The flow of fluids from nozzles at small Reynolds numbers

Abstract

The aim of this paper is to provide a basis for determining the solution of certain free-surface flows when a fluid is extruded from a nozzle. We have chosen here to consider the problem in a form different from that usually adopted for the so-called ‘die-swell problem’, the modified version being considerably easier to set up experimentally and also being well posed mathematically. It is not clear that this latter aspect is true of the conventional die-swell problem, where the fluid is assumed to separate from the die at a sharp lip. Indeed, we have been unable to justify such an assumption; so we prefer to allow the point of attachment of the free surface with the nozzle boundary to remain one of the unknowns to be determined by the solution. An outline is given of a mathematical procedure by which, we claim, problems of this kind can be approached. By considering an alternative version of the problem on a bounded domain, it can be shown that such a problem has a solution within a class of continuous functions. Some experiments are described showing how the free surface does not necessarily separate from the nozzle at a sharp edge, and also illustrating some of the differences between the flow of a Newtonian fluid and that of a non-Newtonian fluid.