Shear, fluid

Slurry Viscosity. Viscosities of magnesium hydroxide slurries are determined by the Brookfield Viscometer in which viscosity is measured using various combinations of spindles and spindle speeds, or other common methods of viscometry. Viscosity decreases with increasing rate of shear. Fluids, such as magnesium hydroxide slurry, that exhibit this type of rheological behavior are termed pseudoplastic. The viscosities obtained can be correlated with product or process parameters. Details of viscosity deterrnination for slurries are well covered in the Hterature (85,86). 

Agglomerates in a sheared fluid rupture when the hydrodynamic stress exceeds a critical value in dimensionless form the criterion for rupture is Fa > Facrjt. Rupture occurs within a short time of application of the critical stress, and thus can be distinguished from erosion, which occurs over much longer time scales. 

In some cases, friction between two surfaces is dominated by the bulk viscosity of the fluid embedded between them.49 In these cases, it is often suitable to model the bulk sheared fluid and neglect the presence of confining walls. In this section, we describe computational approaches for shearing bulk systems and identify the conditions under which it is appropriate to treat the system in this manner. We start in the next section with a discussion of the conditions under which one may neglect confining walls. This is followed with a discussion of how to impose shear on bulk systems. We then close by exploring ways in which the system can be constrained to accurately reproduce certain phenomena. 

The second approach used in first-principles tribological simulations focuses on the behavior of the sheared fluid. That is, the walls are not considered and the system is treated as bulk fluid, as discussed. These simulations are typically performed using ab initio molecular dynamics (AIMD) with DFT and plane-wave basis sets. A general tribological AIMD simulation would be run as follows. A system representing the fluid would be placed in a simulation cell repeated periodically in all three directions. Shear or load is applied to the system using schemes such as that of Parrinello and Rahman, which was discussed above. In this approach, one defines a (potentially time-dependent) reference stress tensor aref and alters the nuclear and cell dynamics, such that the internal stress tensor crsys is equal to aref. When crsys = aref, the internal and external forces on the cell vectors balance, and the system is subject to the desired shear or load. 

There are many examples of nonequilibrium states. A classic example of a NESS is an electrical circuit made out of a battery and a resistance. The current flows through the resistance and the chemical energy stored in the battery is dissipated to the environment in the form of heat the average dissipated power, Pdiss = VI, is identical to the power supplied by the battery. Another example is a sheared fluid between two plates or coverslips and one of them is moved relative to the other at a constant velocity v. To sustain such a state, a mechanical power that is equal toVoc r v has to be exerted on the moving plate, where p is the viscosity of water. The mechanical work produced is then dissipated in the form of... 

As in the case of capillary-tube units, the shear rate (rotational speed) should be variable over wide ranges (10- to 1000-fold) and baffles or other obstructions which could interfere with the laminar-flow pattern must be absent. Since the fluid is sheared for long periods of time in these instruments, temperature control is much more critical, especially in the case of high-consistency materials, for which temperature rises of over 20°C. (W2) have been recorded. Weltmann and Kuhns (W5) subsequently presented an erudite mathematical analysis of the temperature distribution within the layers of sheared fluid. 

The approaches of Daivis and Matin and Taniguchi and Morriss are essentially exact, in that they are applicable generally to simple shearing fluids in the... 

Comparison with Other MCT Inspired Approaches to Sheared Fluids. 73... 

The decomposition of the tensor [Gfcm] into the symmetric and antisymmetric parts corresponds to the representation of the velocity field of a linear shear fluid flow as the superposition of linear straining flow with extension coefficients Ei, 2, 3 along the principal axes and the rotation of the fluid as a solid at the angular velocity u = ( 32,013, SI21)-... 

Application of Shear Stress. The Rice University ROM-8 viscometer has been described previously (9). This apparatus permits volumes of 8 mL of fluid to undergo uniform shear stress exposure at readily quantifiable levels. For the present experiments, all surfaces coming into contact with leukocyte suspensions were coated with silicone (Siliclad), which had been demonstrated earlier to minimize or eliminate surface-mediated effects on PM Ns (2). The surface-to-volume ratio in the viscometer could be varied by a factor of three using different bobs. Effectively, the fluid volume was varied at nearly constant surface area. Increasing the surface-to-volume ratio increased the accessibility of the surface to cellular elements in the sheared fluid. Shear stress levels were 100 and 300 dyn/cm2 for the 10-min exposure, which had been documented previously to produce functional alterations in PM Ns. Control samples were placed into the viscometer for 10 min, but were not subjected to rotational shear stress. After exposure to the viscometer, cell suspensions were assayed without further delay as described in the next section. 

Fig. 2 Slurry in the stainless-steel holding tank of the Microfluidizer after continuous high shear fluid processing of chitosan powder for mechanical disassembly into nanofibrils. Scaleable results are produced for pilot and production purposes...

This equation implies that the value of Yyx at any point within the sheared fluid is determined only by the current value of shear stress at that point or vice versa. Depending upon the form of the fimction in equation (1.10) or (1.11), these fluids may be further subdivided into three types ... 

Serra, T. and Logan, B. E. (1999). Collision frequencies of fractal bacterial aggregates with small particles in a sheared fluid. Environ. Set Technol., 33, 2247-2251. 

For a one-dimensional steady shear flow of a fluid between two planes, the velocities of an infinitesimal element of fluid in the y- and z-directions are zero. The velocity in the x-direction is a function of y only. Note that in addition to the shear stress Tyx (refer to t subsequently), there are three normal stresses denoted by Txx, Tyy, within the sheared fluid. Weissenberg in 1947 [6] was the first to observe that the shearing motion of a viscoelastic fluid gives rise to tmequal normal stresses, known as Weissenberg effects. Since the pressure in a non-Newtonian fluid cannot be deflned, and as the normal stress differences... 

P. C. Johnson and R. Jackson. "Frictional-collisional constitutive relations for granular materials, with application to plane shearing," /. Fluid Mech., 176, 67-93, 1987. 

In fact, b is directly related to the friction coefficient between the fluid and the surface. This can be easily seen by evaluating the friction force transmitted to the solid by the sheared fluid, either as the product of the velocity at the interface. Vs, by friction coefficient between the solid and the fluid, k, or as the product of the fluid viscosity by the velocity gradient at the surface, i.e. Ff =kVs =ti9V/3z q H s/b One sees... 

On a molecular scale, however, the energy is dissipated within the sheared fluid and must therefore be regarded as a bulk loss. 

Shear Shear and shear stress involve opposing forces acting in opposite directions but not in direct alignment with each other. Cutting and tearing actions involve shear. Fluids and materials that act much like fluids (sand and some other loose or wet sods) have very little shear capacity. 

Many fluids also exhibit time-dependent viscous effects. With some pastes, drilling muds, and latex paints, for example, there is a drop in viscosity with time when they are sheared at a constant shear rate. This effect, known as thixotropy," " is illustrated in Fig. 19.18. There is an opposite effect, rheopexy, where there is an increase in viscosity with time under shear. Fluids with this property are relatively rare, however. 

The total thrust force F produced during shear can be related to the normal stress difference in shear. Integrating Equation 8.37 yields PJf) = xjf) -p(r), where P (f) is the integration constant and, physically, is the net pressure exerted by the sheared fluid on a surface with normal vector n. Substituting for p in Equation 8.35 and integrating the resulting equation from rtoR yields... 

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