Residence-time distributions in regions of steady-flow systems

Abstract

Questions often arise in the applied sciences concerning the transport of material through a system^1–4 (for example, a chemical plant, the cardiovascular system or a river basin). Conserved particles such as molecules, blood corpuscles or colloidal particles passing through the system spend different times in the system even when the flow is steady. The theory of residence times^1,2 may be used to relate tracer studies to theoretical or empirical models. Existing theory mainly concerns complete systems, but a few results have been established^2,5–7 concerning the times that particles spend in a specific region (for example, a particular phase in a chemical reactor, an organ or a backwater) while passing through the system. I show here that the distribution of these ‘region residence times’ may be calculated from a system model by using a formalism in which the volumes of all the other regions are reduced to zero, allowing the region distribution to be calculated by well-established methods^1,2 that apply to systems.