Steady state continuous cocurrent

Many chemical and biological processes are multistage. Multistage processes include absorption towers, distillation columns, and batteries of continuous stirred tank reactors (CSTRs). These processes may be either cocurrent or countercurrent. The steady state of a multistage process is usually described by a set of linear equations that can be treated via matrices. On the other hand, the unsteady-state dynamic behavior of a multistage process is usually described by a set of ordinary differential equations that gives rise to a matrix differential equation. 

Suppose the two-phase cocurrent flow is not at steady state. Instead, one of the phases is introduced as a pulse or in an interrupted fashion so that we have pulses of the second phase moving in the positive z-direction as the first phase moves continuously. If this... 

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