Residence time optimised choice of tube diameters and slit heights in distribution systems for non-Newtonian liquids

Abstract

In order to minimise thermal degradation effects such as yellowing and losses in molecular weight, distribution systems for polymer melts and solutions should be designed for residence times as small as possible for a given value of the total pressure loss. Tube and slit flow distributors that can be considered as mainly one-dimensional systems are analysed with respect to an optimal ratio of technical expenditure (pressure loss) and gain in polymer quality (reduction in residence time, i.e. in thermal degradation). Assuming steady, fully developed, laminar flow and excluding changes in the rheology of the liquid with residence time, this leads to mathematical optimisation problems which may be solved by the methods of the calculus of variations. The definition of average residence time turns out to be ambiguous for systems with more than one inlet or one outlet. The problem may be defined in two alternative ways, using different measures of residence time. One of these time measures, called “travel time”, turns out to be superior as a criterion for the optimisation of distributors for polymeric liquids. Based on this criterion, a general design rule for optimising slit and tube distributors is derived. This rule states that, in order to minimise the travel times within a system, it is sufficient to choose the diameter of the tubes or the slit width in such a way that the local apparent wall shear rate is uniform throughout the whole system. This rule has a broad range of applicability. It holds for arbitrary non-linear flow curves of the liquid under consideration and for arbitrary total flow rates. In addition, the choice of a uniform wall shear rate and, hence, a uniform wall shear stress safeguards the highest level of protection against wall fouling throughout the system at the lowest possible cost (pressure loss).