Circulating flows are found in a variety of mixing equipment such as stirred tanks and airlift loop vessels. This paper presents a different route towards modeling the mixing in circulating flows. This route is based on an innovative use of Poincare maps and suspended flows, concepts which are found in dynamical systems theory. The mixing model is developed for an arbitrary recirculating flow and uses a circulation time distribution function that is incorporated into the transport equations for an inert tracer injected into the flow system. Two cases are used to study the application of the mixing model in this work. The first case addresses the question of whether the mixing model can be used to study airlift vessels differing in scale and the second case highlights the application of the model to a standard stirred tank. In the first case, model predictions have been compared with experimental data obtained from two geometrically similar airlift systems of different volumes and good agreement is observed. A single parameter correlation for the mixing time is also proposed. In the second case, computational fluid dynamics was used to obtain the flow field of a standard stirred tank fitted with a six bladed Rushton turbine. From the flow field, the distribution of the circulation times is extracted and used to determine the tracer concentration profile in the stirred tank. Good agreement between the model predictions and published experimental data is observed thus indicating that the mixing model shows promise as a technique for studying the mixing in stirred tanks.