Effect of organic acid chain length on foam performance in a porous medium

We have systematically studied the effect of organic acid chain length on surface dilatational properties and foam flow performance in a porous medium. Surface dilatational properties were studied by oscillating drop module (ODM). ODM results in deionized water show that sufficient long chain length of organic acid is an essential requirement for high surface dilatational modulus. While, to various salinities, surfactant to acid ratio of achieving high surface dilatational modulus varies. Foam flow tests show that surface dilatational modulus has decisive effect on produced foam size, which partially determines foam flow pressure drop. Both surface dilatational modulus and surface tension determine foam flow pressure drop. Besides, surface loss modulus also contributes to pressure drop. Bulk foam tests show that addition of organic acids with proper chain length can enhance foam tolerance to oil significantly. Compared with alkane chain length, acid with longer chain has good ability in stabilizing foam. At last, foam flooding tests show that surface dilatational modulus and foam tolerance to oil play important roles in foam enhanced oil recovery.     

Surfactant mixtures for control of bubble surface mobility in foam studies

A new class of surfactant mixtures is described, which is particularly suitable for studies related to foam dynamics, such as studies of foam rheology, liquid drainage from foams and foam films, and bubble coarsening and rearrangement. These mixtures contain an anionic surfactant, a zwitterionic surfactant, and fatty acids (e.g., myristic or lauric) of low concentration. Solutions of these surfactant mixtures exhibit Newtonian behavior, and their viscosity could be varied by using glycerol. Most importantly, the dynamic surface properties of these solutions, such as their surface dilatational modulus, strongly depend on the presence and on the chain-length of fatty acid(s). Illustrative results are shown to demonstrate the dependence of solution properties on the composition of the surfactant mixture, and the resulting effects on foam rheological properties, foam film drainage, and bubble Ostwald ripening. The observed high surface modulus in the presence of fatty acids is explained with the formation of a surface condensed phase of fatty acid molecules in the surfactant adsorption layer.     

Effect of cationic polymers on foam rheological properties

We study the effect of two cationic polymers, with trade names Jaguar C13s and Merquat 100, on the rheological properties of foams stabilized with a mixture of anionic and zwitterionic surfactants (sodium lauryloxyethylene sulfate and cocoamidopropyl betaine). A series of five cosurfactants are used to compare the effect of these polymers on foaming systems with high and low surface dilatational moduli. The experiments revealed that the addition of Jaguar to the foaming solutions leads to (1) a significant increase of the foam yield stress for all systems studied, (2) the presence of consecutive maximum and minimum in the stress vs shear rate rheological curve for foams stabilized by cosurfactants with a high surface modulus (these systems cannot be described by the Herschel-Bulkley model anymore), and (3) the presence of significant foam-wall yield stress for all foaming solutions. These effects are explained with the formation of polymer bridges between the neighboring bubbles in slowly sheared foams (for inside foam friction) and between the bubbles and the confining solid wall (for foam-wall friction). Upon addition of 150 mM NaCl, the effect of Jaguar disappears. The addition of Merquat does not noticeably affect any of the foam rheological properties studied. Optical observations of foam films, formed from all these systems, show a very good correlation between the polymer bridging of the foam film surfaces and the strong polymer effect on the foam rheological properties. The obtained results demonstrate that the bubble-bubble attraction can be used for efficient control of the foam yield stress and foam-wall yield stress, without significantly affecting the viscous friction in sheared foams.     

Effects of electrolyte and nonelectrolyte additives on adsorption and surface rheological characteristics of humic acid salt solutions

The du Noüy and oscillating droplet shape methods are employed to study the effects of the ionic strength and pH of a medium, as well as the addition of nonelectrolytes (lower alcohols and acetone), on the adsorption and surface rheological characteristics of aqueous solutions of humic acid salts (sodium humates) at the liquid-air interface. When added in concentrations at which the aggregation of humic substances is not yet observed, strong electrolytes (NaCl and HCl) decrease the equilibrium surface tension and increase the dilatational viscoelastic modulus of aqueous sodium humate solutions. The aggregation of humic substances enhances the surface tension and reduces the viscoelastic modulus of surface layers. Nonelectrolyte additives decrease the surface tension and dilatational modulus of aqueous humic acid salt solutions. The equilibrium surface tension of sodium humate-nonelectrolyte mixed solutions is described in terms of two different models, namely, a relatively exact model of polyelectrolyte-nonionic surfactant adsorption and a simple additive model. It is shown that the additive model may be used to predict the equilibrium surface tension for the mixtures of high- and low-molecular-mass surfactants.     

