The electric field strength

Since the ER effect is induced by the electric field, the impact of the electric field strength on the ER effect has been extensively studied. A critical electric field strength, Ej, exists, and the ER fluid could not show any ER effect until the applied electric field strength exceeds the critical one [l,2J. Theoretical treatment [3] shows that the critical electric field may be expressed as  

(1) indicates that the critical electric field strength decreases with the increase of particle concentration. The critical electric field concept was also used in several other theoretical treatments [4-6]. However, the critical electric field was assumed to be a constant only depending on the electric property of the dispersing medium. The liquid-solid phase transition induced by the external electric field is supposed to happen at the critical electric field that is in the order of several hundred to one thousand volts per millimeter. In consideration of electric-field-induced particle aggregation in ER fluids, Khusid [7J suggested that the critical electric field is the function of particle volume fraction, the dielectric constant and conductivity of both the particle and dispersing medium. It should be as low as 14 V/mm, as confirmed experimentally [8] 

The relationship between the shear stress (or yield stress ) and the electric field is complicated. In early literature, the yield stress was reported to linearly increase with the electric field [I]  

---

This perturbation method is claimed to be more efficient than the fluctuating dipole method, at least for certain water models [Alper and Levy 1989], but it is important to ensure that the polarisation (P) is linear in the electric field strength to avoid problems with dielectric saturation. 

The dielectric constant (permittivity) tabulated is the relative dielectric constant, which is the ratio of the actual electric displacement to the electric field strength when an external field is applied to the substance, which is the ratio of the actual dielectric constant to the dielectric constant of a vacuum. The table gives the static dielectric constant e, measured in static fields or at relatively low frequencies where no relaxation effects occur. 

The magnitude of the induced dipole moment depends on the electric field strength in accord with the relationship = nT, where ]1 is the induced dipole moment, F is the electric field strength, and the constant a is caHed the polarizabHity of the molecule. The polarizabHity is related to the dielectric constant of the substance. Group-contribution methods (2) can be used to estimate the polarizabHity from knowledge of the number of each type of bond within the molecule, eg, the polarizabHity of an unsaturated bond is greater than that of a saturated bond. 

The heating effect is the limiting factor for all electrophoretic separations. When heat is dissipated rapidly, as in capillary electrophoresis, rapid, high resolution separations are possible. For electrophoretic separations the higher the separating driving force, ie, the electric field strength, the better the resolution. This means that if a way to separate faster can be found, it should also be a more effective separation. This is the opposite of most other separation techniques. 

No. This happens for only one Uwr value for which the electric field strength E vanishes (Fig. 4.48). 

There are different variants of the conjugate gradient method each of which corresponds to a different choice of the update parameter C - Some of these different methods and their convergence properties are discussed in Appendix D. The time has been discretized into N time steps (f, = / x 8f where i = 0,1, , N — 1) and the parameter space that is being searched in order to maximize the value of the objective functional is composed of the values of the electric field strength in each of the time intervals. 

Thus the IR active modes will be determined by the matrix elements of the polarlsablllty matrix and not by a combination of the surface selection rule and the normal IR selection rules l.e. all of the Raman active modes could become accessible. This effect has been formalized and Its significance assessed In a discussion (12) which compares Its magnitude for a number of different molecules. In the case of acrylonitrile adsorption discussed In the previous section, the Intensity of the C=N stretch band appears to vary with the square of the electric field strength as expected for the Stark effect mechanism. 

Time steps of about 60 s between switching on and off were realized. The performance of the MSE structures depends on their geometry, the electric field strength and the gas pressure. 

Auxiliary electrodes are placed into the solution to set up the electric field that is needed to produce electrophoresis or electroosmosis. Under these conditions an electric current passes through the solution and the external circuit its value depends on the applied voltage and on solution conductivity. The lower this conductivity, the higher will be the electric field strength E (or ohmic voltage drop) in the solution that can be realized at a given value of current. 

When an aqueous phase (noted w) is brought in contact with a second immiscible phase (noted o), the different species dissolved in one or the two phases spontaneously distribute depending on their hydrophilic-lipophilic balance until the thermodynamic equilibrium is reached. The distribution of the charged species generates an interfacial region, in which the electrical field strength differs from zero, so that an electrical Galvani potential difference, is established across the interface ... 

From this one obtains the distribution of the electric field strength according to... 

For very dilute solutions, the motion of the ionic atmosphere in the direction of the coordinates can be represented by the movement of a sphere with a radius equal to the Debye length Lu = k 1 (see Eq. 1.3.15) through a medium of viscosity t] under the influence of an electric force ZieExy where Ex is the electric field strength and zf is the charge of the ion that the ionic atmosphere surrounds. Under these conditions, the velocity of the ionic atmosphere can be expressed in terms of the Stokes law (2.6.2) by the equation... 

The dielectric strength of an insulator is the electric field strength at which it physically breaks down and begins to conduct electricity. High values are required when the material will experience high electrical stresses, such as those found in the insulation surrounding power transmission cables. Dielectric strength decreases as temperature and humidity increase. It also decreases with time, due to the creation of conductive paths on the surface of the material. 

Ionic conduction studies in solids date back to the work of Gunterschultze and Betz,50 who derived the empirical relationship between the electric field strength, E = [(o) " (4>o)jV (cf. Fig. lb), in an oxide and the nonohmic ionic current density, j9... 

However, there are indications that these values depend on the conditions of ionization. Vermilyea88 has interpreted the change from compressive to tensile stress, recorded in the oxide, to be due to the dependence of the transport number of aluminum on the electric field strength. Brown89 has found this transport number to depend on the electrolyte used in anodization. 

---