Viscosity diffuse double layer

Rheology. Flow properties of latices are important during processing and in many latex appHcations such as dipped goods, paint, inks (qv), and fabric coatings. For dilute, nonionic latices, the relative latex viscosity is a power—law expansion of the particle volume fraction. The terms in the expansion account for flow around the particles and particle—particle interactions. For ionic latices, electrostatic contributions to the flow around the diffuse double layer and enhanced particle—particle interactions must be considered (92). A relative viscosity relationship for concentrated latices was first presented in 1972 (93). A review of empirical relative viscosity models is available (92). In practice, latex viscosity measurements are carried out with rotational viscometers (see Rpleologicalmeasurement). 

A corrected and more general analysis of the primary electroviscous effect for weak flows, i.e., for low Pe numbers (for small distortions of the diffuse double layer), and for small zeta potentials, i.e., f < 25 mV, was carried out by Booth in 1950. The result of the analysis leads to the following result for the intrinsic viscosity [rj] for charged particles in a 1 1 electrolyte ... 

How must the expressions derived in the sections above be modified to take into account the variation in rj and the finite distance over which it increases The answer is that rj — the viscosity within the double layer —must be written as a function of location. Our objective in discussing this variation is not to examine in detail the efforts that have been directed along these lines. Instead, it is to arrive at a better understanding of the relationship between f and the potential at the inner limit of the diffuse double layer and a better appreciation of the physical significance of the surface of shear. 

The properties (the effective viscosity and density) of the liquid layer in close vicinity to the interface can differ from their bulk values. There are various reasons for these phenomena. For example, the properties of a thin liquid layer confined between solid walls are determined by interactions with the solid walls [58,59]. In electrochemical system the structuring of a solvent induced by the substrate and a nonuniform ion distribution in the diffuse double layer can significantly influence the properties of the solution at the interface. The nonuniform distribution of species, which influences the properties of the liquid near the electrode, also occurs in the case of diffusion kinetics. The latter was considered in Ref. 60, where the ferro/ferri redox system was studied by the EQCM. This was the case where the velocity decay length ( >25 pm) was much less than the thickness of the diffusion layer ( >100 pm), in which the composition of the solution is different from the bulk composition. 

An attempt to describe the response of the EQCM in the double-layer region only on the basis of the properties of the diffuse double layer was undertaken in Ref. 61. In doing so, the specific adsorption of ions and the potential-dependent specific interactions of the solvent with the metal were entirely ignored. Under these assumptions one could think of three reasons leading to the observed dependence of frequency on potential (1) dependence of the surface tension on potential, (2) electrostatic adsorption of charged species, and (3) a local change in viscosity in the diffuse double layer. 

A difference between the viscosity of the fluid in the diffuse double layer and in the bulk of the solution could be caused by two factors. 

In order to describe both the effect of the electrostatic adsorption of ions and the effect of the viscosity inside the diffuse double layer on the response of the EQCM, one can use the thin-layer model described in Sec. II.C. Since the thickness of the diffuse double layer is much less than the velocity decay length, the corresponding equation of the model is Eqs. (23) and (24), which can be rewritten in the following form ... 

For the film thickness, as a first approximation, one can take that Lf = K. Another simplifying assumption is that the viscosity changes abruptly at the boundary between the film and the solution. Estimation of the viscosity of the film as a function of potential is very difficult, since electro-neutrality is not maintained in the diffuse double layer, and it is difficult to take into account the influence of the electric field in the double layer on the viscosity of the film. Instead, the viscosity of the film, tjf, can be taken as a parameter, to fit the theoretical curve to the experimental results. To do this one substracts from the observed frequency shift the contribution of the mass effect caused by electrostatic adsorption of ions [Eq. (56)]. 

The remaining part of the overall effect can then be ascribed to viscosity effect, rjf. Using pairs of experimental data A/vs. E, and the dependence of surface charge density on potential, the concentration of ions (Ca,c) in the diffuse double layer can be calculated and the dependence of rif on Ca,c can be obtained. An example of such calculations is shown in Fig. 7 [61,97]. 

All these observations are characteristic not only of the cases shown in Fig. 7, but also of all other cases studied HCIO4, LiC104, CsOH [61,97]. Thus, the model described above, taking into consideration the variation of ionic concentration and local viscosity in the diffuse double layer, can account for the potential dependence of the frequency of the EQCM in the double-layer region on gold electrodes. 

It should be noted that in Fig. 7 we ascribed to the viscosity at pzc the value of the bulk viscosity, suggesting that there is no influence of the metal on the solvent in the layer nearest to it. Due to interactions between solvent molecules and the metal, this may not be the case. Hence one should take into account that even at the pzc there could be a film of solvent molecules having a viscosity that is different from the value in the bulk. In this case the influence of the electric field and the composition of the solution inside the diffuse double layer has to depend on the metal and on the nature of the solvent. The latter could lead to a dependence of the EQCM response on the nature of the metal, which is indeed observed when the results for gold... 

