Shear stress measurements, viscosity

A plot of Tvs. G yields a rheogram or a flow curve. Flow curves are usually plotted on a log-log scale to include the many decades of shear rate and the measured shear stress or viscosity. The higher the viscosity of a liquid, the greater the shearing stress required to produce a certain rate of shear. Dividing the shear stress by the shear rate at each point results in a viscosity curve (or a viscosity profile), which describes the relationship between the viscosity and shear rate. The... 

When the measured values of shear stress or viscosity are plotted versus shear rate, various types of behavior may be observed depending upon the fluid properties, as shown in Figs. 3-5 and 3-6. It should be noted that the shear stress and shear rate can both be either positive or negative, depending upon the direction of motion or the applied force, the reference frame, etc. (however, by our convention they are always the same sign). Because the viscosity must always be positive, the shear rate (or shear stress) argument in... 

Viscosity can be defined as the ratio of shear stress to shear rate (. The shear stress is equal to a force measured in dynes divided over an area upon which it acts in square centimeters. Shear stress has the dimensions of dynes per square centimeter. The shear rate is equal to the velocity of a layer due to shear stress measured in centimeters per second divided by the thickness in centimeters the unit of shear rate is given in reciprocal seconds. Viscosity often is expressed in poises. The poise has the dimension of dyne seconds per square centimeter. Dyne seconds per square centimeter is the dimension for shear stress divided by shear rate and therefore is equal to viscosity. 

The viscosity of the suspension at difierent biomass concentration was measured by Modular Compact Rheometer Physica MCR 300 (Paar-Physica). Controlled shear-stress measurements were done using the concentric cylinder system with a FL 100/6W impeller at temperatures of 30, 40, and 50 °C. Samples were mixed before measurements were taken. Then, an appropriate volume was placed into the viscometer, allowing several minutes for the temperature to stabilize. The rheological measurements were performed three times for each value of biomass concentration using a fresh sample each time. 

The viscosity is then measured at ambient temperature at increasing shear rates of 85, 170, 255, 340, and 425 s The shear rate scans are produced in the rotational viscometer by increasing the rotation rate, and the scans are produced in the reciprocating capillary by changing the flow rate in discrete steps. After the initial shear scan, the sample is heated at about 2.7 C/min while being sheared at a constant rate of 170 s The sample temperature is about 80 °C in 25 min time zero is at the start of the ambient temperature scan. Shear scans are taken at 25, 40, 55, and 70 min with the shear rate maintained at 170 s between scans. Power-law parameters n and K are calculated from the shear stress measurements obtained from the scans. The viscosity at 170 s is calculated from these power-law parameters and reported. 

Sacks and Sheu [145] prepared acid- and base-catalyzed silicate systems in which the molar ratios of the components were varied as indicated in Table 16. Acid-catalyzed, low-water systems (compositions 1 and 2) are suitable for drawing fibers composition 3 (r = 20) is suitable for bulk gels, and the dilute, base-catalyzed system, composition 4 (r = 20), results in the formation of particles. Shear stress and viscosity versus shear rate measurements... 

Thanks to their relatively lower viscosity, food and cosmetic products allow this type of behavior to be easily documented, when performing experiments with controlled stress rheometers. There are commercial versions of such instruments, essentially rotating systems (parallel disks or cone-and-plate), which have the capability to measure extremely small rotation rates (in the 10 rad/s, i.e., one revolution in 20 years ). Experiments performed in such conditions are called creep testing using controlled torques as low as 10 Nm with a resolution of 10 Nm. Figure 5.5 shows an example of the shear viscosity function (vs. shear stress) measured on a typical cosmetic product (body cream), using such a controlled stress rheometer. 

Viscous Hquids are classified based on their rheological behavior characterized by the relationship of shear stress with shear rate. Eor Newtonian Hquids, the viscosity represented by the ratio of shear stress to shear rate is independent of shear rate, whereas non-Newtonian Hquid viscosity changes with shear rate. Non-Newtonian Hquids are further divided into three categories time-independent, time-dependent, and viscoelastic. A detailed discussion of these rheologically complex Hquids is given elsewhere (see Rheological measurements). 

Effect of Temperature. In addition to being often dependent on parameters such as shear stress, shear rate, and time, viscosity is highly sensitive to changes in temperature. Most materials decrease in viscosity as temperature increases. The dependence is logarithmic and can be substantial, up to 10% change/°C. This has important implications for processing and handling of materials and for viscosity measurement. 

