Viscosity determination from capillary

Capillary Viscometers. Capillary flow measurement is a popular method for measuring viscosity (21,145,146) it is also the oldest. A Hquid drains or is forced through a fine-bore tube, and the viscosity is determined from the measured flow, appHed pressure, and tube dimensions. The basic equation is the Hagen-Poiseuike expression (eq. 17), where Tj is the viscosity, r the radius of the capillary, /S.p the pressure drop through the capillary, IV the volume of hquid that flows in time /, and U the length of the capillary. 

Absolute viscosities are difficult to measure with capillary viscometers, but viscosities relative to some standard fluid of known viscosity, such as water, are readily determined. The viscometer is caHbrated with the reference fluid, and viscosities of other fluids relative to the reference sample are determined from their flow times. 

Piston Cylinder (Extrusion). Pressure-driven piston cylinder capillary viscometers, ie, extmsion rheometers (Fig. 25), are used primarily to measure the melt viscosity of polymers and other viscous materials (21,47,49,50). A reservoir is connected to a capillary tube, and molten polymer or another material is extmded through the capillary by means of a piston to which a constant force is appHed. Viscosity can be determined from the volumetric flow rate and the pressure drop along the capillary. The basic method and test conditions for a number of thermoplastics are described in ASTM D1238. Melt viscoelasticity can influence the results (160). 

Polymer melts are frequendy non-Newtonian. In this case the earlier expression given for the shear rate at the capillary wall does not hold. A correction factor (3n + 1)/4n, called the Rabinowitsch correction, must be appHed in such a way that equation 21 appHes, where 7 is the tme shear rate at the wall and nis 2l power law factor (eq. 22) determined from the slope of a log—log plot of the tme shear stress at the wad, T, vs 7. For a Newtonian hquid, n = 1. A tme apparent viscosity, Tj, can be calculated from equation 23. 

Assays. Nitrogen assays to determine 1-amidoethylene unit content were done by Kjeldahl method. Limiting viscosity numbers were determined from 4 or more viscosity measurements made on a Cannon-Fenske capillary viscometer at 30°C. Data was extrapolated to 0 g/dL polymer concentration using the Huggins equation(44) for nonionic polymers and the Fuoss equation(45) for polyelectrolytes. Equipment. Viscosities were measured using Cannon-Fenske capillary viscometers and a Brookfield LV Microvis, cone and plate viscometer with a CP-40, 0.8° cone. Capillary viscometers received 10 mL of a sample for testing while the cone and plate viscometer received 0.50 mL. 

To obtain a larger range in viscosities determined with a capillary viscometer, polymers from different batches were used to prepare the emulsions. The results obtained with the capillary viscometer are given in Figure 3. The ratio between the viscosities of the two components of the emulsions is about 10. 

The capillary method is simple to operate and precise (c. 0.01-0.1 per cent) in its results, but suffers from the disadvantage that the rate of shear varies from zero at the centre of the capillary to a maximum (which decreases throughout the determination) at the wall. Thus, with asymmetric particles a viscosity determination in an Ostwald viscometer could cover various states of orientation and the measured viscosity, although reproducible, would have little theoretical significance. 

Although the values of Intrinsic viscosity determined with a low shear viscometer are the only ones which truly represent the Intrinsic viscosity at high molecular weights, the results from the capillary viscometer are shown In Figure 7 to give an Indication of the effect of shear In the viscosity range of the study. The values of Intrinsic viscosity are different for the two types of viscometers, but the trend of Intrinsic viscosity versus conversion Is still the same. 

Although the capillary tube method has recently fallen into disfavour, which is unfortunate, it can with careful work give very accurate results, and some of the best values of g have been found by this method. The tube (which may be freshly drawn) must be free from grease Volkmann washed the tube with potash solution and then distilled water (the chromic-sulphuric acid mixture should always be avoided). Schultzei said the walls of the tube should first be wetted, to fill the capillary pores of the glass surface. The rate of rise of a liquid in a capillary was studied by Le Grand and Reuse. Muller 12 determined surface tension and viscosity simultaneously from the rate of flow back to the equilibrium position in a capillary. 

The viscosity as calculated according to Eq. (44) is meaningful only if the flow is laminar. For a capillary flow the rate of flow should not exceed a critical velocity which can be determined from its Reynolds number (Rk) ... 

For determination of the steady state shear viscosity the Instron capillary viscometer model 3211 was used at 190 C. Six capillaries were used, three each of diameter d = 747 and 1273 ym. The length to diameter ratio In each series varied from L/d > 0.6 to 60. The standard Bagley and Bablnowltsch corrections as well as that for the pressure effects (45) were applied. The extrudate swell was determined on air-cooled extrudates, 5 cm in length. 

