Krishna explicit method

That is, the matrices [A] and [B][ ] are equal and not simply equivalent. Thus, the explicit method of Krishna could equally well be written in the form... 

The explicit method of Krishna (1979d, 1981b) is most successful if the are close together and, therefore (or for other reasons), the total flux is low. At high rates of mass transfer, the assumption of constant (or of [/3][B] ) is a poor one, particularly in... 

The effective diffusivity formula of Stewart (Eq. 6.1.8) is by far the best of this class of methods. This should not come as a surprise since this method is capable of correctly identifying the various interaction phenomena possible in multicomponent systems. Indeed, for equimolar countertransfer, this effective diffusivity method is equivalent to the linearized theory and to both explicit methods discussed above. In fact, for some systems Stewart s effective diffusivity method is superior to Krishna s explicit method (Smith and Taylor, 1983). However, since the explicit methods are actually simpler to use than Stewart s effective diffusivity method (all methods require the same basic data) and, in general... 

The explicit methods developed in Section 8.5 can be generalized in similar ways. Krishna (1979a, 1981b), for example, assumes constancy of the matrix product and obtains... 

A number of investigators used the wetted-wall column data of Modine to test multicomponent mass transfer models (Krishna, 1979, 1981 Furno et al., 1986 Bandrowski and Kubaczka, 1991). Krishna (1979b, 1981a) tested the Krishna-Standart (1976) multicomponent film model and also the linearized theory of Toor (1964) and Stewart and Prober (1964). Furno et al. (1986) used the same data to evaluate the turbulent eddy diffusion model of Chapter 10 (see Example 11.5.3) as well as the explicit methods of Section 8.5. Bandrowski and Kubaczka (1991) evaluated a more complicated method based on the development in Section 8.3.5. The results shown here are from Furno et al. (1986). 

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