Permittivity of the fluid

Unlike charges attract and like charges repel each other, so there is a high concentration of counterions attracted to the particle surface whilst co-ions (those with the same sign charge as that of the surface) are repelled. Thermal motion, i.e. diffusion, opposes this local concentration gradient so that the counterions are in a diffuse cloud around the particle. Of course particles which have a like charge will also repel each other but the interaction of the particle surfaces will be screened by the counterion clouds between the particles. The interaction potential is a function of the surface potential, i]/o, and the permittivity of the fluid phase, e = r80, where r is the relative permittivity.12,27... 

We now consider the same parallel-plate condenser immersed in the dielectric medium. The charges on the two plates are represented again by the symbols +Q and — Q. The permittivity of the fluid, s, is defined by... 

When a DC electric field is imposed on the soil, it will move the mobile cation shell toward the cathode and drag the fluid between the shearing surfaces by a plug flow mechanism, resulting in the electroosmotic flow of fluid from the anode toward the cathode. The shearing surface in the fluid may be taken as a plane parallel to the surface at a distance 5 (m) from it. If e (F/m) is the permittivity of the fluid between these hypothetical plates, then it is known from electrostatics that... 

In (32.12), H/j, is a dimensionless parameter comparing the viscosity of the fluid used in an electrospray to other fluid parameters such as fluid surface tension, fluid density, dielectric permittivity of the fluid and also the dielectric permittivity of free space. When is much greater than 1 then viscous effects are negligible. 

Thus, a streaming potential can be measured across the capillary by placing electrodes at the inlet and outlet, and can be related to a zeta potential at the hydrodynamic plane of shear, given the viscosity and permittivity of the fluid and the applied pressure (or flow rate through the capillary). 

The higher the value of /, the smaller the value of A. Here is Faraday s constant, R is the universal gtis constant, T is the absolute temperature and e is the electrical permittivity of the fluid. This quantity e is the product of the relative dielectric constant of the medium (for water = 78.54 at 25 °C) and the electrical permittivity So of vacuum (= 8.8542 x 10 farad/cm or coulomb/volt-cm = 8.854 x 10 cou-lomh /newton-m, where recall that 1 newton-m = 1 volt-coulomh = 1 joule). In a uni-univalent electrolyte solution of 0.1 M strength (of, say, NaCl) the value of A at 25 °C is 9.6 X 10 cm, i.e. 0.96 nm (Newman, 1973). The ions of opposite charge shield the charge of the ion of interest, and the effect of the ion of interest decays very rapidly with distance. So the description of the electrical force on an ion in an applied field E by definition (3.1.8) is generally satisfactory. 

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