Film junction effect on foam drainage

Foam drainage is modelled by the flow of liquid through Plateau borders (PBs) that are the liquid channels resulting from the merging of three liquid films separating the gas bubbles. Available models generally neglect the influence of these films. Yet, within drainage conditions, experimental observations indicate a strong coupling of these films with the channels. We consider the influence of films on foam drainage through their effect on the cross-section geometry of the channels. More precisely, we assume that the Plateau border cross-section is enclosed by three circular arcs that are not always tangent but instead exhibit a non-zero contact angle θ as it has been observed experimentally. The liquid flow through the channels is studied using numerical simulations whose parameters are θ and the Boussinesq number, Bo, that reflects the surface shear viscosity of the interface. We show that, for values of Bo relevant for foam drainage conditions, a slight increase of θ results in a strong decrease of the average liquid velocity.     

Model for Plateau border drainage of power-law fluid with mobile interface and its application to foam drainage

A model for drainage of a power-law fluid through a Plateau border is proposed which accounts for the actual Plateau border geometry and interfacial mobility. The non-dimensionalized Navier-Stokes equations have been solved using finite element method to obtain the contours of velocity within the Plateau border cross section and average Plateau border velocity in terms of dimensionless inverse surface viscosity and power-law rheological parameters. The velocity coefficient, the correction for the average velocity through a Plateau border of actual geometry compared to that for a simplified circular geometry of the same area of cross section, was expressed as a function of dimensionless inverse surface viscosity and flow behavior index of the power-law fluid. The results of this improved model for Plateau border drainage were then incorporated in a previously developed foam drainage model [G. Narsimhan, J. Food Eng. 14 (1991) 139] to predict the evolution of liquid holdup profiles in a standing foam. Foam drainage was found to be slower for actual Plateau border cross section compared to circular geometry and faster for higher interfacial mobility and larger bubble size. Evolution of liquid holdup profiles in a standing foam formed by whipping and stabilized by 0.1% beta-lactoglobulin in the presence of xanthan gum when subjected to 16g and 45g centrifugal force fields was measured using magnetic resonance imaging for different xanthan gum concentrations. Drainage resulted in the formation of a separate liquid layer at the bottom at longer times. Measured bubble size, surface shear viscosity of beta-lactoglobulin solutions and literature values of power-law parameters of xanthan gum solution were employed in the current model to predict the evolution of liquid holdup profile which compared well with the experimental data. Newtonian model for foam drainage for zero shear viscosity underpredicted drainage rates and did not agree with the experimental data.     

Liquid drainage in single plateau borders of foam

This paper reports on an investigation of the influence of the interfacial shear viscosity on the liquid drainage in single Plateau borders of foam. The simplified Navier-Stokes equation governing the liquid flow is solved for the liquid velocity by the numerical computational method. The numerical results show significant influence of the interfacial shear viscosity on the liquid velocity in the Plateau border. Comparison of the numerical results for the average velocity over the cross-section area of the Plateau border to the available analytical solution shows that the available analytical solution underestimates the average velocity. New, simple yet accurate correlations for the dependence of the average velocity on the radius of the cross section of the Plateau border, the pressure gradient, and the interfacial shear viscosity are obtained using the asymptotic analysis and the numerical data.     

Modeling oil droplets in plateau borders

It is widely known that oil droplets can decrease the stability of aqueous films and foams. While less widely recognized, it has also been observed that oil droplets can, under certain circumstances, increase the stability of foams, especially if they are caught in the Plateau borders. In this paper, how the oil droplet deforms and is, in turn, deformed by the Plateau border is modeled using Surface Evolver. The two dimensionless parameters that affect these shapes are the size of the oil droplet relative to the Plateau border and the ratio of the oil-water interfacial tension to the air-water interfacial tension. The calculated pressures in all the phases were used to obtain the pressure exerted on the oil-water-air pseudoemulsion film, which allows the factors that influence the stability of these droplets in the Plateau border to be investigated. The final section of the paper demonstrates that the presence of an oil droplet in a Plateau border can have a major influence on the drainage of the aqueous phase along the Plateau border. This retardation of the flow would result in the oil droplets in the Plateau borders increasing the stability of foams in which they are found.     

Foam drainage on the microscale I. Modeling flow through single Plateau borders

The drainage of liquid through a foam involves flow in channels, also called Plateau borders, which generally are long and slender. We model this flow by assuming the flow is unidirectional, the shear is transverse to the flow direction, and the liquid/gas interfaces are mobile and characterized by a Newtonian surface viscosity, which does not depend on the shear rate. Numerical finite difference simulations are performed, and analytical approximations for the velocity fields inside the channels and the films that separate the bubbles are given. We compare the liquid flow rates through interior channels, exterior channels (i.e., channels contacting container walls) and films. We find that when the number of exterior channels is comparable to the number of interior channels, i.e., narrow container geometries, the exterior channels can significantly affect the dynamics of the drainage process. Even for highly mobile interfaces, the films do not significantly contribute to the drainage process, unless the amount of liquid in the films is within a factor of ten of the amount of liquid in the channels.     