Control of Ostwald ripening by using surfactants with high surface modulus

We describe results from systematic measurements of the rate of bubble Ostwald ripening in foams with air volume fraction of 90%. Several surfactant systems, with high and low surface modulus, were used to clarify the effect of the surfactant adsorption layer on the gas permeability across the foam films. In one series of experiments, glycerol was added to the foaming solutions to clarify how changes in the composition of the aqueous phase affect the rate of bubble coarsening. The experimental results are interpreted by a new theoretical model, which allowed us to determine the overall gas permeability of the foam films in the systems studied, and to decompose the film permeability into contributions coming from the surfactant adsorption layers and from the aqueous core of the films. For verification of the theoretical model, the gas permeability determined from the experiments with bulk foams are compared with values, determined in an independent set of measurements with the diminishing bubble method (single bubble attached at large air-water interface) and reasonably good agreement between the results obtained by the two methods is found. The analysis of the experimental data showed that the rate of bubble Ostwald ripening in the studied foams depends on (1) type of used surfactant-surfactants with high surface modulus lead to much slower rate of Ostwald ripening, which is explained by the reduced gas permeability of the adsorption layers in these systems; (2) presence of glycerol which reduces the gas solubility and diffusivity in the aqueous core of the foam film (without affecting the permeability of the adsorption layers), thus also leading to slower Ostwald ripening. Direct measurements showed that the foam films in the studied systems had very similar thicknesses, thus ruling out the possible explanation that the observed differences in the Ostwald ripening are due to different film thicknesses. Experiments with the Langmuir trough were used to demonstrate that the possible differences in the surface tensions of the shrinking and expanding bubbles in a given foam are too small to strongly affect the rate of Ostwald ripening in the specific systems studied here, despite the fact that some of the surfactant solutions have rather high surface modulus. The main reason for the latter observation is that the rate of surface deformation of the coarsening bubbles is extremely low, on the order of 10(-4) s(-1), so that the relaxation of the surface tension (though also slow for the high surface modulus systems) is still able to reduce the surface tension variations down to several mN/m. Thus, we conclude that the main reason for the reduced rate of bubble Ostwald ripening in the systems with high surface modulus is the low solubility and diffusivity of the gas molecules in the respective condensed adsorption layers (which have solid rather than fluid molecular packing).     

Effect of equilibrium and dynamic surface activity of surfactant on foam transport in porous medium

An apparatus containing a visual porous medium plate model and digital video recorder was employed to investigate the transportation of foam stabilized by sodium polyoxyethylene alkylether sulfate (AES), sodium dodecyl benzene sulfonate (SDBS) and TritonX-100 in porous medium. The results showed that transfiguration and fracture were the main transport manners for foam in the porous medium at high gas and liquid transfusion rate. The increase in probability of transfiguration in foam transport process corresponded to the higher flow impedance. A simple U-shape device was designed to investigate the rigidity of surfactant layer at the gas/liquid interface, and the equilibrium surface tension was assigned to be the key parameter which manifests the rigidity of surfactant interface layer. The dynamic surface tension of different surfactant system has also been measured, and the parameters gotten by Rosen model might be the measurement of dynamic elasticity of surfactant interface layer. There is consanguineous relation between the equilibrium surface activity or dynamic activity of the surfactants and the transport of the foam in the porous medium.     

