Conservation of species

The three terms on the right hand side indicate that the species transfer in phase k is due to diffusion, migration, and convection, respectively. In the above equation. 

Equation 25.8 is valid in both phases,with representing the lithium ion concentration in the electrolyte and lithium concentration in the solid active material. 

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In addition to the Burke and Schumann model (34) and the Displacement Distance theory, a comprehensive laminar diffusion flame theory can be written using the equations of conservation of species, energy, and momentum, including diffusion, heat transfer, and chemical reaction. 

The Gaussian Plume Model is the most well-known and simplest scheme to estimate atmospheric dispersion. This is a mathematical model which has been formulated on the assumption that horizontal advection is balanced by vertical and transverse turbulent diffusion and terms arising from creation of depletion of species i by various internal sources or sinks. In the wind-oriented coordinate system, the conservation of species mass equation takes the following form ... 

For our estimations and the adiabatic control volume in Figure 4.10, 7b should be the adiabatic flame temperature. Consider a fuel-lean case in which no excess fuel leaves the control volume. All the fuel is burned. Then by the conservation of species,... 

A conservation of species with the possibility of chemical reaction can be functionally represented from Equation (3.22) for species i with a chemical yield, y,- (mass of species i per mass of reacted fuel) ... 

The mass conservation of species for a batch reactor, which is characterized by a fixed amount of mass, is given simply as... 

A two-dimensional, electrochemical, and transport-coupled transient fuel cell model is developed based on the laws of conservation of species and charge14 ... 

Air channels Navier-Stokes (2 eq.), Continuity, Energy, Conservation of species (1 eq.) 40000... 

The problem under consideration is shown schematically in Figure 9.9. The governing equation for this problem was given previously in Equation (9.8), where the species fluxes, are determined from Equation (9.7). Equation (9.7), for i = 1 to J — 1, provides a linear set of independent ordinary differential equations. To solve for all J components, an additional equation is needed. For this we use the conservation of species ... 

Equation (3.45) is the general continuum statement of mass conservation of species i written in terms of the mass flux density f, and the concentration field c,. 

A more general description of transport is based on conservation of species, m given b) ... 

Substitution of the definition for concentration (equation (11.44) into the expression for conservation of species i (equation (11.41)) yields... 

The conservation of species i in a packed CRAE column is given by... 

When we substitute (2.32) in (2.1). the equation of conservation of species in the presence of an external force Held becomes... 

Variations in atmospheric aerosol compositions can be linked to aerosol dynamics through 1------ -----i- conservation of. species for the chemical components in the submicron... 

S.L. Pimm (1991). The Balance of Naturel Ecological Issues in the Conservation of Species and Communities. The University of Chicago Press, Chicago. 

Some important features of these models are summarized in the next section. However, it should be noted that a comprehensive quantitative mathematical model for PTC, accounting for the intrinsic kinetics of ion-exchange and main organic reaction, mass conservation of species, overall mass conservation, interphase and intraphase mass transfer, catalyst loading and activity, equilibrium partitioning of catalyst, location of reaction (organic phase, aqueous or solid phase, or interface), and flow patterns for each phase, are yet to be developed. 

The conservation of species equations, whether expressed in terms of mass Eq, (2.2-2)) or moles [Eq. 2.2-4)], are entirely equivalent) the choice of which to use is made on the basis of convenience. The steady-state forms of these material balances are universally employnd in the desiga and analysis of chemical processes including separation devices.J 4 Many examples will be encountered in later chaprem of this book. The primary purpose here is to set the stage for the differential balance formulation to follow shortly. 

In the conservation of species equation for a binary system (Eq. 3.3.17), it is sometimes assumed that the velocity u is given by the solution to the momentum equation for the solvent. Determine a criterion for this assumption to be valid that is dependent on the solute volume fraction , the ratio of the density of the solvent particle to the density of the solute particle, and the ratio of the velocity of the solute species to the velocity of the solvent species. Is the condition [Pg.80]

The concentration c is not known in advance, but must be determined from the overall conservation of species if we know the initial uniform species concentration and the concentration drop across the cell, which for a given voltage or current is specified by the solution. Integrating Eq. (6.1.16) and applying this boundary condition gives... 

In this equation, from conservation of species we have used the condition c. + = 2cq, where is the initial uniform reduced species concentration. This... 

The solution to this laminar boundary layer problem must satisfy conservation of species mass via the mass transfer equation and conservation of overall mass via the equation of continuity. The two equations have been simplified for (1) two-dimensional axisymmetric flow in spherical coordinates, (2) negligible tangential diffusion at high-mass-transfer Peclet numbers, and (3) negligible curvature for mass flux in the radial direction at high Schmidt numbers, where the mass transfer... 

Conservation of species can also be expressed on a molar basis as shown by Eq. (2.2-4) ... 

The species conservation equations in cylindrical and spherical coordinates are shown in Table 2.2-2. In rectangular coordinates the cotieqionding conservation of species equations in molar units ate... 

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