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Flux material species

A mathematical description of an electrochemical system should take into account species fluxes, material conservation, current flow, electroneutrality, hydrodynamic conditions, and electrode kinetics. While rigorous equations governing the system can frequently be identified, the simultaneous solution of all the equations is not generally feasible. To obtain a solution to the governing equations, we must make a number of approximations. In the previous section we considered the mathematical description of electrode kinetics. In this section we shall assume that the system is mass-transport limited and that electrode kinetics can be ignored. [Pg.242]

In the above conservations equations, expressions for the fluxes are required. This has already been accounted for in the energy and momentum balances (Eqs. 11 and 12, respectively) to provide second-order equations the reason being that they are highly coupled and remain general for many systems. However, understanding the fluxes and transport expressions for the material species including ions (Eq. 2) is critical in determining the resistances in the ionic and electronic phases and the overall response of the porous electrode thus, they are discussed in more detail. [Pg.1208]

The nature of such an effective diffusivity is illustrated in Fig. 2.4 on a plot of the effective diffusivity/molecular diffusivity ratio against the porosity for various granular materials. Numerous methods have been proposed for both the estimation of the effective diffusivity and for the representation of pore diffusion through the use of this parameter. A detailed review of these would be beyond the scope of this monograph, so here we shall present a recent treatment proposed by Mason and coworkers [29, 30], who suggested that the diffusive flux of species A in a binary mixture in an isothermal porous solid may be represented by the expression... [Pg.25]

Chemical Reaction Measurements. Experimental studies of incineration kinetics have been described (37—39), where the waste species is generally introduced as a gas in a large excess of oxidant so that the oxidant concentration is constant, and the heat of reaction is negligible compared to the heat flux required to maintain the reacting mixture at temperature. The reaction is conducted in an externally heated reactor so that the temperature can be controlled to a known value and both oxidant concentration and temperature can be easily varied. The experimental reactor is generally a long tube of small diameter so that the residence time is well defined and axial dispersion may be neglected as a source of variation. Off-gas analysis is used to track both the disappearance of the feed material and the appearance and disappearance of any products of incomplete combustion. [Pg.57]

Although inhibitors are deliberately added to the silicone formulation to control cure rate, unwanted cure inhibition can be caused by other species that react to form strong complexes with the platinum catalyst. Most notable of these undesired inhibitors include organotin and other organometallic compounds, sulfur, polysulfides, polysulfones or other sulfur-containing materials, amines, urethanes or amine-containing materials, unsaturated hydrocarbons in plasticizers, and some solder flux residues. [Pg.687]

It should be kept in mind that all transport processes in electrolytes and electrodes have to be described in general by irreversible thermodynamics. The equations given above hold only in the case that asymmetric Onsager coefficients are negligible and the fluxes of different species are independent of each other. This should not be confused with chemical diffusion processes in which the interaction is caused by the formation of internal electric fields. Enhancements of the diffusion of ions in electrode materials by a factor of up to 70000 were observed in the case of LiiSb [15]. [Pg.532]

The sediment surface separates a mixture of solid sediment and interstitial water from the overlying water. Growth of the sediment results from accumulation of solid particles and inclusion of water in the pore space between the particles. The rates of sediment deposition vary from a few millimeters per 1000 years in the pelagic ocean up to centimeters per year in lakes and coastal areas. The resulting flux density of solid particles to the sediment surface is normally in the range 0.006 to 6 kg/m per year (Lerman, 1979). The corresponding flux density of materials dissolved in the trapped water is 10 to 10 kg/m per year. Chemical species may also be transported across the sediment surface by other transport processes. The main processes are (Lerman, 1979) ... [Pg.81]

In order to illustrate the effects of media structure on diffusive transport, several simple cases will be given here. These cases are also of interest for comparison to the more complex theories developed more recently and will help in illustrating the effects of media on electrophoresis. Consider the media shown in Figure 18, where a two-phase system contains uniform pores imbedded in a matrix of nonporous material. Solution of the one-dimensional point species continuity equation for transport in the pore, i.e., a phase, for the case where the external boundaries are at fixed concentration, Ci and Cn, gives an expression for total average flux... [Pg.566]

The flux of charge, connected with the mass flux of the electrically charged species, is given by Faraday s law for the equivalence of the current density and the material fluxes ... [Pg.96]

Consider a dilute electrolyte solution containing s components (nonelectrolytes and various ionic species) in which concentration gradients of the components and an electric field are present. The material flux of the ith component is then given by a combination of Eqs (2.3.11) to (2.3.20) ... [Pg.121]

Diffusion is a more subtle phenomenon and depends on the fact that if a concentration gradient exists between two points in a solution, there will be a flux of material from the region of higher to lower concentration. If we consider Figure 1.9, this shows the presence of a stream of material through two planes, at x and x + Sx. If the concentration gradient at x is dc/dx, where c is the concentration of the species at x, then the flux of material per unit area, J, across the plane at x in the positive direction of x, is given by Fick s first law ... [Pg.27]


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See also in sourсe #XX -- [ Pg.402 ]




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