Electric potential gradient, impose

An acid-base transition also drives reversal of the PS Il-induced charge separation indicated by luminescence [84]. The reaction again requires preprovision of an oxidized partner by preillumination, and is stimulated by a simultaneously imposed electric potential gradient of the proper polarity [85]. 

Fig. 4 Imposing an electrical potential gradient across a charged membrane produces a convective solvent flow in the direction of counter-ion transport (i.e., from anode-to-cathode in the case of skin). This electroosmotic effect (EO) adds to electrorepulsion (ER) to enhance the transport of cationic compounds during iontophoresis (4a) while acting against the electromigration of anions (4b).

When an electrical potential gradient is imposed on the stack, alternate compartments become enriched and depleted in sodium chloride. A typical module of an electrodialytic salt plant has 1500 pairs of membranes, each with an effective membrane area of 1 m2. The current density is 3.65 A/dm2 at 620 V with a membrane spacing of about 0.75 mm. A brine concentrate containing about 118 g/1 of chloride can be attained. The overall current efficiency is 73% for Na+ and 85% for Cl". Typically, the membranes are divinylbenzene cross-linked polystyrene with sul-phonic acid, or quaternary ammonium exchange groups the exchange capacity is 1.8 to 2.8 meq/g at 25 °C34). 

The most characteristic properties of ions are their abilities to move in solution in the direction of an electrical field gradient imposed externally. The conductivity of an electrolyte solution is readily measured accurately with a 1 kHz alternating potential in a virtually open circuit, in order to avoid electrolysis. The molar conductance of a completely dissociated electrolyte is A2 = A2°° - 2 + EC2 In C2 + J iR ) C2 — J" R")c2, where S, E, f, and f are explicit expressions, containing contributions from ionic atmosphere relaxation and electrophoretic effects, the latter two depending also on ion-distance parameters R. The infinite dilution can be split into the limiting molar ionic conductivities by using experimentally measured transport numbers extrapolated to infinite dilution, t+° and i °° = 1 - <+°°. For a binary electrolyte, Aa = 2+°° -I- and = i+ A2. Values of the limiting ionic molar conductivities in water at 298.15 K [1] are accurate to 0.01 S cm mol (S = Q ). 

The measurement of thermopower is based on the Seebeck effect, which consists of the generation of a difference in the electrical potential aeross imposed temperature gradient. For a nondegenerate semiconductor, in which one type of electronic charge carrier predominates, one may formulate interrelationships between thermopower (S) and the concentration of electronic carriers. For n-type and p-type regimes the following expressions may be written ... 

The origin of the ohmic potential difference was described in Section 2.5.2. The ohmic potential gradient is given by the ratio of the local current density and the conductivity (see Eq. 2.5.28). If an external electrical potential difference AV is imposed on the system, so that the current I flows through it, then the electrical potential difference between the electrodes will be... 

It should be noted that in addition to mechanical forces such as electric or magnetic fields that couple to charges and polarization in our system, other kinds of forces exist whose effect cannot be expressed by Eq. (11.2). For example, temperature or chemical potential gradients can be imposed on the system and thermal or material fluxes can form in response. In what follows we limit ourselves first to linear response to mechanical forces whose effect on the Hamiltonian is described by Eqs (11.2) or (11.3). 

Electroosmosis The motion of liquid through a porous medium caused by an imposed electric field. The term replaces the older terms elec-trosmosis and electroendosmosis. The liquid moves with an electroos-motic velocity that depends on the electric surface potential in the stationary solid and on the electric field gradient. The electroosmotic volume flow is the volume flow rate through the porous plug and is usually expressed per unit electric field strength. The electroosmotic pressure is the pressure difference across the porous plug that is required to just stop electroosmotic flow. 

ElectrocapUlary phenomenon refers to the modification of the interfacial tension by the presence of electrical charges. The first comprehensive investigations on electrocapillary phenomena were performed by Lippman, way back in 1875 [1]. In Lippman s experimental apparatus, the interfacial tension modulation due to electrical effects was observed through a capillary rise phenomenon and hence was later termed as electrocapillarity. A decisive advantage of electrocapillary actuation, in comparison to its thermal counterpart (i.e., the thermocapUlary effect, in which surface tension differentials are created by imposed temperature gradients), is the speed with which electrical potentials can be applied and regulated, with possible characteristic timescales of even less than a few milliseconds. Further, electrocapdlary-based microactuators consume much less power, as compared to the typical thermocapillary microdevices. 

The treatment of membrane separation processes in this book merits some deliberation. The most commonly used driving force in membrane separation processes is negative chemical potential gradient a few processes also employ electrical force. Figure 3.4.5 identifies the variety of feed phase-membrane type combinations with variations due to the nature of the permeate phase when negative chemical potential gradient is imposed across the membrane. Section... 

The motion of polymer molecules in a solution under chemical potential gradients or externally imposed electric fields is an example of the drift-diffusion stochastic processes. We have introduced several equivalent formalisms for studying these processes biased random walk, master equation, and Langevin equation of motion. In each of these lines of arguments, we have arrived at the Fokker-Planck-Smoluchowski equation. 

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