FIG. 7. Comparison of the effective film viscosity, calculated for the concentrations prevailing in the diffuse double layer in 0.1 M solutions of KOH (open circles) and KNO3 (open squares, positive surface charge densities closed squares, negative charge densities) with the dependence of the viscosity in the bulk, as a function of concentration [178]. (From Ref. 98.)... 

The effect is dependent on the electrical double layer (q.v.) at the interface, and if a plane surface can be assumed (i.e. if the curvature is negligible compared with the thickness of the diffuse double layer), the interface can be treated as a parallel plate capacitor. For steady conditions, the electrical force applied must balance the frictional force. Now the viscosity of the liquid rj is the force per unit area per unit velocity gradient. The velocity of the liquid is zero at the surface of shear and the velocity gradient can be written as u/k where is... 

An increase in pressure will also affect the rate of the diffusion of molecules to and from the electrode surface it will cause an increase in the viscosity of the medium and hence a decrease in diffusion controlled currents. The consequences of increased pressure on the electrode double layer and for the adsorption of molecules at the electrode surface are unclear and must await investigation. 

The electroviscous effect present with solid particles suspended in ionic liquids, to increase the viscosity over that of the bulk liquid. The primary effect caused by the shear field distorting the electrical double layer surrounding the solid particles in suspension. The secondary effect results from the overlap of the electrical double layers of neighboring particles. The tertiary effect arises from changes in size and shape of the particles caused by the shear field. The primary electroviscous effect has been the subject of much study and has been shown to depend on (a) the size of the Debye length of the electrical double layer compared to the size of the suspended particle (b) the potential at the slipping plane between the particle and the bulk fluid (c) the Peclet number, i.e., diffusive to hydrodynamic forces (d) the Hartmarm number, i.e. electrical to hydrodynamic forces and (e) variations in the Stern layer around the particle (Garcia-Salinas et al. 2000). 

What happens when the dimensions are furthermore reduced Initially, an enhanced diffusive mass transport would be expected. That is true, until the critical dimension is comparable to the thickness of the electrical double layer or the molecular size (a few nanometers) [7,8]. In this case, diffusive mass transport occurs mainly across the electrical double layer where the characteristics (electrical field, ion solvent interaction, viscosity, density, etc.) are different from those of the bulk solution. An important change is that the assumption of electroneutrality and lack of electromigration mass transport is not appropriate, regardless of the electrolyte concentration [9]. Therefore, there are subtle differences between the microelectrodic and nanoelectrodic behaviour. 

A significant number of studies have characterized the physical properties of eutectic-based ionic liquids but these have tended to focus on bulk properties such as viscosity, conductivity, density and phase behavior. These are all covered in Chapter 2.3. Some data are now emerging on speciation but little information is available on local properties such as double layer structure or adsorption. Deposition mechanisms are also relatively rare as are studies on diffusion. Hence the differences between metal deposition in aqueous and ionic liquids are difficult to analyse because of our lack of understanding about processes occurring close to the electrode/liquid interface. 

In conclusion we will note that the main difference between aqueous emulsion films and foam films involves the dependences of the various parameters of these films (potential of the diffuse double electric layer, surfactant adsorption, surface viscosity, etc.) on the polarity of the organic phase, the distribution of the emulsifier between water and organic phase and the relatively low, as compared to the water/air interface, interfacial tension. 

Many more-sophisticated models have been put forth to describe electrokinetic phenomena at surfaces. Considerations have included distance of closest approach of counterions, conduction behind the shear plane, specific adsorption of electrolyte ions, variability of permittivity and viscosity in the electrical double layer, discreteness of charge on the surface, surface roughness, surface porosity, and surface-bound water [7], Perhaps the most commonly used model has been the Gouy-Chapman-Stem-Grahame model 8]. This model separates the counterion region into a compact, surface-bound Stern" layer, wherein potential decays linearly, and a diffuse region that obeys the Poisson-Boltzmann relation. 

The Helmholtz-von Smoluchowski equation indicates that under constant composition of the electrolyte solution, the electro-osmotic flow depends on the magnitude of the zeta potential which is determined by many different factors, the most important being the dissociation of the silanol groups on the capillary wall, the charge density in the Stern layer, and the thickness of the diffuse layer. Each of these factors depends on several variables, such as pH, specific adsorption of ionic species in the compact region of the electric double layer, ionic strength, viscosity, and temperature. 

This formula for the electroosmotic velocity past a plane charged surface is known as the Helmholtz-Smoluchowski equation. Note that within this picture, where the double layer thickness is very small compared with the characteristic length, say alX t> 100, the fluid moves as in plug flow. Thus the velocity slips at the wall that is, it goes from U to zero discontinuously. For a finite-thickness diffuse layer the actual velocity profile has a behavior similar to that shown in Fig. 6.5.1, where the velocity drops continuously across the layer to zero at the wall. The constant electroosmotic velocity therefore represents the velocity at the edge of the diffuse layer. A typical zeta potential is about 0.1 V. Thus for = 10 V m" with viscosity that of water, the electroosmotic velocity U 10 " ms, a very small value. 

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