Shear stress rotational

A number of techniques have been developed to measure melt viscosity. Some of these are listed in Table 3.8. Rotational viscometers are of varied structures. The Couette cup-and-bob viscometer consists of a stationary inner cylinder, bob, and an outer cylinder, cup, which is rotated. Shear stress is measured in terms of the required torque needed to achieve a fixed rotation rate for a specific radius differential between the radius of the bob and the cup. The Brookfield viscometer is a bob-and-cup viscometer. The Mooney viscometer, often used in the rubber industry, measures the torque needed to revolve a rotor at a specified rate. In the cone-and-plate assemblies the melt is sheared between a flat plate and a broad cone whose apex contacts the plate containing the melt. 

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. 

Torque (rotational shear stress) Torsional strain Torsional modulus... 

Figure 5,16. It is assumed that by using an exactly symmetric cone a shear rate distribution, which is very nearly uniform, within the equilibrium (i.e. steady state) flow held can be generated (Tanner, 1985). Therefore in this type of viscometry the applied torque required for the steady rotation of the cone is related to the uniform shearing stress on its surface by a simplihed theoretical equation given as...

A rotational viscometer connected to a recorder is used. After the sample is loaded and allowed to come to mechanical and thermal equiUbtium, the viscometer is turned on and the rotational speed is increased in steps, starting from the lowest speed. The resultant shear stress is recorded with time. On each speed change the shear stress reaches a maximum value and then decreases exponentially toward an equiUbrium level. The peak shear stress, which is obtained by extrapolating the curve to zero time, and the equiUbrium shear stress are indicative of the viscosity—shear behavior of unsheared and sheared material, respectively. The stress-decay curves are indicative of the time-dependent behavior. A rate constant for the relaxation process can be deterrnined at each shear rate. In addition, zero-time and equiUbrium shear stress values can be used to constmct a hysteresis loop that is similar to that shown in Figure 5, but unlike that plot, is independent of acceleration and time of shear. 

In most rotational viscometers the rate of shear varies with the distance from a wall or the axis of rotation. However, in a cone—plate viscometer the rate of shear across the conical gap is essentially constant because the linear velocity and the gap between the cone and the plate both increase with increasing distance from the axis. No tedious correction calculations are required for non-Newtonian fluids. The relevant equations for viscosity, shear stress, and shear rate at small angles a of Newtonian fluids are equations 29, 30, and 31, respectively, where M is the torque, R the radius of the cone, v the linear velocity, and rthe distance from the axis. 

Controlled Stress Viscometer. Most rotational viscometers operate by controlling the rotational speed and, therefore, the shear rate. The shear stress varies uncontrollably as the viscosity changes. Often, before the stmcture is determined by viscosity measurement, it is destroyed by the shearing action. Yield behavior is difficult to measure. In addition, many flow processes, such as flow under gravity, settling, and film leveling, are stress-driven rather than rate-driven. 

The Weissenberg Rheogoniometer (49) is a complex dynamic viscometer that can measure elastic behavior as well as viscosity. It was the first rheometer designed to measure both shear and normal stresses and can be used for complete characteri2ation of viscoelastic materials. Its capabiUties include measurement of steady-state rotational shear within a viscosity range of 10 — mPa-s at shear rates of, of normal forces (elastic... 

Rheometric Scientific markets several devices designed for characterizing viscoelastic fluids. These instmments measure the response of a Hquid to sinusoidal oscillatory motion to determine dynamic viscosity as well as storage and loss moduH. The Rheometric Scientific line includes a fluids spectrometer (RFS-II), a dynamic spectrometer (RDS-7700 series II), and a mechanical spectrometer (RMS-800). The fluids spectrometer is designed for fairly low viscosity materials. The dynamic spectrometer can be used to test soHds, melts, and Hquids at frequencies from 10 to 500 rad/s and as a function of strain ampHtude and temperature. It is a stripped down version of the extremely versatile mechanical spectrometer, which is both a dynamic viscometer and a dynamic mechanical testing device. The RMS-800 can carry out measurements under rotational shear, oscillatory shear, torsional motion, and tension compression, as well as normal stress measurements. Step strain, creep, and creep recovery modes are also available. It is used on a wide range of materials, including adhesives, pastes, mbber, and plastics. 

