Interface dilation

FIG. 28 Dependence of the interface dilatation modulus e on the concentration c of homologous alkanesuifonates and decylbenzenesulfonate according to Ref. 48. O, Sodium tetradecanesulfonate x, sodium decylbenzenesulfonate , sodium dodecanesulfonate A, sodium decanesulfonate). 

This class considers cases in which the oil/water interfacial extent is bounded by the three phase contact line, even if the contact angle is zero. Thus widening flow results in interface dilation, with the interfacial tension either remaining constant (for systems with no surfactant components) or increasing. 

The concepts of interface rheology are derived from the rheology of three-dimensional phases. Characteristic for the interface rheology is the coupling of the motions of an interface with the flow processes in the bulk close to the interface. Thus, in interface rheology the shear and dilatational stresses of the interface are in equilibrium with the corresponding shear stress in the bulk. An important feature is the compressibility of the adsorption layer of an interface in contrast, the flow elements of the bulk are incompressible. As a result, compression or dilatation of the adsorption layer of a soluble surfactant is associated with desorption and adsorption processes by which the interface tends to reinstate the adsorption equilibrium with the bulk phase. 

Effectiveness of a crude oil demulsifier is correlated with the lowering of shear viscosity and dynamic tension gradient of the oil-water interface. Using the pulsed drop technique, the interfacial dilational modulii with different demulsifiers have been measured. The interfacial tension relaxation occurs faster with an effective demulsifier. Electron spin resonance with labeled demulsifiers indicate that the demulsifiers form reverse micelle like clusters in bulk oil. The slow unclustering of the demulsifier at the interface appears to be the rate determining step in the tension relaxation process. 

Our goal is to develop a property-performance relationship for different types of demulsifiers. The important interfacial properties governing water-in-oil emulsion stability are shear viscosity, dynamic tension and dilational elasticity. We have studied the relative importance of these parameters in demulsification. In this paper, some of the results of our study are presented. In particular, we have found that to be effective, a demulsifier must lower the dynamic interfacial tension gradient and its ability to do so depends on the rate of unclustering of the ethylene oxide groups at the oil-water interface. 

The shape of the curves for the dilational modulus (Figures 7 and 8) suggests a single relaxation mechanism, probably the unfolding of the demulsifier molecules at the interface. The frequency peak in the e"(f) plot is a measure of the characteristic relaxation time. A shorter relaxation time, by inducing faster film drainage, increases demulsification efficiency. 

For effective demulsification of a water-in-oil emulsion, both shear viscosity as well as dynamic tension gradient of the water-oil interface have to be lowered. The interfacial dilational modulus data indicate that the interfacial relaxation process occurs faster with an effective demulsifier. The electron spin resonance with labeled demulsifiers suggests that demulsifiers form clusters in the bulk oil. The unclustering and rearrangement of the demulsifier at the interface may affect the interfacial relaxation process. 

The dynamic surface tension of a monolayer may be defined as the response of a film in an initial state of static quasi-equilibrium to a sudden change in surface area. If the area of the film-covered interface is altered at a rapid rate, the monolayer may not readjust to its original conformation quickly enough to maintain the quasi-equilibrium surface pressure. It is for this reason that properly reported II/A isotherms for most monolayers are repeated at several compression/expansion rates. The reasons for this lag in equilibration time are complex combinations of shear and dilational viscosities, elasticity, and isothermal compressibility (Manheimer and Schechter, 1970 Margoni, 1871 Lucassen-Reynders et al., 1974). Furthermore, consideration of dynamic surface tension in insoluble monolayers assumes that the monolayer is indeed insoluble and stable throughout the perturbation if not, a myriad of contributions from monolayer collapse to monomer dissolution may complicate the situation further. Although theoretical models of dynamic surface tension effects have been presented, there have been very few attempts at experimental investigation of these time-dependent phenomena in spread monolayer films. 

The rheological properties of a fluid interface may be characterized by four parameters surface shear viscosity and elasticity, and surface dilational viscosity and elasticity. When polymer monolayers are present at such interfaces, viscoelastic behavior has been observed (1,2), but theoretical progress has been slow. The adsorption of amphiphilic polymers at the interface in liquid emulsions stabilizes the particles mainly through osmotic pressure developed upon close approach. This has become known as steric stabilization (3,4.5). In this paper, the dynamic behavior of amphiphilic, hydrophobically modified hydroxyethyl celluloses (HM-HEC), was studied. In previous studies HM-HEC s were found to greatly reduce liquid/liquid interfacial tensions even at very low polymer concentrations, and were extremely effective emulsifiers for organic liquids in water (6). 

Surface-tension forces act in a direction tangent to the interface. Boussinesq (B6) assumed, for a surface undergoing dilatation, that there must also be another force acting normal to the interface. Utilizing the same assumptions as Hadamard, he arrived at a Stokes-law correction factor of... 

Boussinesq (B4) proposed that the lack of internal circulation in bubbles and drops is due to an interfacial monolayer which acts as a viscous membrane. A constitutive equation involving two parameters, surface shear viscosity and surface dilational viscosity, in addition to surface tension, was proposed for the interface. This model, commonly called the Newtonian surface fluid model (W2), has been extended by Scriven (S3). Boussinesq obtained an exact solution to the creeping flow equations, analogous to the Hadamard-Rybczinski result but with surface viscosity included. The resulting terminal velocity is... 

Dilatational surface rheology is a less discriminating experimental technique. At air-water and sunflower oil-water interfaces, it is found (Lucassen-Reynders and Benjamins, 1999) that both disordered p-casein... 

