Axial annular flow of a nonlinear viscoelastic fluid - an analytical solution

• Type: Article in International Scientific Journal
• Date: 2000

Authors

Fernando Tavares de Pinho (Author) FEUP; Paulo J. Oliveira (Author) Other

Journal

Title: Journal of Non-Newtonian Fluid Mechanics

Vol. 93 No. 2-3

Pages: 325-337

ISSN: 0377-0257

Publisher: Elsevier

Indexing

ISI Web of Knowledge - 43 Citations

ISI Web of Science

Scopus - 62 Citations

Other information

Authenticus ID: P-000-YQ4

DOI: 10.1016/s0377-0257(00)00113-0

Abstract (EN): An analytical solution is given for the kinematic and stress variations across the radial gap of a concentric annular flow in fully developed conditions. The fluid is viscoelastic and obeys the non-linear rheological constitutive equation proposed by Phan-Thien and Tanner [1]. This constitutive model simulates well the material functions of many polymer melts and solutions and therefore, the present results are useful in a number of practical situations. The ratio of pressure drop to flow rate drop is found to be a complex mathematical function of the radial position of zero shear stress and this, in turn, depends weakly on the elasticity, based on the product of an elongational parameter by a Deborah number defined with an averaged velocity. There is thus a non-linear coupling which could not be solved in an explicit way for the inverse problem of an imposed flow rate, but an iterative procedure gives a ready result. For the direct problem of a given pressure drop the present results represent an exact explicit solution to the axial annular flow problem. Representative profiles of the solution are given and discussed. It is found that, for a given flow rate, the pressure drop scaled with the corresponding Newtonian value is independent of the diameter ratio.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 13