Fig. 2. Schematic diagram of the flow of liquid and vapor phases in tray n; the direction of mass transfer is assumed from vapor phase to liquid phase.
It is assumed that the direction of mass transfer is from vapor phase to liquid phase. Thus,
At the steady-state of nonequilibrium thermodynamics (i.e. in the linear range), we obtain:
Some questions may arise in solving the explicit formulation of Maxwell-Stefan equation, that is, d In y
The general way to calculate d\n/j dx, is by the so-called perturbation method. For instance, provided a minute perturbation( xi —» x, + 0.0001 ), then d In y: ^ In y, (T, jc,. +0.0001)- In (T, x, ) dx, ~ (x,+0.0001)-(x,)
The activity coefficient, yt, can be derived, as shown in Table 2.
(2) how to calculate the (c-l)X(c-l) inverse matrix [B'k\x and [5^]"'?
This is essentially a mathematical problem, and can be solved by the following computer program (see Table 12), which is programmed with Visual Basic Language and can be called by the interested readers.
The computer program of solving the (c-l)X(c-l) inverse matrix of [Bik ]
If i o kThen
The binary mass transfer coefficients of K'ka and K-'ka (mol s"1) are the most important in the Maxwell-Stefan equation. For packing distillation column, these are obtained from the experimental data, depending on physical properties of the mixture, flow pattern of vapor and liquid, packing configuration and so on. For tray distillation column, often with sieve tray, it is believed that K'j ka and K.'ka can be predicted from the empirical correlation of the AIChE method . However, in the AIChE method, only estimation of the numbers of mass transfer unit in the liquid and vapor sides, i.e. TV, and NG, are given. In terms of the famous two-film theory, the relationship between mass transfer coefficient and number of mass transfer unit is derived as follows: For the liquid phase,
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