The European Physical Journal Applied Physics

Research Article

Unsteady flow in cone and plate geometry: how computation can help rheometry

J. Passarda1, R. Kouitat Njiwaa2 and P. Perréa3

Université Henri Poincaré, Laboratoire d'Énergétique et de Mécanique (LEMTA), IUT Nancy Brabois, dept. Génie Civil, 54601 Villers-lès-Nancy Cedex, France

Laboratoire de Sciences et Génie des Surfaces (LSGS), École des mines, Parc de Saurupt, 54042 Nancy Cedex, France

Laboratoire des Sciences Forestières, École Nationale du Génie Rural des Eaux et Forêt (ENGREF), 14 rue Girardet, 54042 Nancy Cedex, France


The use of rheometers for the evaluation of rheological properties and the establishment of behaviour laws for fluids requires the knowledge of the shear rate at any moment and everywhere in the region between the cone and the plate, referred to as “the gap” throughout this paper. However, the accurate determination of the shear rate supposes that the constitutive equation of the fluid is known beforehand. In order to avoid this paradox, rheometers are generally built such that the shear rate is supposed to be approximately constant throughout the gap. This approximation is realistic for steady flow but may be crude for other types of fluid motion. The aim of the present work is to determine the limits of validity of such an approximation when testing complex fluids in a cone and plate geometry. In this paper, only purely viscous properties are taken into account. The numerical solution is based on the control-volume method. When non-linear and time-dependent effects occur, it is shown that the flow cannot be represented by simple shearing conical surfaces. This result is especially important for the characterisation of time-dependent fluids (as thixotropic fluids), typical of unsteady flow. Finally the abilities of the proposed model which is named “RHEOUTIL” are highlighted by comparison between numerical simulations and experimental results. The analysis of non Newtonian fluids emphasises the limits of the code “RHEOUTIL”. Indeed, the model has to evolve in order to take into account the whole complexity of the fluid, which may also exhibit viscoelastic properties, yield stress and so on.

(Received November 12 1997)

(Revised May 26 1998)

(Accepted June 2 1998)

(Online publication September 15 1998)


  • 47.50.+d – Non Newtonian fluid flows;
  • 83.50.By – Transient deformation and flow; time-dependent properties: start-up, stress relaxation, creep, recovery, etc. ;
  • 83.85.Cg – Rheological measurements