Surface rheology of saponin adsorption layers

Extracts of the Quillaja saponaria tree contain natural surfactant molecules called saponins that very efficiently stabilize foams and emulsions. Therefore, such extracts are widely used in several technologies. In addition, saponins have demonstrated nontrivial bioactivity and are currently used as essential ingredients in vaccines, food supplements, and other health products. Previous preliminary studies showed that saponins have some peculiar surface properties, such as a very high surface modulus, that may have an important impact on the mechanisms of foam and emulsion stabilization. Here we present a detailed characterization of the main surface properties of highly purified aqueous extracts of Quillaja saponins. Surface tension isotherms showed that the purified Quillaja saponins behave as nonionic surfactants with a relatively high cmc (0.025 wt %). The saponin adsorption isotherm is described well by the Volmer equation, with an area per molecule of close to 1 nm(2). By comparing this area to the molecular dimensions, we deduce that the hydrophobic triterpenoid rings of the saponin molecules lie parallel to the air-water interface, with the hydrophilic glucoside tails protruding into the aqueous phase. Upon small deformation, the saponin adsorption layers exhibit a very high surface dilatational elasticity (280 ± 30 mN/m), a much lower shear elasticity (26 ± 15 mN/m), and a negligible true dilatational surface viscosity. The measured dilatational elasticity is in very good agreement with the theoretical predictions of the Volmer adsorption model (260 mN/m). The measured characteristic adsorption time of the saponin molecules is 4 to 5 orders of magnitude longer than that predicted theoretically for diffusion-controlled adsorption, which means that the saponin adsorption is barrier-controlled around and above the cmc. The perturbed saponin layers relax toward equilibrium in a complex manner, with several relaxation times, the longest of them being around 3 min. Molecular interpretations of the observed trends are proposed when possible. Surprisingly, in the course of our study we found experimentally that the drop shape analysis method (DSA method) shows a systematically lower surface elasticity, in comparison with the other two methods used: Langmuir trough and capillary pressure tensiometry with spherical drops. The possible reasons for the observed discrepancy are discussed, and the final conclusion is that the DSA method has specific problems and may give incorrect results when applied to study the dynamic properties of systems with high surface elasticity, such as adsorption layers of saponins, lipids, fatty acids, solid particles, and some proteins. The last conclusion is particularly important because the DSA method recently became the preferred method for the characterization of fluid interfaces because of its convenience.     

起泡剂C12E8的表面流变学性质

利用表面波技术研究起泡剂C_(12)E_8的表面流变学性质以及解释表面变形所产生的表面张力梯度的修复机理．实验结果表明，起泡剂C_(12)E_8的表面具有粘弹性质，其减胀模量与表面变形频率有关系．在低浓度时，随着溶液浓度的增加，表面吸附量的增加很高了膨胀模量．而在高浓度时，由于表面与溶液之间的扩散交换抵消了膨胀模量的增加，这导致膨胀模量随着溶液浓度增加反而降低．     

Foaming and interfacial properties of hydrolyzed beta-lactoglobulin

beta-lactoglobulin (beta-lg) was hydrolyzed with three different proteases and subsequently evaluated for its foaming potential. Foam yield stress (tau0) was the primary variable of interest. Two heat treatments designed to inactivate the enzymes, 75 degrees C/30 min and 90 degrees C/15 min, were also investigated for their effects on foam tau0. Adsorption rates and dilatational rheological tests at a model air/water interface aided data interpretation. All unheated hydrolysates improved foam tau0 as compared to unhydrolyzed beta-lg, with those of pepsin and Alcalase 2.4L(R) being superior to trypsin. Heat inactivation negatively impacted foam tau0, although heating at 75 degrees C/30 min better preserved this parameter than heating at 90 degrees C/15 min. All hydrolysates adsorbed more rapidly at the air/water interface than unhydrolyzed beta-lg, as evidenced by their capacity to lower the interfacial tension. A previously observed relationship between interfacial dilatational elasticity (E') and tau0 was generally confirmed for these hydrolysates. Additionally, the three hydrolysates imparting the highest tau0 not only had high values of E' (approximately twice that of unhydrolyzed beta-lg), they also had very low phase angles (essentially zero). This highly elastic interfacial state is presumed to improve foam tau0 indirectly by improving foam stability and directly by imparting resistance to interfacial deformation.     

Effect of surface tension and surface elasticity of a fluid-fluid interface on the motion of a particle immersed near the interface

The motion of a particle immersed in a fluid near a fluid-fluid interface is studied on the basis of the linearized Navier-Stokes equations. The motion is influenced by surface tension, dilatational surface elasticity modulus, and surface shear modulus, as well as by gravity. The backflow at the location of the particle after a sudden impulse has some universal features that are the same as for a rigid wall with stick boundary conditions. At short times the flow depends only on the mass densities of the two fluids. The nature of the short-time flow is calculated from potential flow theory. At a somewhat later time the particle shows a pronounced rebound. The maximum value of the rebound and the time at which the maximum occurs depend on the elastic properties of the interface.     

