β Scribed by Friedrich G. Helfferich
No coin nor oath required. For personal study only.
Steady-state multiplicity under idealized conditions in a single column, or in a column section with fixed entry conditions at both ends, depends critically on whether the model postulates infinite or finite column length or mass-transfer rates. Like the.multiplicity in a column with infinite mass-transfer rates, that in an infinitely long column with finite mass-transfer rates is exclusively a matter of phase equilibrium and Sow-rate and hold-up ratios and is independent of mass-transfer effects. Such a multiplicity does not exist if both the column length and mass-transfer rates are finite, but the approach to the unique steady state may be exceedingly slow ("creep"), a phenomenon known from asymmetric dynamics. Mathematically exact multiplicity in finite columns with finite mass-transfer rates requires an unusual mass-transfer behavior as well as entry conditions different from those for multiplicity in infinitely long columns or in finite columns with infinite mass-transfer rates.
π SIMILAR VOLUMES
Numerical results are presented in graphical form for a range of parameters where multiple solutions may occur. These results provide valuable material for a further theoretical examination of multiplicity. It is also shown that in multiple cases the Danckwerts boundary conditions are consistent wit