Perhaps the most familiar technique is the capillary-flow method. The working principle is the Hagen-Poiseuille relationship between the flow rate through a tube of fixed diameter, the pressure drop, and the viscosity. In practice, because the capillary diameter appears to the fourth power in the working equation and is difficult to determine accurately, capillary viscometers are usually calibrated with reference fluids such as water or reference oils that are available from viscometer manufacturers and some national laboratories. 

The methodology of capillary viscometry of liquids rests on the laws of flow through a fine-bore tube. The viscosity is determined from the measured flow rate under a known applied pressure through a tube of known dimensions. 

The shear stresses and the shear rates in Fig. 8 were computed by the appropriate formula for Newtonian flow at the capillary wall. But if the results of such a computation indicate that the viscosity varies with shear rate, then the Rabinowitsch analysis is applied to determine the correct shear rate at the wall for non-Newtonian behavior (c. References 2 and 3). Figure 4-9 illustrates how the addition of a polymeric viscosity modifier to a paraffinic petroleum base oil changes the viscosity behavior from Newtonian (Fluid B) to non-Newtonian (Fluids C, D and E). The shear rates and the shear stresses have a hundred-fold range. 

The rate of flow under gravity of a liquid through a capillary tube depends on a number of factors, including the viscosity tj) and density (p) of the liquid as well as the size and shape of the tube. For a standard capillary viscometer (see Figure 4.10) the time taken (r) for a set volume of liquid to flow between points A and B is proportional to tjfp so that, after appropriate calibration with known liquids, the viscosity of any sample can be determined from its flow time, t. 

The viscosity coefficient of gases may be determined from measurements of the rate of fiow through a capillary tube of known radius under a given pressure difference, and from the result the mean free path, I, may be calculated. For simple gases at atmospheric pressure it is of the order 10- cm. It varies inversely as the pressure, and long before the highest vacuum given by a modern pump is reached it exceeds the dimensions of ordinary small-scale laboratory apparatus. 

The theory can be generalized to the case of oblique incidence/ Martinoty and Candau found that the viscosity coefficients determined by the ultrasonic technique compare fairly well with those derived from capillary flow. 

If/m is the maximum packing density of the particles, which is defined as the volume fraction at which the particles touch one another, so that flow is not possible, then the actual particle volume firaction/used in injection molding is lower than/m by 5-10 vol%. This means that in a well-dispersed suspension, the particles are separated from one another by a thin layer of polymer with a thickness of about 50 nm dming the molding, so that the mixture is able to flow. Therefore, the volume fraction of particles / is determined by the particle size and distribution and the particle shape. In practice, the volume firaction of ceramic powders is determined from viscosity measurements by using a capillary rheometer. Data for the relative viscosity, i.e., the viscosity of the mixture divided by the viscosity of the unfilled polymer versus particle concentration can be well fitted by the following equation [209] ... 

The intrinsic viscosity and Mark-Houwink constants of standards can be determined from a static capillary viscometer or an on-line viscometer detector in an SEC system. If the intrinsic viscosity is to be used for constructing a universal calibration curve, it is important to use the identical conditions in performing the SEC analysis and the intrinsic viscosity measurement. A Mark-Houwink plot for five PAM standards and one PAA standard is shown in Figure 4. The intrinsic viscosity of PAM may decrease with time and becomes constant after about one week. It is recommended that the PAM solution be analyzed while still fresh. 

The viscosity fj was measured with a capillary viscosimeter. The correlation radius of the concentration fluctuations was determined from the radiation dizigram (hxjua-tions 100-102). 

From the dimensions of the MI apparatus, the weight on the plunger, and the MI value, one can determine the approximate shear stress, shear rate, and viscosity. By using Eqs. 6.48 and 6.49, the shear stress at the capillary wall can be determined from ... 

In viscosimetry, the (d5mamic) viscosity of a diluted solution of a special solvent and HDPE resin is determined, e.g. by capillary viscosimetry as per EN ISO 1628-3 2003 Plastics - Determination of Viscosity of Polymers in Dilute Solution Using Capillary Viscometers - Part 3 Polyetl l-enes and Polypropylenes. The flow time of the solution t and of the pure solvent to is measured in a capillary immersed in a hot bath at an elevated temperature. The coefficient of viscosity J is determined from this flow times. It is defined as the relative change of the viscosity of the solution p (proportional to t) with the concentration c related to the viscosity of the solvent rjQ (proportional to to) ... 

The volume fraction of powder that can be reasonably incorporated into the mixture is best determined from viscosity measurements using a capillary rheometer over the range of conditions expected in the forming operation. Data for the relative viscosity (the viscosity of the mixture divided by the viscosity of the unfilled polymer) versus particle concentration can be well fitted by the equation (66)... 

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