Measurement of viscosity

The viscosity of polymer solutions, rj, is usually measured by capillary or rotational viscometers. The capillary-type viscometer has the following advantages high accuracy, ease of operation, speed and low cost of instrumentation. The rotational-type viscometer is frequently used in cases where the mass of the sample available is limited and the viscosity over a wide range of shear rates is required. 

In order to determine the molecular weight the absolute value of the viscosity of the solution is not necessary. It is sufficient to measure the viscosity ratio Tjr. In dilute polymer solution p can be regarded as being equal to that of the solvent po. Then rir is expressed from eqn (5.43) as  

Another automatic capillary viscometer which directly detects the pressure difference AP (eqn (5.42)) has recently come on the market. The Relative Viscometer manufactured by the Viscotek Co. includes two capillaries (capillary 1 and 2) connected in series, with the sample injection valve located between the two capillaries. Differential pressure transducers (DPT) are connected in parallel to each capillary. The sample is injected into capillary 2 and a pressure change is detected by the DPT. The viscosity ratio v r is determined as the ratio of the pressures divided by the instrument constant. 

The proportionality constant (rj) is known as the coefiident of viscosity or simply as viscosity. This equation is more typically in the form  

There are generally two approaches to the measurement of viscosity namely, controlled stress and controlled strain. In controlled stress, a known stress is applied to the fluid and the resultant shear rate is measured. Conversely, in controlled strain a known strain, or more accurately rate of strain (shear rate) is applied and the stress is measured. A falling ball viscometer is a controlled stress viscometer in which the applied stress comes from the size of the ball and gravity whereas the Brookfield viscometer is an example of a controlled strain instrument where the rate of strain is related to the rotational speed applied. 

Automated viscometers are commercially available. To measure the viscosity of liquids in the centipoise range, it is, however, more common to use a capillary flow viscometer, unless the measurement is routinely conducted. This classical method is inexpensive, yet can measure the viscosity with a sufficient accuracy. 

The measurement is based on the capillary flow. If the flow is slow and therefore laminar, the velocity profile in the capillary is of a parabolic cone. The velocity maximizes at the center line and declines to zero toward the wall (Fig. 3.34). The Poiseuille law holds for the viscosity of the fluid and the pressure drop AP along the length I of the capillary (Fig. 3.35)  

The pressure difference can be generated by a liquid pump, but, in the capillary viscometer in the vertical position, it is the gravity that causes AP, which is given by 

Note that Trr g/(8V) is a constant for a given viscometer. The constant can be determined by using a fluid of a known kinematic viscosity. Once calibrated, the 

If the fluid is too viscous, the elution takes too long. If it is too fluid, the flow will be too fast, causing a nonlaminar flow. A given viscometer can be used for a finite range of viscosity. To allow for the viscosity measurement of fluids in a wide range of viscosity, Ubbelohde viscometers are available in different radii of the capillary. 

We performed calibration tests for three low-impedance wedge materials, polyetherimide, acrylic (Lucite), and polystyrene. Table 5-4 lists the liquids used for the calibration tests note that all of the liquids have similar densities but vary in viscosity. The calibration results are shown in Fig. 5-40, which reveals that Lucite is the best of the three as a wedge material for measuring viscosity. However, all of the measured viscosities are lower than their expected values. The discrepancies may be attributed to non-Newtonian fluid behavior, surface wetting, and poor sensitivity. 

FIGURE 5-40 Viscosity calibration data for various wedge materials. 

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As should be expected, both (fg ) and r show the same dependence on the degree of polymerization or molecular weight. Since the radius of gyration can be determined experimentally through the measurement of viscosity or light scattering, it is through this quantity that we shall approach the evaluation of 1. 

The speed at which a sphere roUs down a cylindrical tube filled with a fluid or down an angled plate covered with a film of the fluid also gives a measure of viscosity. For the cylindrical tube geometry, equation 35, a generalized form of the Stokes equation is used for any given instmment, where p is the translational velocity of the rolling sphere and k is the instmment constant determined by caUbration with standard fluids. 

Viscosity can also be determined from the rising rate of an air bubble through a Hquid. This simple technique is widely used for routine viscosity measurements of Newtonian fluids. A bubble tube viscometer consists of a glass tube of a certain size to which Hquid is added until a small air space remains at the top. The tube is then capped. When it is inverted, the air bubble rises through the Hquid. The rise time in seconds may be taken as a measure of viscosity, or an approximate viscosity in mm /s may be calculated from it. In an older method that is commonly used, the rate of rise is matched to that of a member of a series of standards, eg, with that of the Gardner-Holdt bubble tubes. Unfortunately, this technique employs a nonlinear scale of letter designations and may be difficult to interpret. 

There is no entirely satisfactory way of measuring flow. In the BS 2782 flow cup test an amount of moulding powder is added to the mould to provide between 2 and 2.5 g of flash. The press is closed at a fixed initial rate and at a fixed temperature and pressure. The time between the onset of recorded pressure and the cessation of flash (i.e. the time at which the mould has closed) is noted. This time is thus the time required to move a given mass of material a fixed distance and is thus a measure of viscosity. It is not a measure of the time available for flow. This property, or rather the more important length of flow or extent of flow, must be measured by some other device such as the flow disc or by the Rossi-Peakes flow test, neither of which are entirely satisfactory. Cup flow times are normally of the order of 10-25 seconds if measured by the BS specification. Moulding powders are frequently classified as being of stiff flow if the cup flow time exceeds 20 seconds, medium flow for times of 13-19 seconds and soft flow or free flow if under 12 seconds. 