Capillary viscometers are useful for measuring precise viscosities of a large number of fluids, ranging from dilute polymer solutions to polymer melts. Shear rates vary widely and depend on the instmments and the Hquid being studied. The shear rate at the capillary wall for a Newtonian fluid may be calculated from equation 18, where Q is the volumetric flow rate and r the radius of the capillary the shear stress at the wall is = r Ap/2L. 

Gla.ss Ca.pilla.ry Viscometers. The glass capillary viscometer is widely used to measure the viscosity of Newtonian fluids. The driving force is usually the hydrostatic head of the test Hquid. Kinematic viscosity is measured directly, and most of the viscometers are limited to low viscosity fluids, ca 0.4—16,000 mm /s. However, external pressure can be appHed to many glass viscometers to increase the range of measurement and enable the study of non-Newtonian behavior. Glass capillary viscometers are low shear stress instmments 1—15 Pa or 10—150 dyn/cm if operated by gravity only. The rate of shear can be as high as 20,000 based on a 200—800 s efflux time. 

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. 

Additional complications can occur if the mode of deformation of the material in the process differs from that of the measurement method. Most fluid rheology measurements are made under shear. If the material is extended, broken into droplets, or drawn into filaments, the extensional viscosity may be a more appropriate quantity for correlation with performance. This is the case in the parting nip of a roUer in which filamenting paint can cause roUer spatter if the extensional viscosity exceeds certain limits (109). In a number of cases shear stress is the key factor rather than shear rate, and controlled stress measurements are necessary. 

At yet higher temperatures (>1.4T ) the secondary bonds melt completely and even the entanglement points slip. This is the regime in which thermoplastics are moulded linear polymers become viscous liquids. The viscosity is always defined (and usually measured) in shear if a shear stress o produces a rate of shear 7 then the viscosity (Chapter 19) is... 

Studies of melt flow properties of polypropylene indicate that it is more non-Newtonian than polyethylene in that the apparent viscosity declines more rapidly with increase in shear rate. The melt viscosity is also more sensitive to temperature. Van der Wegt has shown that if the log (apparent viscosity) is plotted against log (shear stress) for a number of polypropylene grades differing in molecular weight, molecular weight distribution and measured at different temperatures the curves obtained have practically the same shape and differ only in position. 

The rate of mastication, as measured by changes in plasticity or viscosity, is a complex function of temperature (Figure 11.16) with the rate going through a minimum at about 105°C. Below this temperature the increasing viscosity of the rubber causes increased shearing stresses at constant shearing rates and this... 

Assuming that the melt viscosity is a power law function of the rate of shear, calculate the percentage difference in the shear stresses given by the two methods of measurement at the rate of shear obtained in the cone and plate experiment. 

PEs, as other polymers, exhibit nonlinear behavior in their viscous and elastic properties under practical processing conditions, i.e., at high-shear stresses. The MFI value is, therefore, of little importance in polymer processing as it is determined at a fixed low-shear rate and does not provide information on melt elasticity [38,39]. In order to understand the processing behavior of polymers, studies on melt viscosity are done in the high-shear rate range viz. 100-1000 s . Additionally, it is important to measure the elastic property of a polymer under similar conditions to achieve consistent product quality in terms of residual stress and/or dimensional accuracy of the processed product. 

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. 

The resistance when moving one layer of liquid over another is the basis for the laboratory method of measuring absolute viscosity. Poise viscosity is defined as the force (pounds) per unit of area, in square inches, required to move one parallel surface at a speed of one centimeter-per-second past another parallel surface when the two surfaces are separated by a fluid film one centimeter thick. Figure 40.16. In the metric system, force is expressed in dynes and area in square centimeters. Poise is also the ratio between the shearing stress and the rate of shear of the fluid. 

Modification of filler s surface by active media leads to the same strong variation in viscosity. We can point out as an example the results of work [8], in which the values of the viscosity of dispersions of CaC03 in polystyrene melt were compared. For q> = 0.3 and the diameter of particles equal to 0.07 nm a treatment of the filler s surface by stearic acid caused a decrease in viscosity in the region of low shear rates as compared to the viscosity of nontreated particles more than by ten times. This very strong result, however, should not possibly be understood only from the point of view of viscometric measurements. The point is that, as stated above, a treatment of the filler particles affects its ability to netformation. Therefore for one and the same conditions of measuring viscosity, the dispersions being compared are not in equivalent positions with respect to yield stress. Thus, their viscosities become different. 

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