Une méthode exacte de détermination des constantes rhéologiques des corps plastiques de Bingham à l'aide du viscosimètre type Couette

An exact method for the determination of plastic-flow constants for Bingham bodies with the aid of a Couette-type viscometer

Docteur-ingénieur, Ecole supérieure d'Agriculture de Wroclaw (Pologne), en stage aux Laboratoires de Mécanique des Fluides de l'Université de Grenoble.

Résumé

Most visco-plastic substances encountered in practical engineering behave as Bingham bodies (soil/water mixtures, sludges, muds, etc.). The exact determination of plastic flow constants t0 and ηp is therefore most important. The most convenient viscometers for this kind of substance are of the Couette type. Analysis of previous work shows the lack of a suitable method of choosing a Couette-type viscometer giving exact creep "pseudo-curves" within the region of validity of the classical Reiner-Riwlin equation (1). Starting out from this equation, it is shown that the linear region of the creep "pseudo-curve" is mainly limited by the following : - a) The lower velocity gradient limit (dv/dr)bl given by equation (8); b) The maximum velocity gradient, which is limited by the maximum angular velocity Ωmax of the considered instrument (equation 12). The linear velocity gradient region thus depends on the main parameters of the Couette instrument, i.e. the square of the radius ratio and the maximum angular velocity, as well as on the plastic flow constant ratio t0/ηp. The approximate value of this ratio is in the range between 102 S-l and 103 S-l for most Bingham bodies ; Table 1 lists numerical values of the ratio in terms of substance concentration s' for 17 different bodies. A (dv/dr)lin vs. α diagram constructed from equations (8) and (12) is shown in fig. 3. The (dv/dr)bl curves in this graph are plotted for t0/ηp = (10, 102, 103 and 104) s-1, and the (dv/dr)m curves for Wmax = (1,000, 600, 400, 200 and 100) r.p.m. Values of (dv/dr)lin for the considered instrument can be read off this graph, for the t0/ηp ratio applicable to the considered fluid. An analysis of commercial instruments based on this graph has shown that the limit values for certain viscometers are liable to lie so close together as to partly or even completely eliminate the linear region of the creep "pseudo-curve"; correct measurement is quite impossible under such conditions (see Tables 2 and 3). To ensure reliable measurement of plastic flow constants for Bingham bodies, it is necessary to use viscometers covering a wide range of linear velocity gradients. This is ensured by instruments for which α is small (less than 1.2) and rotation al speeds are high (exceeding 800 r.p.m.).