Dynamics of coarsening foams: accelerated and self-limiting drainage

The evolution of a foam is determined by drainage flow of the continuous (liquid) phase and coarsening (aging) of the dispersed phase (gas bubbles). Free-drainage experiments with slow- and fast-coarsening gases show markedly different dynamics and elucidate the importance of the coupling of the two effects. Strong coarsening leads to drainage times that are shorter (accelerated drainage) and independent of the initial liquid content (self-limiting drainage). A model incorporating the physics of both drainage and diffusive coarsening shows quantitative agreement with experiment.     

一维液态泡沫渗流实验研究及表面能和粘性耗散分析

液态泡沫由大量气泡密集堆积在微量表面活性剂溶液中形成，是远离平衡态的软物质. 泡沫强制渗流在微观上是指以恒定流率输入的液体在气泡间隙内的微流动过程，是影响泡沫稳定的主要因素之一. 采用在表面活性剂溶液中添加微量色素以显示泡沫中液体流动的方法，确定了透射率与液体分率的对应关系，测量得到了一维液态泡沫强制渗流中渗流波传播规律以及液体分率的演变规律；理论推导了泡沫基本单元，即开尔文单元结构(Kelvin cell)的粘性耗散能表达式，并依据Surface Evolver软件计算得到了不同液体分率时开尔文单元结构对应的的表面能，并计算出了与实验系统对应的开尔文单元结构的表面能和粘性耗散. 基于开尔文单元结构内液体分率演变的准静态假设，分析了表面能和粘性耗散的演变规律.     

Bubble rearrangement duration in foams near the jamming point

We investigate the dynamics of bubble rearrangements in coarsening foams, using a time-resolved multiple light scattering technique. We measure the average duration of such events as a function of the foam confinement pressure. Rearrangements slow down as the pressure is decreased toward the jamming point. Our results are explained by a scaling law based on the balance of pressure and Darcy flow, highlighting an analogy between wet foams with mobile interfaces and suspensions of hard grains.     

Enhanced drainage and coarsening in aqueous foams

Experiments are presented elucidating how the evolution of foam microstructure by gas diffusion from high to low pressure bubbles can significantly speed up the rate of gravitational drainage, and vice versa. This includes detailed data on the liquid-fraction dependence of the coarsening rate, and on the liquid-fraction and the bubble-size profiles across a sample. These results can be described by a "coarsening equation" for the increase of bubble growth rate for drier foams. Spatial variation of the average bubble size and liquid fraction can also affect the growth and drainage rates.     

Rheology of steady-state draining foams

We developed the foam drainage rheology technique in order to perform rheological measurements of aqueous foams at a set liquid fraction epsilon and fixed bubble radius R without the usual difficulties associated with fluid drainage and bubble coarsening. The shear stress exhibits a power-law dependence on strain-rate, tau approximately gamma[over]n where n approximately 0.2. The stress exhibits an inverse dependence on liquid content, tau approximately (1+h'epsilon)(-1), where h'=theta(10) exhibits a diminishing logarithmic trend with gamma[over]. We propose a model based upon film shearing as the dominant source of viscous dissipation.     

Monitoring foam coarsening using a computer optical mouse as a dynamic laser speckle measurement sensor

In this paper, we present an experimental approach to track coarsening process of foam using a computer optical mouse as a dynamic laser speckle measurement sensor. The dynamics of foam coarsening and rearrangement events cause changes in the intensity of laser speckle backscattered from the foam. A strong negative correlation between the average speed of the cursor and the evolution of bubble diameter was found. We used microscopic images to demonstrate that decrease in speed is related to increase in bubble size. The proposed set-up is not very expensive, is highly portable and can be used in laboratory measurements of dynamics in other kinds of opaque materials.     