Lucassen-Reynders, E.H., Benjamins, J. (1999). Dilational rheology of proteins adsorbed at fluid interfaces. In Dickinson, E., Rodriguez Patino, J.M. (Eds). Food Emulsions and Foams Interfaces, Interactions and Stability, Cambridge, UK Royal Society of Chemistry, pp. 195-206. 

Incoherent Clusters. As described in Section B.l, for incoherent interfaces all of the lattice registry characteristic of the reference structure (usually taken as the crystal structure of the matrix in the case of phase transformations) is absent and the interface s core structure consists of all bad material. It is generally assumed that any shear stresses applied across such an interface can then be quickly relaxed by interface sliding (see Section 16.2) and that such an interface can therefore sustain only normal stresses. Material inside an enclosed, truly incoherent inclusion therefore behaves like a fluid under hydrostatic pressure. Nabarro used isotropic elasticity to find the elastic strain energy of an incoherent inclusion as a function of its shape [8]. The transformation strain was taken to be purely, dilational, the particle was assumed incompressible, and the shape was generalized to that of an... 

To determine the adsorption kinetics, the effective age of the drop interface must be calculated. However, experimental data yield only interfacial tension values as a function of drop formation time. To determine the true age of the interface, both the fluid flow within the droplet and the dilation of the droplet interface must be interpreted using appropriate models. Miller et al. (1992) showed that the drop formation time, r op, can be converted into the effective age of the drop interface ... 

We can distinguish between two types of stresses on an interface a shear stress and a dilatational stress. In a shear stress experiment, the interfacial area is kept constant and a shear is imposed on the interface. The resistance is characterized by a shear viscosity, similar to the Newtonian viscosity of fluids. In a dilatational stress experiment, an interface is expanded (dilated) without shear. This resistance is characterized by a dilatational viscosity. In an actual dynamic situation, the total stress is a sum of these stresses, and both these viscosities represent the total flow resistance afforded by the interface to an applied stress. There are a number of instruments to study interfacial rheology and most of them are described in Ref. [1]. The most recent instrumentation is the controlled drop tensiometer. 

Figure 24. A comparison of the data obtained from a range of surface rheological measurements of samples of /3-lg as a function of Tween 20 concentration. ( ), The surface diffusion coefficient of FITC-jS-lg (0.2 mg/ml) at the interfaces of a/w thin films (X), the surface shear viscosity of /3-lg (0.01 mg/ml) at the o/w interface after 5 hours adsorption ( ), the surface dilational elasticity and (o) the dilational loss modulus of /3-lg (0.2 mg/ml).

The surface rheological properties of the /3-lg/Tween 20 system at the macroscopic a/w interface were examined by a third method, namely surface dilation [40]. Sample data obtained are presented in Figure 24. The surface dilational modulus, (E) of a liquid is the ratio between the small change in surface tension (Ay) and the small change in surface area (AlnA). The surface dilational modulus is a complex quantity. The real part of the modulus is the storage modulus, e (often referred to as the surface dilational elasticity, Ed). The imaginary part is the loss modulus, e , which is related to the product of the surface dilational viscosity and the radial frequency ( jdu). 

Experiments with the /3-lg/Tween 20 system were performed at a macroscopic a/w interface at a /3-lg concentration of 0.2 mg/ml [40]. The data obtained relate to the properties of the interface 20 minutes after formation. Up to R = 1, the storage modulus (dilational elasticity) was large and relatively constant, whereas the loss modulus (dilational viscosity) increased with increasing R. As R was increased to higher values there was a marked decrease in the storage modulus (dilational elasticity) and a gradual increase in the loss modulus (dilational viscosity). In summary, the data show the presence of a transition in surface dilational behavior in this system at a solution composition of approximately R = 1. At this point, there is a transformation in the adsorbed layer properties from elastic to viscous. 

Unlike in three dimensions, where liquids are often considered incompressible, a surfactant monolayer can be expanded or compressed over a wide area range. Thus, the dynamic surface tension experienced during a rate-dependent surface expansion, is the result of the surface dilational viscosity, the surface shear viscosity, and elastic forces. Often, the contributions of shear and/or the dilational viscosities are neglected during stress measurements of surface expansions. Isolating interfacial viscosity effects is difficult because, since the interface is connected to the substrate on either side of it, the interfacial viscosity is coupled to the two bulk viscosities. 

J. Lucassen, Capillary forces between solid particles in fluid interfaces, Colloids Surf. 65, 131-137 (1992) Dynamic dilational properties of composite surfaces, Colloids Surf. 65, 139-149 (1992). 

An impact modifier is a rubber phase dispersed in particulate form throughout the matrix of a polymer solid. Unlike plasticizers, the rubber particles retain their intrinsic properties as a separate phase. The glass transition temperature of the parent matrix is not lowered by the addition of an impact modifier. The rubber particles do two things to the parent matrix phase (2,3,4) they act as stress concentrators (i.e., a large strain will start in the matrix near the interface) and they enhance the multi-axiality in stress. As multiaxial tensile strength near the interface further enhances dilatation, which shortens the mechanical relaxation time, the otherwise brittle polymer solid of the matrix will undergo plastic deformation in the vicinities of the rubber particles. 

In Eq. (10) that gives the toughness in dilatational plasticity the factors C and A are dependent on craze microstructure and will not vary significantly. The stress and temperature dependence of the craze velocity while quite determinate in the interface convolution process of craze matter production will also be quite sensitive to micro-structural detail of phase distribution in block copolymers. The appUed stress = Y ... 

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