Viscosity thick electrical double layers

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. 

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. 

It is now apparent that the EOF depends upon the surface charge density, the field strength, the thickness of the electrical double layer, and the viscosity of the separation medium, which in turn is dependent upon the temperature. In a packed capillary, the vast majority of the total surface area is contributed by the packing material, thus it is reasonable to approximate the surface charge density of the system (both the capillary wall and the packing) using the value for the sorbent. 

Coalescence frequency J depends on dimensionless parameters k, p, Sa, Sr, t, y, a. The parameter k characterizes relative sizes of interacting drops p is the viscosity ratio of drops and ambient liquid Sa and Sr are the forces of molecular attraction and electrostatic repulsion of drops r is the relative thickness of electric double layer, which depends, in particular, on concentration of electrolyte in ambient liquid y is the electromagnetic retardation of molecular interaction a is relative potential of surfaces of interacting drops. Let us estimate the values of these parameters. For hydrosols, the Hamaker constant is F 10 ° J. For viscosity and density of external liquid take m /s, 10 kg/m. ... 

Consider a thin liqmd Aim in air for which the Hamaker constant Ah is 5 x K)- erg and electrical double-layer effects are negligible. If viscosity is 1 cp, density is 1 g/cm. Aim thickness is 50 nm, and surface tension is 40 mN/m, And the wavenumbers and of the critical and fastest growing disturbances and the time factor (3 for growth of the latter using the inextmisible interface results given above. Compare with the corresponding results for a free interface in the inviscid approximation. 

Tlie discussions of the basic features of filtration given thus far illustrate that the unit operation involves some rather complicated hydrodynamics that depend strongly on the physical properties of both fluid and particles, as well as interaction with a complex porous medium. The process is essentially influenced by two different groups of factors, which can be broadly lumped into macro- and micro-properties. Macrofactors are related to variables such as the area of a filter medium, pressure differences, cake thickness and the viscosity of the liquid phase. Such parameters are readily measured. Micro-factors include the influences of the size and configuration of pores in the cake and filter medium, the thickness of the electrical double layer on the surface of solid particles, and other properties. 

Reciprocal electrical double layer thickness, m Compressibility index Viscosity of filtrate or liquid in a feed. Pa s Dimensionless time... 

Ion adsorption at day partides is a dynamic process, so that an exchange of ions can take place readily in response to the changing pH. These changes in pH influence the thickness of the Hehnholtz-Gouy-Chapman electrical double layer, and in turn the value of the so-called zeta potential (Q that behaves inversely to the viscosity (see Figure 2.20). 

Smoluchowsky [161] and Booth [162] both accounted for the increase in viscosity as due to the electrical double layer round a charged particle in an electrolyte and gave expressions for e which included the specific conductivity of the electrolyte, the dielectric constant of the suspending medium, the electrokinetic potential of the particles with respect to the electrol)de and tt e radius of tiie particle (which was to be large in comparison with the thickness of the double layer for the validity of ttie expression). Experimental verification by Chan and Goring [163] of tiie expressions for e, provided by Smoluchowsky [161] and Booth [162] gives confidence for their use. 

Here, p is defined as the electrophoretic mobility (particle velocity/ applied electric field) of a particle of radius a. C is the zeta potential, and q is the viscosity of the suspending solution./(A ), a) is Henry s function and depends on the Debye length (see Section 5.5.2). This variable represents the thickness of the electric double layer. 

Particles dispersed in an aqueous medium invariably carry an electric charge. Thus they are surrounded by an electrical double-layer whose thickness k depends on the ionic strength of the solution. Flow causes a distortion of the local ionic atmosphere from spherical symmetry, but the Maxwell stress generated from the asymmetric electric field tends to restore the equilibrium symmetry of the double-layer. This leads to enhanced energy dissipation and hence an increased viscosity. This phenomenon was first described by Smoluchowski, and is now known as the primary electroviscous effect. For a dispersion of charged hard spheres of radius a at a concentration low enough for double-layers not to overlap (d> 8a ic ), the intrinsic viscosity defined by eqn. (5.2) increases... 

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... 

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)]. 

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