Permeability of aqueous foams

We perform forced-drainage experiments in aqueous foams and compare the results with data available in the literature. We show that all the data can be accurately compared together if the dimensionless permeability of the foam is plotted as a function of liquid fraction. Using this set of coordinates highlights the fact that a large part of the published experimental results corresponds to relatively wet foams ( ∼ 0.1 . Yet, most of the foam drainage models are based on geometrical considerations only valid for dry foams. We therefore discuss the range of validity of the different models in the literature and their comparison to experimental data. We propose extensions of these models considering the geometry of foam in the relatively wet-foam limit. We eventually show that if the foam geometry is correctly described, forced drainage experiments can be understood using a unique parameter --the Boussinesq number.     

Heterogeneous dynamics of coarsening systems

We show by means of experiments, theory, and simulations that the slow dynamics of coarsening systems displays dynamic heterogeneity similar to that observed in glass-forming systems. We measure dynamic heterogeneity via novel multipoint functions which quantify the emergence of dynamic, as opposed to static, correlations of fluctuations. Experiments are performed on a coarsening foam using time-resolved correlation, a recently introduced light scattering method. Theoretically we study the Ising model, and present exact results in one dimension, and numerical results in two dimensions. For all systems the same dynamic scaling of fluctuations with domain size is observed.     

Steady drainage in emulsions: corrections for surface Plateau borders and a model for high aqueous volume fraction

We compare extensive experimental results for the gravity-driven steady drainage of oil-in-water emulsions with two theoretical predictions, both based on the assumption of Poiseuille flow. The first is from standard foam drainage theory, applicable at low aqueous volume fractions, for which a correction is derived to account for the effects of the confinement of the emulsion. The second arises from considering the permeability of a model porous medium consisting of solid sphere packings, applicable at higher aqueous volume fractions. We find quantitative agreement between experiment and the foam drainage theory at low aqueous volume fractions. At higher aqueous volume fractions, the reduced flow rate calculated from the permeability theory approaches the master curve of the experimental data. Our experimental data demonstrates the analogy between the problem of electrical flow and liquid flow through foams and emulsions.     

Origin of the slow linear viscoelastic response of aqueous foams

We have studied the slow linear viscoelastic response of wet aqueous foams by macroscopic creep compliance measurements, combined to a diffusing-wave spectroscopy investigation of the local dynamics. The data strongly suggest that this rheological response arises from two distinct relaxation mechanisms: The first is due to the coarsening induced bubble rearrangements and governs the steady-state creep; the second results from the interplay between surface tension and surface viscosity of the gas-liquid interfaces and gives rise to a transient relaxation.     

Numerical simulations of two-dimensional foam by the immersed boundary method

In this paper, we present an immersed boundary (IB) method to simulate a dry foam, i.e., a foam in which most of the volume is attributed to its gas phase. Dry foam dynamics involves the interaction between a gas and a collection of thin liquid-film internal boundaries that partition the gas into discrete cells or bubbles. The liquid-film boundaries are flexible, contract under the influence of surface tension, and are permeable to the gas, which moves across them by diffusion at a rate proportional to the local pressure difference across the boundary. Such problems are conventionally studied by assuming that the pressure is uniform within each bubble. Here, we introduce instead an IB method that takes into account the non-equilibrium fluid mechanics of the gas. To model gas diffusion across the internal liquid-film boundaries, we allow normal slip between the boundary and the gas at a velocity proportional to the (normal) force generated by the boundary surface tension. We implement this method in the two-dimensional case, and test it by verifying the von Neumann relation, which governs the coarsening of a two-dimensional dry foam. The method is further validated by a convergence study, which confirms its first-order accuracy.     

Recirculation model for liquid flow in foam channels

Although extensively studied in the past, drainage of aqueous foams still offers major unaddressed issues. Among them, the behaviour of foam films during drainage has great significance as the thickness of the films is known to control the Ostwald ripening in foams, which in turn impacts liquid drainage. We propose a model relating the films’ behavior to the liquid flow in foam channels. It is assumed that Marangoni-driven recirculation counterflows take place in the transitional region between the foam channel and the adjoining films, and the Gibbs elasticity is therefore introduced as a relevant parameter. The velocity of these counterflows is found to be proportional to the liquid velocity in the channel. The resulting channel permeability is determined and it is shown that Marangoni stresses do not contribute to rigidify the channel’s surfaces, in strong contrast with the drainage of horizontal thin liquid films. New experimental data are provided and support the proposed model.     

