Electrical force field

The physical separation of charge represented allows externally apphed electric field forces to act on the solution in the diffuse layer. There are two phenomena associated with the electric double layer that are relevant electrophoresis when a particle is moved by an electric field relative to the bulk and electroosmosis, sometimes called electroendosmosis, when bulk fluid migrates with respect to an immobilized charged surface. 

Ion-Electrode Interactions. Similarly to water molecules in contact with the electrode (see Section 6.7.2), ions in contact with a charged metal experience different types of forces operating between the ion and the metal electrode. These include electric field forces, image forces, dispersion forces, and electronic forces. 

The electric field forces arise because the ions, with their negative or positive charges, are attracted or repelled by the charge on the metal (Section 6.3 J). 

The velocity of the ion (v) can be described then as the ratio of electrical field force (E) and magnetic field force (B) ... 

Baird et al. [350]). In the following analysis, the functional forms, p(E), which have been proposed (see below) to represent the field-dependence of the drift mobility are used for electric fields up to 1010Vm 1. The diffusion coefficient of ions is related to the drift mobility. Mozumder [349] suggested that the escape probability of an ion-pair should be influenced by the electric field-dependence of both the drift mobility and diffusion coefficient. Baird et al. [350] pointed out that the Nernst— Einstein relationship is not strictly appropriate when the mobility is field-dependent instead, the diffusion coefficient is a tensor D [351]. Choosing one orthogonal coordinate to lie in the direction of the electric field forces the tensor to be diagonal, with two components perpendicular and one parallel to the electric field. 

It results from the balance between the electrical field force, Fei, and the frictional force, FP... 

We introduce the force F as an electric field force by the gradient of the electrostatic potential (x),... 

Most dielectrophoretic separations of cells to date have used steric-DEP-FFF. The cells are usually effectively immobilized in potential energy minima [282] near the electrodes by a combination of gravity and electrical field forces. Afterwards, the applied hydrodynamic flow forces transport those particles that are held less strongly at the electrodes. 

If we consider that the flow is steady, two-dimensional, and fully developed, and there is no pressure gradient in the microchannel, the general equation of motion is given by a balance between the viscous or shear stresses in the fluid and the externally imposed electrical field force ... 

Figure 5-5 After attaining the pH where protein A has a net charge of zero (A°), diffusion toward the cathode bestows a negative charge on A (A ), and migration In the electric field forces A back to A°. Diffusion toward the anode causes A to take on the opposite charge A-f, and migration is toward the cathode and to the point where A° exists. IF processes of this kind cause sharp zones to form (i.e., the protein is focused).

A common feature of electrokinetic phenomena is a relative motion of the charged surface and the volumetric phase of the solution. The charged surface is affected by the electric field forces, and the movement of such surfaces toward each other induces the electrical field. That is a question of slip plane between the double layer and a medium. The layer bounded by the plane at the distance d from surface (OHP) can be treated as immobile in the direction perpendicular to the surface, because the time of ion residence in the layer is relatively long. Mobilty of ions in the parallel direction to the interfacial surface should also be taken into account. However, it seems that the ions in the double layer and in the medium surrounding it constitute a rigid whole and that the layer from x = 0 to X = d is immobile also in the sense of resistance to the tangent force action. There is no reason why the boundary plane of the solution immobile layer should overlap accurately with the OHP plane. It can be as well placed deeply in the solution. The potential in the boundary plane of the solution immobile layer is called potential (. Strictly speaking it is not a potential of interface because it is created in the liquid phase. It can be considered as the difference of potentials between a point far from the surface (in the bulk solution) and that in the slip plane. 

The electric field, force of interaction and work done... 

A liquid interface is the first requirement for all the many forms of capillarity. At least one phase must be sufficiently fluid. The shape of a liquid with an interface to air or another liquid is determined by the surface or interface tension. The shape of a liquid surface or interface at rest changes only when the surface tension, forces of gravity, and in some cases the electric field forces (Lorentz forces) are altered, provided the solid boundaries have constant dimensions and certain angles. The shape of pendant drops, sessile drops on a solid substrate, a meniscus against a solid wall and the length of so-called surface waves are well-known examples of capillarity. These phenomena need separate examination of liquid interfaces, as the surface state between two phases cannot be deduced from their bulk properties. 

For the transport of heavy ions to a solid surface coated with an adherent water film, like aluminium oxide, the visco-elastic properties of electric field forces and the concentration of heavy ions may be important for the rate of adsorption. For this reason we need information not only on relaxations restricted to a surface of an extended liquid, but also on the adherent water layer at the adsorbents. The last issue may be a bridge to the thermodynamics and flow properties of thin liquid films have been studied by some excellent research groups. 

It remains to evaluate the inertia free, viscous velocity field subject to the combined electric field force. The Navier-Stokes equation in this case is... 

The NO radical was originally believed [39] to be constrained to a fixed orientation in either a potassium ion or azide ion vacancy by crystalline electric-field forces. With this assumption it was necessary to explain certain features of the ESR spectrum on the basis of a 2 ground state rather than the well-established 7T ground state of NO. This led Fuller and Tarr [40] to propose that the resonances were due to NOl instead. Subsequently, studies of NO were extended to rubidium and cesium azides [41], which have the same crystal structure as potassium azide. The directions of the principal axes of the spin-Hamiltonian were reinterpreted to be consistent with a ground state. A possible rotation of the NO molecule was also suggested. 

Physicists took to designing devices to accelerate charged particles in an electric field, forcing them to move faster and faster and therefore to possess more and more energy. The English physicist John Douglas Cockcroft (1897- ) and his co-worker,... 

As seen fromEq. (12.19), the induced dipole moment with the components pq—pL q may have a different direction from the applied electric field (due to the tensor character of the polarizability and hyperpolarizabilities). This is quite understandable because the electrons will move in a direction that will represent a compromise between the direction the electric field forces them to move in and the direction where the polarization of the molecule is easiest (Fig. 12.4). 

If non-diagonal components of the polarizability tensor are nonzero, then the charge flow direction within the molecule will differ from the direction of the field. This would happen when the electric field forced the electrons to flow into empty space, while they had a highway" to travel along some chemical bonds (cf. Fig. 12.4). 

An externally applied electric field is a vectorial perturbation for chemical or orientational distributions involving interacting molecules or molecular organizations. Unlike the isotropic temperature and pressure effects on chemical-conformational transformations, direct sensitivity to electric field forces is bound to certain electrical properties of the chemical structures involved. Major structural-chemical changes in electric fields require the presence of ions, or ionized groups, or permanent or induced dipolar charge configurations, preferably in macromolecular structures. 

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