The Q-Cascade Explanation

Transient processes in Q-cascades for separation of multicomponent mixtures

“…Considering that the values of the Q i constants are small enough (Q i {1, (Zeng et al, 2012)) and moving in Eq. (4) from finite differences to differentials (which is justified in the case of "weak" enrichment) one can obtained for non-stationary mass transfer of the ith component in a Q-cascade the following equation…”

“…Due to the fact that for a Q-cascade the values of the partial cuts over cascade stages are constant (φ i s ð Þ ¼ const (Zeng et al, 2012)), Eq. (3) can be rewritten in the following form:…”

“…From a physical point of view, such boundary conditions imply that the concentrations of the components in a feed point of a cascade at the arbitrary time moment are equal to that in the initial separated mixture and the flow of a working substance at the product end of a cascade vanishes (Zeng et al, 2012).…”

“…Assume that the stages of the cascade under consideration are connected by a counter-symmetric way (Zeng et al, 2012). In a general case, the balance of the partial flows coming through the cross sections between the sth and (s þ1)th stages at the time moment t is written as:…”

“…The incoming flows at the entrance to each stage of MARC have the same relative concentrations for the specified pair of components. The research on the Q-cascades acquires a second wind at the beginning of the 21st century Zeng et al, 2011Zeng et al, , 2012Zeng et al, , 2013Tolstoy, 2010;Smirnov and Sulaberidze, 2013). It allowed us, in particular, to identify the physical nature of a Q-cascade (Zeng et al, 2012), to demonstrate the physical equivalence of a Q-cascade and a "quasi-ideal" one, to study the regularities of molecular selective mass transfer in a Q-cascade in the presence of loss of working substance at its stages (Zeng et al, 2013;Smirnov and Sulaberidze, 2013).…”