Gradient Electric Force

Kumar and coworkers proposed a mechanism on the basis of the observation that an electric field component in the direction of mass flow was required (Yang et ah, 2006 Bian et al., 2000 Viswanathan et ah, 1999a Kumar et ah, 1998). This force is essentially an optical gradient force (Chaumet and Nieto-Vesperinas, 2000 Ashkin, 1997, 1970). Spatial variation of light (electric field intensity and orientation) leads to a variation of the material susceptibility, %, at the sample surface. The electric field then polarizes the material. The induced polarization is related to the light intensity and local susceptibility  

Forces then occur between the polarized material and the light field, analogous to the net force on an electric dipole in an electric field gradient. The time-averaged force was derived to be (Viswanathan et al., 1999a) as follows  

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Electrical trees consist of visible permanent hoUow channels, resulting from decomposition of the material, and show up clearly in polyethylene and other translucent soHd dielectrics when examined with an optical microscope. Eresh, unstained water trees appear diffuse and temporary. Water trees consist of very fine paths along which moisture has penetrated under the action of a voltage gradient. Considerable force is required to effect this... 

The most important driving forces for the motion of ionic defects and electrons in solids are the migration in an electric field and the diffusion under the influence of a chemical potential gradient. Other forces, such as magnetic fields and temperature gradients, are commonly much less important in battery-type applications. It is assumed that the fluxes under the influence of an electric field and a concentration gradient are linearly superimposed, which... 

The velocity v of liquid motion can be found from the condition that the electric force should be compensated by the viscous friction force /f. The latter is proportional to the velocity gradient in the layer of slipping charges ... 

One observes, comparing Eqs. (45) and (46) for permeating ions of comparable size and valence with Eq. (47), that the diffusion of cations across the negatively charged pore is increased by the potential gradient. In contrast, the diffusion of anions is decreased by the electrical forces. In other words, P+ or P is composed of the permeability coefficient of its neutral image upon which the contribution... 

Figure 8.9 Isoelectric focusing. The motion of a protein undergoing isoelectric focusing is depicted (circles). The protein is shown near its pi in a pH gradient. Both the pH gradient and the motion of the protein are governed by an applied electric field. At pH values lower than the pi, the protein is positively charged (+) and it is driven toward the cathode as shown by the arrow. Above its pi, the protein is negatively charged (-) and it moves toward the anode. There is no net electrical force on the protein at its pi (0). The protein focuses in a Gaussian distribution centered at the pi.

When charges are separated, a potential difference develops across the interface. The electrical forces that operate between the metal and the solution constitute the electrical field across the electrode/electrolyte phase boundary. It will be seen that although the potential differences across the interface are not large ( 1 V), the dimensions of the interphase region are very small (—0.1) and thus the field strength (gradient of potential) is enormous—it is on the order of 10 V cm. The effect of this enormous field at the electrode/electrolyte interface is, in a sense, the essence of electrochemistry. 

According to (1.3b), the nonconvectional electro-diffusion flux component j. is a superposition of the following two terms. The first is the diffusional Fick s component proportional to the concentration gradient VC. The second is the migrational component, proportional to the product of the ionic concentration Cj and the electric force —ZiFV

proportionality factor. Einstein s equality (1.3c) relates ionic mobility to diffusivity >. ... 

In heterogeneous solid state reactions, the phase boundaries move under the action of chemical (electrochemical) potential gradients. If the Gibbs energy of reaction is dissipated mainly at the interface, the reaction is named an interface controlled chemical reaction. Sometimes a thermodynamic pressure (AG/AK) is invoked to formalize the movement of the phase boundaries during heterogeneous reactions. This force, however, is a virtual thermodynamic force and must not be confused with mechanical (electrical) forces. 

Electric-force mixing is adequate for mixing flows at very low Reynolds number (-1). By lamination of two fluids with different electric conductivity and/or permittivity in a micro mixer, a steep cross-sectional gradient of the respective properties can be established [91]. The electric field may be parallel or perpendicular to the fluid interface, which is also a boundary where electric properties abruptly... 

The electric force per unit charge is therefore given by the negative of the gradient of the electrostatic potentials, and the region of space in which the force operates is known... 

This dependence of rtk on mass must also hold, if instead of a chemical force (concentration gradient) an electrical force is the cause of the transport. 

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