Element conservation

However, since the chemical source term can be expressed in terms of T and R, the element conservation constraints can be rewritten as8... 

Note that the right-hand side of this expression is an E x I null matrix, and thus element conservation must hold for any choice of e e l,E and i e 1Moreover, since the element matrix is constant, (5.10) can be applied to the scalar transport equation ((1.28), p. 16) in order to eliminate the chemical source term in at least E of the K equations.9 The chemically reacting flow problem can thus be described by only K - E transport equations for the chemically reacting scalars, and E transport equations for non-reacting (conserved) scalars.10... 

The results presented above were discussed in terms of the special case of elementary reactions. However, if we relax the condition that the coefficients vfai and uTai must be integers, (5.1) is applicable to nearly all chemical reactions occurring in practical applications. In this general case, the element conservation constraints are no longer applicable. Nevertheless, all of the results presented thus far can be expressed in terms of the reaction coefficient matrix T, defined as before by... 

Reaction-stoichiometry plus element-conservation constraints put non-trivial bounds on the composition vector 0. The interior of these bounds forms the allowable region (see Fig. 6.1). 

Application of the element-conservation constraints, in particular, and linear transformations, in general, to the transport equations forces us to seek mixing models that preserve... 

Realizability and boundedness of all variables are assured. In particular, since the chemical source term is treated exactly, mass and element conservation is guaranteed at the notional-particle level. 

The elemental conservation equation is laid down on the same principles as the continuity equation. The rate of variation of the amount of element i contained in... 

There are p + 4 unknowns however, there are 4 flow equations as listed above arid xv element conservation equations. Just as in the solution of the equilibrium flame temperature problem discussed in section II. B. 5., M - a additional equations are required. Except instead of using the equilibrium equations, one must adopt the chemical kinetic rate equations. The form used with the present problem is ... 

Cu 0.20 element. Conservative limits recommended due to lack of knowledge on its toxicity to plants Toxic to a number of plants at 0.1—1.0 mg L-1... 

LESNICK, M. L., CHANDLER, V. L., Activation of the maize anthocyanin gene a2 is mediated by an element conserved in many anthocyanin promoters, Plant Physiol., 1998,117,437-445. 

Next we apply three fundamental laws to this fluid element Conservation of mass, conservation of momentum, and conservation of energy to obtain the continuity, momentum, and energy equations for laminar flow in boundary layers. 

For a CFD volume element, conservation of momentum can be expressed by the following statement ... 

Not all of the balance equations are independent of one another, thus the set of equation used to solve particular problems is not solely a matter of convenience. In chemical reactor modeling it is important to recall that all chemical species mass balance equations or all chemical element conservation equations are not independent of the total mass conservation equation. In a similar manner, the angular momentum and linear momentum constraints are not independent for flow of a simple fluid . 

Key Words Multiple alignment alignment tool evolutionary conservation conserved elements conserved transcription factor binding sites. 

Anthropogenic Trace Elements in the Ocean. Conservative Elements. Conservative Elements. Refractory Metals. Transition Metals and Heavy Metal Speciation. 

Due to the choice of the examples used to introduce chemical phenomena to children (see De Vos Verdonk, 1985a) students reserve an important role for energetic effects. Teachers always try to use these examples to teach the characteristics of chemical change as they see them, i.e. as evidences of the disappearance and appearance of substances, the laws of mass conservation and element conservation. For them, the energetic... 

The practical utilization of the concept of Gibbs free energy is therefore that equilibrium of the system requires that any possible (element-conserving) chemical reaction that the system could undertake must satisfy the relation... 

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