Mean residence times in continuous flow systems

Abstract

INDIVIDUAL elements of a material which enters a system at a constant rate, resides for some time, and then leaves, can take different paths through the system, travel at different speeds, and be delayed for many reasons. For example, by diffusing into stagnant zones, or by transferring, perhaps across a membrane, into a separate phase, they may take part in any activity that does not destroy them which does not preclude chemical reaction where atoms of flow material (which may be combined in any way with other components in the flow streams) are being considered. The process must, however, be a steady-state one, which implies that the quantities of material or ‘holdups’ in all parts of the system do not vary with time, and that the rate at which material leaves the system is equal to its rate of entry. As an example, we could consider a stretch of river swept by water, or an effluent component in the water; or a continuous chemical reactor into and out of which a conserved material (atoms or ions perhaps) flows at a constant rate; or a respiratory system, fed with oxygen which is transported to the various parts of the body before leaving in part as carbon dioxide. At first sight it seems unlikely that quantitative deductions of the behaviour of so abstract a structure are possible; however, one such deduction has been made¹, and this letter reports another.