Shear-induced stress relaxation in a two-dimensional wet foam

We report on experimental measurements of the flow behavior of a wet, two-dimensional foam under conditions of slow, steady shear. The initial response of the foam is elastic. Above the yield strain, the foam begins to flow. The flow consists of irregular intervals of elastic stretch followed by sudden reductions of the stress, i.e., stress drops. We report on the distribution of the stress drops as a function of the applied shear rate. We also comment on our results in the context of various two-dimensional models of foams.     

Influence of Vertical Foam Flow Liquid Drainage on Tube Bundle Heat Transfer Intensity

The results of an experimental investigation of staggered tube bundle heat transfer to upward and downward moving vertical foam flow are presented in this article. It was determined that a dependency exists between tube bundle heat transfer intensity on foam volumetric void fraction, foam flow velocity and direction, and liquid drainage from foam. In addition to this, the influence of tube position of the bundle on heat transfer was investigated. Experimental results were summarized by criterion equations, which can be applied in the design of foam type heat exchangers.     

Uniform foam production by turbulent mixing: new results on free drainage vs. liquid content

An apparatus is described for rapidly producing large quantities of foam via turbulent mixing of gas with a narrow jet of a surfactant solution inside a delivery tube. By controlling relative flow rates, the gas volume fraction in the resulting foam may be easily varied across . Using such foams, we present a comprehensive set of data for free drainage as a systematic function of gas fraction and sample geometry. The qualitative behavior can be understood in terms of simple theoretical considerations, emphasizing the importance of controlling the initial foam conditions. Quantitative features are compared with two approximate versions of the drainage equation, highlighting the crucial role of capillarity for very dry foams and small samples. Received 15 February 1999     

Self-assembly of two-dimensional islands via strain-mediated coarsening

We demonstrate two distinctive effects of strain-induced island-island interaction on island size and spatial distribution during coarsening of 2D islands. When coarsening proceeds via only mass transport between islands, the interaction broadens the island size distribution, leading to a power-law dependence of island size uniformity on island number density. When coarsening proceeds via island migration in addition to mass transport between islands, the interaction can effectively direct island motion through island edge diffusion, leading to self-organized formation of a regular array of islands with both uniform size and spacing.     

Pneumatic foam generation in the presence of a high-intensity ultrasound field

Designer foams find applications in a wide range of industries. Foam quality is mostly determined by its complex cellular structure which defines its texture, rheology and stability. In addition to formulation design, the formation process is crucial to the development of a foam with an optimum structure. There is, therefore, a need for techniques that can assist in the generation of controlled foam structures. The work described in this paper demonstrates the potential of using high-intensity ultrasound to control foam structure during production. Foam generated in the presence of ultrasound usually exhibits a narrower bubble size distribution, i.e. a more uniform texture. Such enhanced homogeneity in texture is desirable to reduce the presence of aesthetically unattractive large cavities, and to reduce the destabilising effects of foam coarsening. In addition, a smaller mean bubble size and a slower rate of foam collapse usually result when ultrasound is applied. The work shows the effects on foams stabilised with different surfactants.     

Computational study on cell structure evolution of random liquid and metal-melt foams

A method for geometrical and topological modeling the evolution of close-cell metallic foams based on the Voronoi tessellation in three-dimensional space is presented. Numerical computations were carried out to examine the evolution of the bubble size distribution and topological and geometric properties of aluminum foams in the liquid state, which were implemented by using McPherson’s new theory on coarsening of microstructures as well as the topological transition rules (T1 and T2 processes) in 3D foams, accounting for remarkable effects of both the gas diffusion and surface tension. Computational results show that the bubble size distributions of metallic foams are strongly coupled to the evolution of the cellular structure and dependent on the gas diffusivity and surface tension. The way of foam coarsening can be expressed as RR ₃₂=−mt ²+1 approximately, and gas diffusion between bubbles dominates the evolution of bubble sizes and foam structures. It is found that the average number of faces per bubble is 〈f〉=13.8, which is in good agreement with the values reported in the literature.