Matrix Representation of the Generalized Ficks Law

The Hth component diffusion flux independent and is obtained from Eq. 2.1.19. 

The matrix [D] of Fick diffusion coefficients is a square matrix of dimension n — 1 X n — 1 

It is important to note that for multi-(H-)-component diffusion, the nondiagonal or off-diagonal elements or cross-coefficients (i = j = 1,2. n — 1) are, in general, nonzero. 

For a ternary system (n = 3), the matrix representation of the generalized Fick s law (Eq. 3.2.5) is two dimensional. Using the property of matrix multiplication we recover Eqs. 

The reader should satisfy himself/herself that the three formulations (Eqs. 3.2.3, 3.2.4, and 3.2.5) are entirely equivalent to one another. It is not only in the interests of economy and elegance of presentation that we shall consistently prefer the matrix formulation (Eq. 3.2.4) we shall see later that matrix formulations lend themselves to easy manipulations and in many cases the At-component mass transfer relations can be written down as n — 1 dimensional matrix analogs of the corresponding binary mass transfer relationships (Chapter 5). 

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