Download e-book for kindle: Advances in Chemical Engineering, Vol. 24 by James Wei (Ed.)

By James Wei (Ed.)

ISBN-10: 0120085240

ISBN-13: 9780120085248

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Extra resources for Advances in Chemical Engineering, Vol. 24

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51), one concludes that p* lies in the orthogonal complement, that is, that p* can be expressed as - r p* = Z crLaL. 1 The coefficients aLplay the role of the usual Lagrange multipliers in the determination of the minimum of Gibbs free energy. Any set of aL’sdetermines an equilibrium point (but infinitely many of these are not accessible from the initial composition). The great advantage of the orthogonal complement method is that the number of linear constraints, C, is invariably small, regardless of how large N and R might be.

96) The overall concentration C(t)is given by C(t) = ; (97) that is, C(t) is a Laplace transform of c(y,O), with the dimensionless time t playing the rather unusual role of the transform parameter. Notice that -dC/dt (the overall rate of consumption) equals ; that is, it is equal to the first moment of c(x, r). OCONE AND G . ASTARITA Now suppose c(x,O) is the gamma distribution c$(a,x). One can now eliminate an alias ( A r i s and Astarita, 1989a), an explicit relationship between -dCldt and C: -dC/& = C(a+I)/a (98) c(x,t) between the equations to obtain Equation (98) should be discussed in some detail.

One can now eliminate an alias ( A r i s and Astarita, 1989a), an explicit relationship between -dCldt and C: -dC/& = C(a+I)/a (98) c(x,t) between the equations to obtain Equation (98) should be discussed in some detail. When a approaches m (which is the case where only reactant x = 1 is present in the mixture), it correctly predicts the single-reactant result dC/dt = -C. This is worded by saying that the alias satisfies the single-componentidentity (SCI): When the initial concentration distribution approaches a delta function, one recovers the result for a single component.

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Advances in Chemical Engineering, Vol. 24 by James Wei (Ed.)


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