Foam drainage

This review focuses on recent works on foam drainage + including both the advanced theoretical and experimental studies into foam drainage, standard and extended drainage theories with analytical and numerical solutions. Highlights of recent works include the effect of physico-chemical properties of the gas–liquid interface on foam drainage, and the foam-structure related properties governing the channel-and node-dominated drainage regimes. Important results obtained using the foam pressure drop technique which allows a systematic investigation of foam drainage with the constant and varying Plateau border radius are discussed. The free and forced drainage methods have also been the useful experimental techniques for revealing two important drainage regimes by the channels and the nodes. Finally, the influence of the syneresis on the foam stability and destruction is reviewed.     

Decay of standing foams: drainage,coalescence and collapse

A summary of recent theoretical work on the decay of foams is presented. In a series of papers, we have proposed models for the drainage, coalescence and collapse of foams with time. Each of our papers dealt with a different aspect of foam decay and involved several assumptions. The fundamental equations, the assumptions involved and the results obtained are discussed in detail and presented within a unified framework.Film drainage is modeled using the Reynolds equation for flow between parallel circular disks and film rupture is assumed to occur when the film thickness falls below a certain critical thickness which corresponds to the maximum disjoining pressure. Fluid flow in the Plateau border channels is modeled using a Hagen-Poiseuille type flow in ducts with triangular cross-section.The foam is assumed to be composed of pentagonal dodecahedral bubbles and global conservation equations for the liquid, the gas and the surfactant are solved to obtain information about the state of the decaying foam as a function of time. Homogeneous foams produced by mixing and foams produced by bubbling (pneumatic foams) are considered. It is shown that a draining foam eventually arrives at a mechanical equilibrium when the opposing forces due to gravity and the Plateau-border suction gradient balance each other. The properties of the foam in this equilibrium state can be predicted from the surfactant and salt concentration in the foaming solution, the density of the liquid and the bubble radius.For homogeneous foams, it is possible to have conditions under which there is no drainage of liquid from the foam. There are three possible scenarios at equilibrium: separation of a single phase (separation of the continuous phase liquid by drainage or separation of the dispersed phase gas via collapse), separation of both phases (drainage and collapse occurs) or no phase separation (neither drainage nor collapse occurs). It is shown that the phase behavior depends on a single dimensionless group which is a measure of the relative magnitudes of the gravitational and capillary forces. A generalized phase diagram is presented which can be used to determine the phase behavior.For pneumatic foams, the effects of various system parameters such as the superficial gas velocity, the bubble size and the surfactant and salt concentrations on the rate of foam collapse and the evolution of liquid fraction profile are discussed. The steady state height attained by pneumatic foams when collapse occurs during generation is also evaluated.Bubble coalescence is assumed to occur due to the non-uniformity in the sizes of the films which constitute the faces of the polyhedral bubbles. This leads to a non-uniformity of film-drainage rates and hence of film thicknesses within any volume element in the foam. Smaller films drain faster and rupture earlier, causing the bubbles containing them to coalesce. This leads to a bubble size distribution in the foam, with the bubbles being larger in regions where greater coalescence has occurred.The formation of very stable Newton black films at high salt and surfactant concentrations is also explained.     

Integrated single-walled carbon nanotube/microfluidic devices for the study of the sensing mechanism of nanotube sensors

A method to fabricate integrated single-walled carbon nanotube/microfluidic devices was developed. This simple process could be used to directly prepare nanotube thin film transistors within the microfluidic channel and to register SWNT devices with the microfludic channel without the need of an additional alignment step. The microfluidic device was designed to have several inlets that deliver multiple liquid flows to a single main channel. The location and width of each flow in the main channel could be controlled by the relative flow rates. This capability enabled us to study the effect of the location and the coverage area of the liquid flow that contained charged molecules on the conduction of the nanotube devices, providing important information on the sensing mechanism of carbon nanotube sensors. The results showed that in a sensor based on a nanotube thin film field effect transistor, the sensing signal came from target molecules absorbed on or around the nanotubes. The effect from adsorption on metal electrodes was weak.     

