreading of droplets of surfactant solutions on agar gels, which is accompanied by cracking of the gel layers. The cracking progresses via the formation of patterns that resemble ``starbursts,'' which have been reported recently in the literature by Daniels et al. Marangoni stresses generated by surface tension gradients between the surfactant droplet and the uncontaminated gel layer are identified to be the driving force behind these phenomena. The morphology and dynamics of the starburst patterns are investigated for droplets of different surfactant solutions, including sodiumdodecylsulphate, spreading on gel layers of different strengths. The instability is characterised in terms of the number of arms that form, and their mean width and length as a function of time. In addition, photoelasticity is used to provide information about the stress field of the material, which, combined with the results from our direct visualisation, can elucidate further the mechanisms underlying the pattern formation and the nature of the interactions between the liquid and the gel.   

Effects of dilution on elastohydrodynamic coating flow of an anti-HIV microbicide vehicle

Elastohydrodynamic lubrication over soft substrates characterizes the drug delivery of anti-HIV topical microbicides carried in gel vehicles. These gels are under development to prevent HIV transmission into vulnerable vaginal mucosa during intercourse. Their effectiveness depends on completeness and durability of coating, as well as on the active ingredients. Here we investigate the influence of dilution by vaginal fluid on the coating flows that serve to protect the user. The effects of dilution by vaginal fluid simulant are assessed through rheological experiments at variable dilution of the gel vehicle. This involves determination of the way parameters in a Carreau model of a shear-thinning gel are modified by dilution. The changes in coating are determined from a computational model, based on dilution rheology measured in the laboratory. The elastohydrodynamic lubrication model of Szeri, et al. Physics of Fluids (2008) is supplemented with a convective-diffusive transport equation to handle dilution, and solved using a multi-step scheme in a moving domain.   

Lift-Force-Driven Microfluidic Droplet Sorting Device

A long ($\sim $ 5-7 centimeters) rectangular micro channel is used to sort perfluorcarbon (PFC) droplets by size.This study is motivated by a novel gas embolotherapy technique which aims to treat cancer by infarcting tumors with gas emboli that are formed by selective acoustic vaporization of $\sim $6 micrometer, intravascular, PFC droplets. Droplets smaller and larger than $\sim $6-micrometer proved to be less effective, or even detrimental, in the gas embolotherapy. From a suspension of micro PFC droplets, the sorting device designed in this study eliminates droplets with higher and lower diameters than $\sim $6-micrometer. This is done by the use of a difference in lateral lift force (which depends on droplet diameter) that is exerted on the droplets. When a mixture of droplets is introduced at the entrance of a straight micro channel, larger droplets will tend to move to an equilibrium position at 0.6R, R being the half width of the channel, in shorter time and distance than smaller droplets. When splitting up the end of the channel in two smaller outer channels (which contain the large droplets) and one smaller inner channel (which contains the small droplets), the droplets can, in theory, be sorted with high accuracy. This work is supported by NIH grant R01EB006476.   

Viscous Fingering of Reactive Finite Slices in a Hele-Shaw Cell

Coupling of hydrodynamics and chemical reactions have been studied for a miscible reactive slice of fluid displaced by another fluid in a rectilinear Hele-Shaw cell. Under this configuration, one of the two reactants is sandwiched between two layers of the other one. Assuming an exponential dependency of viscosity on the solution concentrations, the fluid fronts at both ends of the finite slice may become unstable. Full nonlinear simulations are conducted to solve the continuity equation, the momentum balance equation in the form of Darcy's law, and a volume-averaged mass balance equation in the form of convection-diffusion-reaction equations for the transport of solute and solutions. Simulation results indicate the importance of the frontal instabilities on the disappearing rate of the reactant fluid in the slice. The effects of the viscosity ratios between the two reactants and chemical product on the finger structures, the slice distortion and chemical reaction progress are examined both qualitatively and quantitatively.   

Influence of miscible viscous fingering on an adsorbed solute dynamics

Viscous fingering between miscible fluids of different viscosities can affect the dispersion of finite width samples in porous media. We investigate here the influence of such VF due to a difference between the viscosity of the displacing fluid and that of the sample solvent on the spatio-temporal dynamics of the concentration of a passive solute initially dissolved in the injected sample and undergoing adsorption on the porous matrix. Such a three component system is modeled using Darcy's law for the fluid velocity coupled to mass-balance equations for the sample solvent and solute concentrations. Depending on the conditions of adsorption, the spatial distribution of the solute concentration can either be deformed by viscous fingering of the sample solvent concentration profiles or disentangle from the fingering zone. In the case of deformation by fingering, a parametric study is performed to analyze the influence of parameters such as the log-mobility ratio, the ratio of dispersion coefficients, the sample length and the adsorption retention parameter $k'$ on the widening of the solute concentration peak.