Surface dilatational moduli of poly(vinyl acetate) (PVAc) and PVAc-poly(n-hexyl isocyanate) (PHIC) blend films at the air-water interface

Surface dilatational moduli of poly(vinyl acetate) (PVAc) film and blend films of PVAc and poly(n-hexyl isocyanate) (PHIC) were measured at the air-water interface. PVAc formed a film that was looser and also more stable against strain than the PHIC film. The apparent surface dilatational modulus and surface pressure of the blend films were superimposed on the lower concentration of PVAc, irrespective of the composition of PVAc. However, the additivity rule was not applicable to the apparent surface dilatational modulus and surface pressure. The scaling exponents of the apparent surface dilatational modulus against the added surface concentration decreased with an increase in the proportion of PVAc, suggesting that blend films gradually change from glass material to expanded films.     

Disruption of viscoelastic beta-lactoglobulin surface layers at the air-water interface by nonionic polymeric surfactants

Nonequilibrium interfacial layers formed by competitive adsorption of beta-lactoglobulin and the nonionic triblock copolymer PEO99-PPO65-PEO99 (F127) to the air-water interface were investigated in order to explain the influence of polymeric surfactants on protein film surface rheology and foam stability. Surface dilatational and shear rheological methods, surface tension measurements, dynamic thin-film measurements, diffusion measurements (from fluorescence recovery after photo bleaching), and determinations of foam stability were used as methods. The high surface viscoelasticity, both the shear and dilatational, of the protein films was significantly reduced by coadsorption of polymeric surfactant. The drainage rate of single thin films, in the presence of beta-lactoglobulin, increased with the amount of added F127, but equilibrium F127 films were found to be thicker than beta-lactoglobulin films, even at low concentration of the polymeric surfactant. It is concluded that the effect of the nonionic triblock copolymer on the interfacial rheology of beta-lactoglobulin layers is similar to that of low molecular weight surfactants. They differ however in that F127 increases the thickness of thin liquid films. In addition, the significant destabilizing effect of low molecular weight surfactants on protein foams is not found in the investigated system. This is explained as due to long-range steric forces starting to stabilize the foam films at low concentrations of F127.     

Interfacial dynamics and rheology of polymer-grafted nanoparticles at air-water and xylene-water interfaces

Particle-stabilized emulsions and foams offer a number of advantages over traditional surfactant-stabilized systems, most notably a greater stability against coalescence and coarsening. Nanoparticles are often less effective than micrometer-scale colloidal particles as stabilizers, but nanoparticles grafted with polymers can be particularly effective emulsifiers, stabilizing emulsions for long times at very low concentrations. In this work, we characterize the long-time and dynamic interfacial tension reduction by polymer-grafted nanoparticles adsorbing from suspension and the corresponding dilatational moduli for both xylene-water and air-water interfaces. The dilatational moduli at both types of interfaces are measured by a forced sinusoidal oscillation of the interface. Surface tension measurements at the air-water interface are interpreted with the aid of independent ellipsometry measurements of surface excess concentrations. The results suggest that the ability of polymer-grafted nanoparticles to produce significant surface and interfacial tension reductions and dilatational moduli at very low surface coverage is a key factor underlying their ability to stabilize Pickering emulsions at extremely low concentrations.     

Interfacial and foaming properties of prolylenglycol alginates. Effect of degree of esterification and molecular weight

In the present work we have studied the characteristics of propylene glycol alginates (PGA) adsorption at the air–water interface and the viscoelastic properties of the films in relation to its foaming properties. To evaluate the effect of the degree of PGA esterification and viscosity, different commercial samples were studied—Kelcoloid O (KO), Kelcoloid LVF (KLVF) and Manucol ester (MAN). The temperature (20 °C) and pH (7.0) were maintained constant. For time-dependent surface pressure measurements and surface dilatational properties of adsorbed PGA at the air–water interface an automatic drop tensiometer was used. The foam was generated by whipping and then the foam capacity and stability was determined. The results reveal a significant interfacial activity for PGA due to the hydrophobic character of the propylene glycol groups. The kinetics of adsorption at the air–water interface can be monitored by the diffusion and penetration of PGA at the interface. The adsorbed PGA film showed a high viscoelasticity. The surface dilatational modulus depends on the PGA and its concentration in the aqueous phase. Foam capacity of PGA solutions increased in the order KO > MAN > KLVF, which followed the increase in surface pressure and the decrease in the viscosities of PGA solutions. The stability of PGA foams monitored by the drainage rate and collapse time follows the order MAN > KLVF > KO. The foam stability depends on the combined effect of molecular weight/degree of esterification of PGA, solution viscosity and viscoelasticity of the adsorbed PGA film.     