Electrohydrodynamic conduction pumps with cylindrical electrodes for pumping of dielectric liquid film in an open channel

In the present study, electrohydrodynamic conduction pumping of n-hexane and n-decane liquid films in an open channel has been investigated experimentally. These two dielectric liquids have nearly the same electrical properties but with their different viscosities. The effects of film thicknesses, the arrangement of electrodes and the gap between pumps on the flow rate of liquid films have been also studied. The pumps with cylindrical electrodes have been installed in the channel. The best performance of the conduction pumps, revealing with experimental results, has been achieved at 8 mm thickness of liquid film with the gap size of 55 mm for both dielectric liquids in the present layout of the pumps.     

The titration of clay minerals I. Discontinuous backtitration technique combined with CEC measurements

Evolution of liquid holdup profile in a standing foam formed by whipping and stabilized by sodium caseinate in the presence of xanthan gum when subjected to 16 and 29g centrifugal force fields was measured using magnetic resonance imaging for different pH, ionic strength, protein and xanthan gum concentrations. Drainage resulted in the formation of a separate liquid layer at the bottom at longer times. Foam drainage was slowest at pH 7, lower ionic strength, higher protein and gum concentrations. Foam was found to be most stable at pH 5.1 near the isoelectric point of protein, lower ionic strength and higher protein and xanthan gum concentrations. A predicted equilibrium liquid holdup profile based on a previous model (G. Narsimhan, J. Food Eng. 14 (1991) 139) agreed well with experimental values at sufficiently long times. A proposed model for velocity of drainage of a power law fluid in a Plateau border for two different simplified geometries was incorporated in a previously developed model for foam drainage (G. Narsimhan, J. Food Eng. 14 (1991) 139) to predict the evolution of liquid holdup profiles. The model predictions for simplified circular geometry of Plateau border compared well with the experimental data of liquid holdup profiles at small times. At longer times, however, the predicted liquid holdup profile was larger than the observed, this discrepancy being due to coarsening of bubble size and decrease in foam height not accounted for in the model. A Newtonian model for foam drainage under predicted drainage rates did not agree with the experimental data.     

Lattice Poisson-Boltzmann simulations of electro-osmotic flows in microchannels

This paper presents the numerical results of electro-osmotic flows in micro- and nanofluidics using a lattice Poisson-Boltzmann method (LPBM) which combines a potential evolution method on discrete lattices to solve the nonlinear Poisson equation (lattice Poisson method) with a density evolution method on discrete lattices to solve the Boltzmann-BGK equation (lattice Boltzmann method). In an electrically driven osmotic flow field, the flow velocity increases with both the external electrical field strength and the surface zeta potential for flows in a homogeneous channel. However, for a given electrical field strength and zeta potential, electrically driven flows have an optimal ionic concentration and an optimum width that maximize the flow velocity. For pressure-driven flows, the electro-viscosity effect increases with the surface zeta potential, but has an ionic concentration that yields the largest electro-viscosity effect. The zeta potential arrangement has little effect on the electro-viscosity for heterogeneous channels. For flows driven by both an electrical force and a pressure gradient, various zeta potential arrangements were considered for maximize the mixing enhancement with a less energy dissipation.     

Bubble motion measurements during foam drainage and coarsening

We have studied bubble motion within a column of foam allowed to undergo free drainage. We have measured bubble motion upward with time and as a function of their initial positions. Depending on the gas used, which sets the coarsening and drainage rates, different bubble upward motion types have been identified (constant speed, acceleration or deceleration) and explained in relation with liquid downward flows. The proofs of the consistency between bubble upward motion and liquid downward flow are obtained both by comparing the bubble motion curves to the liquid drainage ones, and by comparing the time variations of the liquid fraction extracted from bubble motion to direct liquid fraction measurements by electrical conductimetry. The agreement between bubble position tracking and electrical conductivity shows in particular that it is possible to determine the drainage regime from such simple bubble motion measurements. This work also allowed us to demonstrate a special case of foam coarsening and expansion, occurring when the foam gas is less soluble than the outside one, caused by diffusion of this external gas into the foam. All these results allow us to build a picture of drainage and coarsening seen from the bubble point of view.     

Plane hydrodynamic flow in thin free suspended nematic liquid crystal films

Abstract

Radial hydrodynamic flows in free suspended films (with thickness h ≥ 20 μm) of some liquid crystal materials was observed in a narrow temperature range before the line nematic-smectic C transition. The observed flows are explained by a non-linear temperature dependence of the surface tension (Marangoni effect).

Upon thinning the liquid crystal films to a thickness 6 μ < h < 20 μm the hydrodynamic flow changes its character: instead of radial flow with sinking seeding particles we observe two circular plane hydrodynamic flows symmetrical to the film's diameter. The temperature distribution in the free film and the surface tension field are discussed. A model for the established circular flows in thin liquid crystal films is presented.     