In laminar flow < 10), 1/A Re nd P c< [LN D. Since shear stress is proportional to rotational speed, shear stress can be increased at the same power consumption by increasing N proportionally to as impeller diameter is decreased. 

Here, [L is the coefficient of internal friction, ( ) is the internal angle of friction, andc is the shear strength of the powder in the absence of any applied normal load. The yield locus of a powder may be determined from a shear cell, which typically consists of a cell composed of an upper and lower ring. The normal load is applied to the powder vertically while shear stresses are measured while the lower half of the cell is either translated or rotated [Carson Marinelli, loc. cit.]. Over-... 

Fig. 19.7. A rotation viscometer. Rotating the inner cylinder shears the viscous glass. The torque (and thus the shear stress aj is measured for a given rotation rate (and thus shear strain rate y).

Where momentum is transfeiTed by shearing stresses, in which the transfer is perpendicular to the direction of flow. This category includes the rotating disc and cone agitators. 

Power is the external measure of the mixer performance. The power put into the system must be absorbed through friction in viscous and turbulent shear stresses and dissipated as heat The power requirement of a system is a function of the impeller shape, size, speed of rotation, fluid density and viscosity, vessel dimensions and internal attachments, and posidon of the impeller in this enclosed system. 

Sundararajan et al. [131] in 1999 calculated the slurry film thickness and hydrodynamic pressure in CMP by solving the Re5molds equation. The abrasive particles undergo rotational and linear motion in the shear flow. This motion of the abrasive particles enhances the dissolution rate of the surface by facilitating the liquid phase convective mass transfer of the dissolved copper species away from the wafer surface. It is proposed that the enhancement in the polish rate is directly proportional to the product of abrasive concentration and the shear stress on the wafer surface. Hence, the ratio of the polish rate with abrasive to the polish rate without abrasive can be written as... 

If there is no laminar viscosimeter flow, only the shear stress acting on the rotating cylinder surfaces can be calculated. It can be derived by the equilibrium of forces on the rotating cylinder ... 

Ti and Nei in Eq. (13) are valid for the case of the Searle type and T2 and Ne2 for the Couette type. The shear stress from Eq. (13) is the maximum shear which occurs in the gap close to the rotating cylinder. The uniformity of stress inside the gap decrease with increasing Re number. If the particles have the tendency to flow close to the moving wall, they will be subjected to the maximum shear. 

Eredictions. A rotating cyhnder within a cyhnder electrode test system as been developed that operates under a defined hydrodynamics relationship (Figs. 25-15 and 25-16). The assumption is that if the rotating electrode operates at a shear stress comparable to that in plant geometry, the mechanism in the plant geometty may be modeled in the laboratory. Once the mechanism is defined, the appropriate relationship between fluid flow rate and corrosion rate in the plant equipment as defined by the mechanism can be used to predict the expected corrosion... 

This is most easily achieved by rotating the inner cylinder and keeping the outer fixed in the laboratory frame. Note, however, that this geometry leads to the formation of Taylor vortex motion if inertial effects become important (Reynolds number Re 1). Most rheo-NMR experiments are actually performed at low Re. In the cylindrical Couette, the natural coordinates are cylindrical polar (q, <(>, z) so the shear stress is denoted and is radially dependent as q 2. The strain rate across the gap is given by [2]... 

For turbulent flow, the local wall shear stress, xr, is given by Eq. (25). Substituting Eqs. (48H50) into Eq. (47) and making use of Eq. (25), one arrives at an expression for the Sherwood number based upon the radius of the rotating hemisphere ... 

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