Foams and surface rheological properties of β-casein, gliadin and glycinin

Interfacial rheological properties and their suitability for foam production and stability of two vegetable proteins were studied and compared to β-casein. Proteins used ranged from flexible to rigid/globular in the order of β-casein, gliadin and soy glycinin. Experiments were performed at pH 6.7. Network forming properties were characterised by the surface dilational modulus (determined with the ring trough) and the critical falling film length (L_still) at which a stagnant protein film will break. Gliadin had the highest dilational modulus, followed by glycinin and β-casein, whereas glycinin formed the strongest film against fracture in the overflowing cylinder. The rate of decrease in the surface tension was studied at the air–water (Wilhelmy plate method) and the oil–water interface (bursting membrane) and the dynamic surface tension during compression and expansion in the caterpillar. Gliadin had the lowest equilibrium interfacial tensions and β-casein the lowest dynamic surface tension during expansion. Hardly any foam could be formed at a concentration of 0.1 g/l by shaking. At a concentration of 1.4 g/l most foam was formed by β-casein, followed by gliadin and glycinin. It seems that in the first place the rate of adsorption is important for foam formation. For the vegetable proteins, adsorption was slow. This resulted in lower foamability, especially for glycinin.     

Polysaccharide charge density regulating protein adsorption to air/water interfaces by protein/polysaccharide complex formation

Because the formation of protein/polysaccharide complexes is dominated by electrostatic interaction, polysaccharide charge density is expected to play a major role in the adsorption behavior of the complexes. In this study, pullulan (a non-charged polysaccharide) carboxylated to four different charge densities (fraction of carboxylated subunits: 0.1, 0.26, 0.51, and 0.56) was used to investigate the effect of charge density on the properties of mixed protein/polysaccharide adsorbed layers at air/water interfaces. With all pullulan samples, soluble complexes with beta-lactoglobulin could be formed at low ionic strength, pH 4.5. It was shown that the higher was the pullulan charge density, the more the increase of surface pressure in time was retarded as compared to that for pure beta-lactoglobulin. The retardation was even more pronounced for the development of the dilatational modulus. The lower dilatational modulus can be explained by the ability of the polysaccharides to prevent the formation of a compact protein layer at the air/water interface due to electrostatic repulsion. This ability of the polysaccharides to prevent "layer compactness" increases with the net negative charge of the complexes. If charge density is sufficient (> or = 0.26), polysaccharides may enhance the cohesion between complexes within the adsorbed layer. The charge density of polysaccharides is shown to be a dominant regulator of both the adsorption kinetics as well as the resulting surface rheological behavior of the mixed layers formed. These findings have significant value for the application of complex protein-polysaccharide systems.     

Foam flow through porous media

There are two parts to the interaction of foam with porous media. How the foam interacts with the surface and the flow within the substrate, which is the focus of this review. Flow-through porous media has been investigated experimentally with the main focus in literature being on enhanced oil recovery and remediation. Recently, investigation of the flow of foam through a deformable substrate for dishwashing application has led to the development of mathematical models. It has been proposed that foam flow through pore channels is similar to the behaviour observed within microchannels. Meaning that to investigate the effects these properties have on foam flow it is best to observe them within a model channel then build up to a 3D structure of interlinking channels to resemble porous media. In this review, it is highlighted that a large amount of work is needed in understanding the interaction of foam and/or liquid within porous networks. Methods that can be applied to better represent foam and liquid flow in porous media are discussed within this review, including both using microchannels to simulate individual pores and using these systems to build up to a 3D structure of interlinking pores. In addition, more advanced imaging techniques to observe the flow through porous materials are discussed, including computed tomography scanning nuclear magnetic resentence and confocal microscopy. There is still more work required to fully understand the flow within porous media, including observing the affect of dead-end pores, closed loops and rough channel walls have on the flow.     

