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J. math. fluid mech. 6 (2004) 253271 1422-6928/04/030253-19

Summary: J. math. fluid mech. 6 (2004) 253­271
c 2004 Birkh¨auser Verlag, Basel
DOI 10.1007/s00021-003-0093-3
Journal of Mathematical
Fluid Mechanics
Quasi-Stability of the Primary Flow in a Cone and Plate
Pascal Azerad and Eberhard B¨ansch
Communicated by D. Kr¨oner
Abstract. We investigate the flow between a shallow rotating cone and a stationary plate. This
cone and plate device is used in rheometry, haemostasis as well as in food industry to study the
properties of the flow w.r.t. shear stress. Physical experiments and formal computations show
that close to the apex the flow is approximately azimuthal and the shear-stress is constant within
the device, the quality of the approximation being controlled essentially by the single parameter
Re 2, where Re is the Reynolds number and the thinness of the cone-plate gap. We establish
this fact by means of rigorous energy estimates and numerical simulations. Surprisingly enough,
this approximation is valid though the primary flow is not itself a solution of the Navier­Stokes
equations, and it does not even fulfill the correct boundary conditions, which are in this particular
case discontinuous along a line, thus not allowing for a usual Leray solution. To overcome this


Source: Azerad, Pascal - Département de Mathématiques, Université Montpellier II


Collections: Mathematics