18.7. Mass Transfer Solutions for Linear Systems

The solution of differential equations is much simpler when the equations are linear. The various sets of differential equations for mass transfer discussed in Section 18.6 are all linear if the equilibrium isotherm is linear and the system is isothermal. (Note that nonisothermal operation introduces the Arrhenius relationship, Eq. (18-7), which is decidedly nonlinear.) This section is limited to isothermal operation of systems with linear isotherms Eqs. (18-5b) or (18-6b).

One characteristic of the solutions for Eqs. (18-54) and (18-55) for linear isotherms is mass transfer resistances and axial dispersion both cause zone spreading that looks identical if the mass transfer parameters or axial dispersion parameters are adjusted. Thus, from an experimental result it is impossible to determine if the spreading was caused solely by mass transfer resistances, solely by axial dispersion, or by a combination of both. This property of linear systems allows us to use simple models to predict the behavior of more complex systems.