Synergistic effects in flows of mixtures of wormlike micelles and hydroxyethyl celluloses with or without hydrophobic modifications

This work presents experimental results on simple shear and porous media flow of aqueous solutions of two hydroxyethyl celluloses (HEC) and two hydrophobically modified hydroxyethyl celluloses (HMHEC) with different molecular weights. Mixtures of these polymers with a cationic surfactant, cetyltrimethylammonium p-toluenesulfonate (CTAT) were also studied. Emphasis was given to the range of surfactant concentrations in which wormlike micelles are formed. The presence of hydrophobic groups, the effect of the molecular weight of the polymers, the surfactant and polymer concentrations, and the effect of the flow field type (simple shear versus porous media flow) were the most important variables studied. The results show that the shear viscosity of HEC/CTAT solutions is higher than the viscosities of surfactant and polymer solutions at the same concentrations, but surface tension measurements indicate that no complex formation occurs between CTAT and HEC. On the other hand, a complex driven by hydrophobic interactions was detected by surface tension measurements between CTAT and HMHEC. In this case, the viscosity of the mixture increases significantly more (up to four orders of magnitude at high CTAT concentrations) in comparison with HEC/CTAT aqueous solutions. Increments in the molecular weight of the polymers increase the interaction with CTAT and the shear viscosity of the solution, but make phase separation more feasible. In porous media flow, the polymer/CTAT mixtures exhibited higher apparent viscosities than in simple shear flows. This result suggests that the extensional component of the flow field in porous media flows leads to a stronger interaction between the polymer and the wormlike micelles, probably as a consequence of change of conformation and growth of the micelles.     

Interfacial and stability study of microbubbles coated with a monostearin/monopalmitin-rich food emulsifier and PEG40 stearate

The stability and presence of micron-scale bubbles (microbubbles) is of considerable interest in environmental, biomedical, and food sciences. Here we show that microbubbles can be formed and stabilized in a solution of low cost food-grade emulsifier (a mixture of saturated long-chain monoglycerides, diglycerides and sodium stearoyl-2-lactylate) in combination with polyethylene glycol (PEG)-40 stearate. Langmuir trough methods and fluorescence microscopy were combined to investigate the surface tension, interfacial elastic modulus, phase behavior and microstructure of monolayer shells coating these microbubbles. Our results strongly suggest that although the PEG40S is necessary to form microbubbles this component, as well as sodium stearoyl-2-lactylate, are "squeezed out" in the form of collapse aggregates. This process leaves a microbubble shell, composed of a condensed-phase low surface tension mono- and diglycerides mixture with some of the PEG40S and SSL2 remaining trapped between the condensed-phase domains. We find that other commercially available emulsifiers, containing unsaturated or bulky components unable to form condensed phases, do not to form or stabilize a microbubble layer, although they may form a foam, a finding that we relate to differences in surface tension.     

Transient interfacial tension and dilatational rheology of diffuse polymer-polymer interfaces

We demonstrate the influence of molecular weight and molecular weight asymmetry across an interface on the transient behavior of the interfacial tension. The interfacial tension was measured as a function of time for a range of polymer combinations with a broad range of interfacial properties using a pendant/sessile drop apparatus. The results show that neglecting mutual solubility, assumed to be a reasonable approximation in many cases, very often does not sustain. Instead, a diffuse interface layer develops in time with a corresponding transient interfacial tension. Depending on the specific combination of polymers, the transient interfacial tension is found to increase or decrease with time. The results are interpreted in terms of a recently proposed model [Shi et al., Macromolecules 37, 1591 (2004)], giving relative characteristic diffusion time scales in terms of molecular weight, molecular weight distribution, and viscosities. However, the time scales obtained from this theoretical approach do not give a conclusive trend. Using oscillatory dilatational interfacial experiments the viscoelastic behavior of these diffusive interfaces is demonstrated. The time evolution of the interfacial tension and the dilatational elasticity show the same trend as predicted by the theory of diffuse interfaces, supporting the idea that the polymer combinations under consideration indeed form diffuse interfaces. The dilatational elasticity and the dilatational viscosity show a frequency dependency that is described qualitatively by a simple Fickian diffusion model and quantitatively by a Maxwell model. The characteristic diffusion times provided by the latter show that the systems with thick interfaces (tens of microseconds and more) can be considered as slower diffusive systems compared to the systems with thinner interfaces (a few micrometers in thickness and less) can be considered as fast diffusive systems.