Residence-Time Distributions in Laminar Flows and During the Passage of Granular Solids Through Rotary Kilns

Data on residence-time distributions are important in the design of apparatus for the chemical industry. Radioactive tracers can be useful in many cases, e.g. where a pulse technique is desired. Two examples are given in which a pulse of radioactive tracer is used. The first example deals with the residence-time distribution of a laminar, Newtonian flow in an annulus. This problem arises especially in the extrusion and injection moulding of polymers and in the coating of wires with plastics. In these cases the fractions of polymer with long residence times may have other properties than the polymer that flows fastest, because the polymerization reaction or the degradation reactions go on during the process. Two difficulties are to be considered: (a) the tracer pulse (a radioactive Au-sol suspended in the liquid used) cannot be distributed over the cross-section in proportion to the local flow velocity, and (b) the outflowing liquid must be sampled discontinuously. Both effects have been studied and corrections are indicated. When these corrections are applied to the measured distribution curve, the result is in fair agreement with the calculated residence-time distribution. The second example considers the residence-time distribution in a granular solid (sand) passing through a rotary kiln. The response was measured at the outlet to a pulse at the inlet of radioactive material (sand impregnated with a solution of radioactive AuCl3). When calculating the residence-time distribution from the experimental data, difficulties were encountered because the duration of the pulse was of the same order of magnitude as the average residence time. Considering this, it was found that the axial dispersion of the flow of sand could be described by an effective dispersion coefficient. This dispersion coefficient proved to be very low (order of magnitude 10-5 m2/s); hence, in practical situations, the flow of granular material through a rotary kiln may often be considered as a plug flow, i.e. all the grains of sand have the same mean velocity. (author)