Experimental measurements of viscosity almost always are recommended when dealing with slurries and extrapolations should be made with caution. Most theoretically based expressions for liquid viscosity are not appropriate for practical calculations or require actual measurements to evaluate constants. For nonclustering particles, a reasonable correlation may be based on the ratio of the effective bulk viscosity, /ig, to the viscosity of the liquid. This ratio is expressed as a function of the volume fraction of liquid x in the slurry for a reasonable range of compositions ... 

Figure 40.18 Viscosity Index (VI) is a relative measure of viscosity change with temperature change...

The melt index (MI) or melt flow index (MFT) is an inverse measure of viscosity. High MI implies low viscosity and low MI means high viscosity. Plastics are shear thinning, which means that their resistance to flow decreases as the shear rate increases. This is due to molecular alignments in the direction of flow and disentanglements. 

If a solution tends to be independent of shear, then the measurement of viscosity (q) is based on Poiseuille s law can be made easy by grouping all those terms related to a specific viscometer as a calibration constant A. 

Crisp, S., Lewis, B. G. Wilson, A. D. (1975). Gelation of polyacrylic acid aqueous solutions and the measurement of viscosity. Journal of Dental Research, 54, 1173-5. 

The diameter of the disc is measured and this gives an indication of the shear strength of the paste. It is not a measure of viscosity because flow has ceased at this point. The shear strength of the paste can be calculated from the following formula, which was derived by Wilson Batchelor (1971). 

Viscosity also is measured with a rotational viscometer. The mud is placed between two concentric cylinders. One cylinder rotates with constant velocity. The other cylinder is connected with a spring. The torque on this cylinder results in a deviation of the position from rest, which may serve as a measure of viscosity. 

The measurement of viscosity is important for many food products as the flow properties of the material relate directly to how the product will perform or be perceived by the consumer. Measurements of fluid viscosity were based on a correlation between relaxation times and fluid viscosity. The dependence of relaxation times on fluid viscosity was predicted and demonstrated in the late 1940 s [29]. This type of correlation has been found to hold for a large number of simple fluid foods including molten hard candies, concentrated coffee and concentrated milk. Shown in Figure 4.7.6 are the relaxation times measured at 10 MHz for solutions of rehydrated instant coffee compared with measured Newtonian viscosities of the solution. The correlations and the measurement provide an accurate estimate of viscosity at a specific shear rate. 

So far the results have been shown in which the metal alkoxide solutions are reacted in the open system. It has been shown that the metal alkoxide solutions reacted in the closed container never show the spinnability even when the starting solutions are characterized by the low acid content and low water content (4). It has been also shown from the measurements of viscosity behavior that the solution remains Newtonian in the open system, while the solution exhibits structural viscosity (shear-thinning) in the closed system. 

We are now going to compare the results of mode analysis with measurements of viscosity on polyethylene melts. With the aid of Eq. (30), which links the viscosity to the relaxation times, we can predict the viscosity using the results of spin-echo measurements and compare it with the viscosity measurement... 

The technical term for the study of and the measurement of viscosity is rheology. Viscosity measurements can be made in a variety of ways. The simplest method is to determine the time it takes for a metal ball to fall through a specified distance of a liquid in a graduated cylinder. The American Society of Testing Materials (ASTM) specifies several methods for the determination of viscosity of specific substances using this method. When the radius of the ball is small compared to the radius of the graduated cylinder, the viscosity will be... 

Djordjevich L, Kashani A, Miller IF, et al. Measurements of viscosity of synthetic erythrocyte suspensions. Biorheology 1987 24 207. 

The values of some of these parameters at room temperature and pressure are given in table 4.26. These values are obtained from measurements of viscosity, thermal conductivity, diffusion, and from deviations from the perfect gas law. 

Until now, we have been primarily concerned with the definition and measurement of viscosity without regard to the nature of the system under consideration. Next we turn our attention to systems containing dispersed particles with dimensions in the colloidal size range. Viscosity measurements can be used to characterize both lyophobic and lyophilic systems we discuss both in the order cited. 

Various measurements of viscosity as a function of solids in diluted and concentrated milk reveal a curvilinear relationship (Bateman and Sharp 1928 Deysher, et al. 1944 Leighton and Kurtz 1930). Eilers et al. (1947) calculated voluminosity at several solids concentrations (skim milk), showing that the voluminosity of the caseinate particles does not change but that the apparent voluminosity of the total solids decreases as the concentration is raised. This may merely signify that... 

Potter, F. E., Deysher, E. F. and Webb, B. H. 1949. A comparison of torsion pendulum type viscosimeters for measurement of viscosity in dairy products. J. Dairy Sci. 32, 452-457. 

Measurements of Viscosity and Elasticity in Shear (Simple Shear) Shear viscosity J] and shear elasticity G are determined by evaluating the coefficients of the variables x and x, respectively, which result when the geometry of the system has been taken into account. The resulting equation of state balances stress against shear rate y (reciprocal seconds) and shear y (dimensionless) as the kinematic variables. For a purely elastic, or Hookean, response ... 

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