Length Debye

Debye-Hiickel equation Debye-length Condenser capacity... 

Assuming that the gas is electricaUy neutral over regions having dimensions larger than the Debye length, typicaUy of the order 10 m in an MHD generator, the electron and ion densities in the bulk of the gas are equal. 

An important characteristic of plasma is that the free charges move in response to an electric field or charge, so as to neutralize or decrease its effect. Reduced to its smaUest components, the plasma electrons shield positive ionic charges from the rest of the plasma. The Debye length, given by the foUowing ... 

The region of the gradual potential drop from the Helmholtz layer into the bulk of the solution is called the Gouy or diffuse layer (29,30). The Gouy layer has similar characteristics to the ion atmosphere from electrolyte theory. This layer has an almost exponential decay of potential with increasing distance. The thickness of the diffuse layer may be approximated by the Debye length of the electrolyte. 

In most electrochemical systems, the double layer is very thin (1—10 nm). The thickness is characterized by the debye length, X,... 

Selecting the values of the parameters for the calculations we have in mind a 1 1 aqueous 1 m solution at a room temperature for which the Debye length is 0.3 nm. We assume that the non-local term has the same characteristic length, leading to b=. For the adsorption potential parameter h we select its value so that it has a similar value to the other contributions to the Hamiltonian. To illustrate, a wall potential with h = 1 corresponds to a square well 0.1 nm wide and 3.0 kT high or, conversely, a 3.0 nm wide square well of height 1.0 kT. 

De Wolff model, manganese oxides 89 dead lithium 344 ff Debye length... 

A new approach to the double-layer capacitance of rough electrodes has been given by Daikhin et al.m m The concept of a Debye length-dependent roughness factor [i.e., a roughness function R LD) that deter-... 

In the limit of large Debye lengths (low electrolyte concentrations) the roughness would not bear on capacitance, which would thus obey Eq. (59). 

In concentrated NaOH solutions, however, the deviations of the experimental data from the Parsons-Zobel plot are quite noticeable.72 These deviations can be used290 to find the derivative of the chemical potential of a single ion with respect to both the concentration of the given ion and the concentration of the ion of opposite sign. However, in concentrated electrolyte solutions, the deviations of the Parsons-Zobel plot can be caused by other effects,126 279"284 e.g., interferences between the solvent structure and the Debye length. Thus various effects may compensate each other for distances of molecular dimensions, and the Parsons-Zobel plot can appear more straight than it could be for an ideally flat interface. 

The Debye length of the electrode material can be determined from the constant B, and the sensitivity factor S from C, provided the diffusion length and the diffusion constant for minority carriers are known. 

With electrochemically studied semiconductor samples, the evaluation of t [relation (39)] would be more straightforward. AU could be increased in a well-defined way, so that the suppression of surface recombination could be expected. Provided the Debye length of the material is known, the interfacial charge-transfer rate and the surface recombination... 

Thermal diffusivity Temperature sensitivity Temperature difference Thickness of tube Aspect ratio, relation of Cp/Cy Fluid dielectric constant Wall zeta potential Dimensionless temperature Friction factor, Debye length Mean free path Dynamic viscosity Kinematic viscosity Bejan number Density... 

Where the slope s determined by the plot is the extension coefficient. The I-1/2 dependence viewed in terms of an increased Debye length can be explained as the electrostatic excluded volume contribution. 

The electroviscous effect present with solid particles suspended in ionic liquids, to increase the viscosity over that of the bulk liquid. The primary effect caused by the shear field distorting the electrical double layer surrounding the solid particles in suspension. The secondary effect results from the overlap of the electrical double layers of neighboring particles. The tertiary effect arises from changes in size and shape of the particles caused by the shear field. The primary electroviscous effect has been the subject of much study and has been shown to depend on (a) the size of the Debye length of the electrical double layer compared to the size of the suspended particle (b) the potential at the slipping plane between the particle and the bulk fluid (c) the Peclet number, i.e., diffusive to hydrodynamic forces (d) the Hartmarm number, i.e. electrical to hydrodynamic forces and (e) variations in the Stern layer around the particle (Garcia-Salinas et al. 2000). 

Note that when the concentration of added salt is very low, Debye length needs to be modified by including the charge contribution of the dissociating counterions from the polyelectrolytes. Because the equilibrium interaction is used, their theory predicts that the intrinsic viscosity is independent of ion species at constant ionic strength. At very high ionic strength, the intrachain electrostatic interaction is nearly screened out, and the chains behave as neutral polymers. Aside from the tertiary effect, the intrinsic viscosity will indeed be affected by the ionic cloud distortion and thus cannot be accurately predicted by their theory. 

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