Electro-viscosity

Charged particles in weak electrolytes have associated with them an electrical double layer. When these particles settle under gravity the double layer is distorted with the result that an electrical field is set up that opposes motion. This effect was first noted by Dorn [74] and was studied extensively by Elton et. al. [75-78] and later by Booth [79,80]. 

For a spherical particle of diameter Z), the electrical force Fg is equal to the product of the electrical field E and the charge q. For a surface charge per unit area crthe force on the sphere is D oE. 

If the sum of this force and the viscous force is set equal to the gravitational force, equation (6.6) is modified to  

The specific conductivity of a solution (k) is equal to the current density divided by the electrical field. 

But N is equal to the total weight of particles in suspension (m) divided by the volume of suspension (V) and the weight of a single particle. 

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Volumic flow rates which are identical are identified and enable us to find the electro viscosity. 

Equation (39) gives the electro viscosity in a microtube with an inner charged surface at the potential f(,. The reduced forward volumic flow rate observed experimentally is interpreted as an increased apparent viscosity. Using the expressions of Ki, K2, s and K3 (respectively Eqs. (15b), (15c), (29) and (30)) it is possible to evidence that iJis liJi is a function of neither the average fluid velocity (C/q) nor the pressure gradient (Pz) but only a function of the microtube diameter and the electrokinetic parameters. The case of two parallel plates has been studied by Mala et al. [6] and will not be presented here. The electroviscosity equation obtained differs slightly from Eq. (39) due to the geometry. 

The 2eta potential (Fig. 8) is essentially the potential that can be measured at the surface of shear that forms if the sohd was to be moved relative to the surrounding ionic medium. Techniques for the measurement of the 2eta potentials of particles of various si2es are collectively known as electrokinetic potential measurement methods and include microelectrophoresis, streaming potential, sedimentation potential, and electro osmosis (19). A numerical value for 2eta potential from microelectrophoresis can be obtained to a first approximation from equation 2, where Tf = viscosity of the liquid, e = dielectric constant of the medium within the electrical double layer, = electrophoretic velocity, and E = electric field. 

The diffusion current Id depends upon several factors, such as temperature, the viscosity of the medium, the composition of the base electrolyte, the molecular or ionic state of the electro-active species, the dimensions of the capillary, and the pressure on the dropping mercury. The temperature coefficient is about 1.5-2 per cent °C 1 precise measurements of the diffusion current require temperature control to about 0.2 °C, which is generally achieved by immersing the cell in a water thermostat (preferably at 25 °C). A metal ion complex usually yields a different diffusion current from the simple (hydrated) metal ion. The drop time t depends largely upon the pressure on the dropping mercury and to a smaller extent upon the interfacial tension at the mercury-solution interface the latter is dependent upon the potential of the electrode. Fortunately t appears only as the sixth root in the Ilkovib equation, so that variation in this quantity will have a relatively small effect upon the diffusion current. The product m2/3 t1/6 is important because it permits results with different capillaries under otherwise identical conditions to be compared the ratio of the diffusion currents is simply the ratio of the m2/3 r1/6 values. 

This hydrodynamic contribution to n is determined by the dielectric constant (e) and the viscosity of water (u), the surface charge density of the pore (Z), the pore radius (rp), and the proton conductivity of the pore (cTpore)- The hydrodynamic electro-osmotic coefficient for a typical pore with Tp = 1 nm is found in the range of [i.e., n ydr -1-10]. 

Equation (6.3.3b) results from assuming a Poiseille flow in a filter s pore of typical radius r, i is the dynamic viscosity of the fluid. Equation (6.3.3c) is a common expression for the electro-osmotic coefficient [13], with d and , respectively, the dielectric constant of the fluid and the -potential of the pore wall. For the time being, we shall assume il> constant (independent of C(x,t)). 

Borkovec et al. [59] also reported on a two-stage percolation process for the ME AOT (Aerosol OT, bis(2-ethylhexyl)sodium sulfosuccinate) system AOT-decane-water. The structural inversions were investigated using viscosity, conductivity, and electro-optical effect measurements. The viscosity results showed a characteristic profile with two maxima, which was interpreted as evidence for two symmetrical percolation processes an oil percolation on the water-rich side of the phase diagram and a water percolation process on the oil-rich side. 

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