EXTENSIONAL FLOW - A MATHEMATICAL PERSPECTIVE

Extensional flow has been studied extensively for less than half the l ifetime of the word ''rheology'', although measurement of viscosity fr om extensional flow experiments can be traced back to the beginning of this century. In recent years extensional flow has, however, attracte d a great deal of attention in conferences, workshops and special issu es of journals. This has coincided with interest, both scientific and industrial, in elasticoviscous fluids, notably polymer solutions and m olten polymers. The particular success of specialized, carefully targe tted or focussed, workshops is highlighted. A personal reflection is o ffered here on some of the issues in extensional flow from the point o f view of an applied mathematician. The state of the art, as far as ex tensional viscosity is concerned, is briefly surveyed. Both theoretica l and practical aspects of the task of obtaining useful extensional fl ow properties are outlined, drawing heavily on a recent review by Jame s and Walters. Particular attention is paid to spinning experiments, d rawing heavily on recent theoretical investigations by the author. The merits of defining a ''spinning viscosity'', in addition to the forma lly defined tensile viscosity, are advanced. The idea of general appro ximations for extensional flows is reviewed and some aspects of this a re highlighted, particularly in connection with Metzner's idea of exte nsional primary field (EPF) approximations. Finally qualitative invest igations of the behaviour of model fluids (in model flows) are illustr ated and a new result on the boundedness of solutions for unsteady uni axial extension of a FENE-P dumbbell model is presented.