Viscoplastic media

The combination of plasticity and viscosity, typical of these media, was discovered in 1889 by Shvedov for gelatin solutions and in 1919 by Bingham for 

The three-dimensional analog of the Shvedov-Bingham law has the form 

The numerical values of the parameters tq and /ip for various disperse systems  

Note that the Casson model (the third model in Table 6.3) fairly well describes various varnishes, paints, blood, food compositions like cocoa mass, and some other fluid disperse systems [443]. 

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Viscoplastic media. General formulas. For viscoplastic media, the shear rate in general depends on the stress as follows ... 

For viscoplastic media with yield stress to, the solution of problem (6.5.7), (6.5.8) has the form... 

Ogibalov, P. M. and Mirzadzhanzade, A. Kh., Unsteady Motions of Viscoplastic Media, Izd. Moskov. Univ., Moscow, 1970 [in Russian],... 

These MRl scans indicate the potential industrial importance of particle settling through viscoplastic media. The general trends had been investigated by Thomas [5] but further experimentation was clearly required. It was decided to construct a cup and bob similar to those of a conventional rotary viscometer, but modified so that the gap between them increases with depth, and thus the strain rate decreases with depth. This apparatus was constructed at Curtin University, Western Australia. A vertical section is shown on Fig. 1. A brief description, together with some preliminary results, was presented by Wilson [6]. Since that time, a second bob has been fabricated. It is also shown on Fig. 1. 

The results of the latest research into helical flow of viscoplastic fluids (media characterized by ultimate stress or yield point ) have been systematized and reported most comprehensively in a recent preprint by Z. P. Schulman, V. N. Zad-vornyh, A. I. Litvinov 15). The authors have obtained a closed system of equations independent of a specific type of rheological model of the viscoplastic medium. The equations are represented in a criterion form and permit the calculation of the required characteristics of the helical flow of a specific fluid. For example, calculations have been performed with respect to generalized Schulman s model16) which represents adequately the behavior of various paint compoditions, drilling fluids, pulps, food masses, cement and clay suspensions and a number of other non-Newtonian media characterized by both pseudoplastic and dilatant properties. 

By virtue of its yield stress, a viscoplastic material in an unsheared state will support an immersed particle for an indefinite period of time. In recent years, this property has been successfiilly exploited in the design of slurry pipelines, as briefly discussed in section 4.3. Before undertaking an examination of the drag force on a spherical particle in a viscoplastic medium, the question of static equilibrium will be discussed and a criterion will be developed to delineate the conditions under which a sphere will either settle or be held stationary in a liquid exhibiting a yield stress. 

In practice, the non-Newtonian materials mentioned above are often viscoplastic. For a material of this sort no strain rate is produced until the applied shear stress r exceeds the yield stress Ty. Hence, if a discrete particle is placed in a quiescent viscoplastic medium, the particle will not settle imless it is heavy enough to produce a shear stress within the medium that exceeds ty. 

The motion of plastic fluids with finite yield stress to has some qualitative specific features not possessed by nonlinearly viscous fluids. Let us consider a layer of a viscoplastic fluid on an inclined plane whose slope is gradually varied. It follows from (6.2.5) that, irrespective of the rheological properties of the medium, the tangential stress decreases across the film from its maximum value Tjnax = pgh sin a on the solid wall to zero on the free surface. Therefore, a flow in a film of a viscoplastic fluid can be initiated only when the tangential stress on the wall becomes equal to or larger than the yield stress to ... 

Shvedov-Bingham Fluids. In the special case of a viscoplastic Shvedov-Bingham medium (the first model in Table 6.3), we have the following expression for the function / in (6.4.9) ... 

Figure 6.3. Velocity profile in the flow of a viscoplastic Shvedov-Bingham medium...

The nature of the suspending medium, whether Newtonian, viscous non-Newtonian, viscoelastic or viscoplastic affects tt e viscosity of the suspension. This has been the subject of research of a number of... 

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