Rheology of particulate rafts,films, and foams

Liquid foam exhibits remarkable rheological behavior although it is made with simple fluids: it behaves similar to a solid at low shear stress but flows similar to a liquid above a critical shear stress. Such properties, which have been proved to be useful for many applications, are even enhanced by adding solid particles. Depending on their hydrophobicity and size, the particles can have different geometrical configurations at the mesoscopic scale, that is, at the air–liquid interfaces, in the films, or in the interstices between the bubbles. In this review, we present rheological studies performed on granular rafts and films, on spherical armored interfaces, on gas marbles, and on aqueous foams laden with hydrophilic grains.     

Sustained superhydrophobic friction reduction at high liquid pressures and large flows

This Article introduces and experimentally explores a novel self-regulating method for reducing the friction losses in large microchannels at high liquid pressures and large liquid flows, overcoming previous limitations with regard to sustainable liquid pressure on a superhydrophobic surface. Our design of the superhydrophobic channel automatically adjusts the gas pressure in the lubricating air layer to the local liquid pressure in the channel. This is achieved by pneumatically connecting the liquid in the microchannel to the gas-pockets trapped at the channel wall through a pressure feedback channel. When liquid enters the feedback channel, it compresses the air and increases the pressure in the gas-pocket. This reduces the pressure drop over the gas-liquid interface and increases the maximum sustainable liquid pressure. We define a dimensionless figure of merit for superhydropbic flows, W(F) = P(L)D/γ cos(θ(c)), which expresses the fluidic energy carrying capacity of a superhydrophobic microchannel. We experimentally verify that our geometry can sustain three times higher liquid pressure before collapsing, and we measured better friction-reducing properties at higher W(F) values than in previous works. The design is ultimately limited in time by the gas-exchange over the gas-liquid interface at pressures exceeding the Laplace pressure. This method could be applicable for reducing near-wall laminar friction in both micro and macro scale flows.     

Stability of aqueous foam films and foams containing polymers: Discrepancies between different length scales

Polymer-stabilized foams and foam films have received considerable attention during the past years. This review paper gives an overview of recent studies dealing with polyelectrolyte/surfactant mixtures, proteins, and microgels adsorbed at single air/water interfaces, in foam films and in macroscopic foams. These polymeric systems have in common that their structure or shape changes when adsorbing at an air/water interface. These structural changes in comparison to their bulk behavior greatly influence the properties of foam films and foams. Regarding the foam stability, formation of adsorbed layers or aggregates plays an important role. The discrepancy between stabilization of macroscopic foams and destabilization of single foam films might be attributed to the blockage of Plateau borders and, therefore, slowed down drainage. Another important parameter is the interfacial viscoelasticity.     

The Acoustics of Liquid Foams

Beside other transport properties of liquid foams, like the optical or electrical ones, the acoustics of liquid foams reveals a great complexity and non-trivial features. Here we present a review of recent experimental and theoretical results on how a sound wave interacts with either a macroscopic foam sample or with its isolated building blocks (films and Plateau borders). The analysis of the literature allows us to determine what is now well understood, what could be measured in foams by acoustics, and what are the remaining issues and perspectives in this research field.     

Effect of powder oxide content on the expansion and stability of PM-route Al foams

The oxide content in Al powders has been found to have a significant effect on the expansion and stability of foams made via a PM route. With low oxide contents (O<0.3 wt%) expansion is moderate and the foam structure is unstable. Larger expansions, improved foam stability and more homogeneous foam structures are achieved if the amount of oxide in the powder is moderate (O=0.3-0.6 wt%). Foaming precursors with excessive oxide contents (O>0.6 wt%) results in small expansions but very stable foam structures. Oxides were observed to form clusters of crumpled films, which at higher levels form a network which restricts the drainage of liquid from the cell walls and Plateau borders, but which also inhibit foam expansion. Oxide clusters in the cell walls lead to a decrease in the minimum cell wall thickness, resulting in an increase in foam expansion.     

Influence of Foam Apparent Viscosity and Viscoelasticity of Liquid Films on Foam Stability

The objective of this research work was to study the relationship among the apparent viscosity of bulk foam, the viscoelasticity of liquid films, and foam stability. Bulk foam tests showed that the drainage half-life of AOS foam was higher than that of sodium dodecyl sulfate (SDS) and hexadecyltrimethyl ammonium bromide (CTAB) foams. The results of foam apparent viscosity revealed that the foam apparent viscosity was related to foam quality rather than foam stability. Higher film viscoelasticity modulus could be assigned for α -olefin sulfonate (AOS) films than those for SDS and CTAB ones. The film conductivity tests indicated that AOS liquid films, compared with SDS and CTAB liquid films, could delay the liquid drainage speed under dynamic conditions. Compared with foam apparent viscosity, the viscoelasticity of liquid films appeared to be a key factor in foam stability.