Shear rate gradient

The Rivlin-Ericksen constitutive equation gives a good account of some characteristics of both the time dependence of the viscoelastic behavior and the normal stress effects. This relationship is based on the assumption that the stress depends not only on the velocity (x ) and the shear rate gradient (dxi/dx ) but also on derivatives of higher order (%, dXp/dXq. .. 8xf /8xi). As a consequence of the principle of material... 

There are several hypotheses as the rheological properties of cement pastes are concerned. As it is commonly known the rheology deals with the flowing and deformation of materials imder stress. The Newtonian fluids show a simple relationship between the shear stress and shear rate. When a thin layer of fluid is placed between the two parallel plates, of which one is fixed and the second will be subjected to the shearing force F, then the shearing of this layer will occur. The dynamic equilibrium will be attained when the force F, in the condition of stationary flow, will be balanced by the viscosity of Newtonian fluid and the relation between the shear stress and shear rate gradient will be linear (Fig. 5.1). 

These were analyzed on a Rheotest-2.1 rheoviscosimeter with metering N/S devices (coaxial cylinders) within ranges for shear rate gradient of 9-1.312 s and for temperature of 288-363 K. 

Since the effects of shear stress are particularly strong in the case of rodlike macromolecules, rotation viscometers are frequently used for measurements on substances such as deoxyribonucleic acid (Figure 9-23). With a sufficiently low rotational speed and a narrow gap between rotor and stator, a linear shear-rate gradient can be produced between the rotor and stator of a rotation viscometer. With such narrow gaps between rotor and stator, the centering of rotor in the stator (or, in some viscometers, vice versa) is particularly important. In rotation viscometers of the Couette type, centering is achieved by use of a mechanical axis. A much better centering system is used in the Zimm-Crothers viscometer. This utilizes... 

Many concentrated solutions of polymers are characterised by a complex rheological behaviour, being classified in systems with instantaneous reversibility, or quasi-instantaneous, systems with retarded reversibility [1009, 1010]. The last ones present so-called the memory of the supported shear rate gradients thus the structure of the hydrodynamic units is influenced by shear rate gradients, tending to a limit. The systems presenting a quasi-instantaneous reversibility are characterised by short periods of structurisation which are inferior to the measurement accuracy. 

As well as these static—essentially geometric—effects that produce depletion at the wall, there are also dynamic effects which enhance the phenomenon. The existence of a shear rate and/or a shear rate gradient in the fluid next to the wall (as in a pipe) results in a further movement of particles away from the wall, towards areas of lower shear rates such as the centre of pipes. Solid particles, emulsion droplets and polymer molecules all show this tendency. 

Figure 10.17 Pictures of experiments of axially rotated containers with mixtures of different-sized particles illustrating relatively simple systems where effects of gravity and shear-rate gradients combined may give rise to complicated segregation patterns, (a) Axially segregation of different-sized particles in a cylindrical partially filled drum. (From Hill, K.M. et al., Phys. Rev. E, 56, 4386, 1997.) (b) Segregation of different-sized particles in a thin rotated box of a solid fraction of 0.65. (From Rietz and Stannarius, Phys. Rev. Lett. 100, 078002, 2008). (c) Pattern from experiments in (b) with velocities superposed, (d) Analogous results from those shown in (b and c), obtained for a fill level of 0.58 (less than the critical amount required for the complex circulation and segregation patterns of (b and c)).

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