The Capillary-Tube Viscometer

Thus, the pressure drop AP for laminar flow through a tube varies in proportion to the viscosity n, the average flow velocity v, and the tube length L, and in inverse proportion to the square of the tube diameter d. Since v is proportional to the total flow rate Q (m s ) and to d, C P should vary in proportion to ft, Q, L, and The principle of the capillary tube viscometer is based on this relationship. 

The capillary tube viscometer is not suitable for settling suspensions. This instrument suffers from the fact that the shear rate is not constant across the tube radius and the fluid cannot be sheared as long as desired. It is... 

The capillary tube viscometer is a flow-through-restriction type. When used carefully, it is capable of accuracies of better than 2 percent over its applicable shear-rate range (300 to 4000 s 1). For laminar flow of a nonnewtonian liquid in a capillary tube, it can be shown [4] that the wall shear stress xw and the shear rate at the wall % are given by... 

The purpose of the capillary tube viscometer is to measure the rheology of a laminar flow under controlled velocity conditions. Tubes are used in a range of diameters from 0.8-12 mm (1/32-1/2 in). The length of the tube is accurately cut to account for entrance effects and end effects. Typically, the length may be as much as 1000 times the inner diameter. 

The capillary tube viscometer is used to plot the average rate versus the shear stress at the wall of the tube. This is called the pseudoshear diagram, as defined by the Mooney-Rabinovitch equation ... 

While there was some interest in general fluid mechanical problems in this era, most of the research effort was directed toward the measurement of the viscosity of a wide range of fluids. While the capillary tube viscometer was known by some, its use was not appreciated by all, leading Twining to lament ... 

More recent developments in the rolling ball area include an automated micro viscometer, the Paar AMV 200, from Paar Physica. The specimen to be measured is introduced into a glass capillary down which a gold-covered steel ball roUs. The rolling time is measured automatically. The shear stress may be varied by changing the inclination angle of the capillary tube. The shear rate range is 10 1000, which makes the instmment useflil for... 

If it is known that a particular form of relation, such as the power-law model, is applicable, it is not necessary to maintain a constant shear rate. Thus, for instance, a capillary tube viscometer can be used for determination of the values of the two parameters in the model. In this case it is usually possible to allow for the effects of wall-slip by making measurements with tubes covering a range of bores and extrapolating the results to a tube of infinite diameter. Details of the method are given by Farooqi and Richardson. 21 ... 

In a series of experiments on the flow of flocculated kaolin suspensions in laboratory and industrial scale pipelines(26-27-2Sl, measurements of pressure drop were made as a function of flowrate. Results were obtained using a laboratory capillary-tube viscometer, and pipelines of 42 mm and 205 mm diameter arranged in a recirculating loop. The rheology of all of the suspensions was described by the power-law model with a power law index less than unity, that is they were all shear-thinning. The behaviour in the laminar region can be described by the equation ... 

Mooney clearly showed that the relationship between the shear stress at the wall of a pipe or tube, DAP/4L, and the term 8V/D is independent of the diameter of the tube in laminar flow. This statement is rigorously true for any kind of flow behavior in which the shearing rate is only a function of the applied shearing stress.1 This relationship between DAP/4L and 8VJD may be conveniently determined in a capillary-tube viscometer, for example. Once this has been done over the range of... 

Viscosities must be determined experimentally. For settlable solids, the suspension viscometer of Orr and DallaValle (05) is recommended. For other suspensions any good rotational or capillary-tube viscometer is suitable (see Section VI). 

The essential features of capillary-tube viscometers may be summarized to be... 

Orr and DallaValle (05) have designed a capillary-tube viscometer which is especially suited for use with suspensions which tend to settle. This instrument, shown in Fig. 13, consists of the following four components ... 

Meyerhoff (4) and Goedhart and Opschoor (5) have measured the viscosity of each eluting GPC fraction by coupling an automatic capillary tube viscometer with the GPC syphon. The low polymer concentration in each fraction necessitated an extremely accurate efflux time measurement to 0.01 second since the flow time of each fraction containing polymer has flow times, th greater than that of pure solvent, t0, by at most 2.00 seconds. The specific viscosity sv. of the ith polymer fraction is calculated from the flow times of the pure solvent and the polymer fraction. 

This method is an adaptation of the Basic Protocol for measuring the viscosity of pure liquids and solutions. The °brix (unithi.4) of the sample is adjusted to a desired value by dilution. In many protocols, a nominal value of 5 °brix is the accepted target value for dilution. The sample is then filtered to remove particles that would plug the capillary tube of the viscometer, and the serum viscosity is measured in a Cannon-Fenske viscometer. 

VIt = (p gl + Apjn/ /Bri/ where p is the density of the fluid, g is the force due to gravity, l is the length of the capillary tube, and Ap is the pressure difference between the entrance and exit of the capillary tube. The equation can be rearranged and further simplified to account for all the constants that characterize the viscometer. This also assumes that the difference in height of the two liquid columns is relatively constant during the time required for flow. Thus, the only pressure difference across the liquid is due to the weight of the liquid. With these conditions ... 

In practice, we can measure viscosity by the efflux time of a liquid in a viscometer (Fig. 47.3). The capillary viscometer is made of two bulbs connected by a tube in which the liquid must flow through a capillary tube. The capillary tube provides a laminary flow in which concentric layers of the liquid slide past each other. Originally, the liquid is placed in the storage bulb (A). By applying suction above the capillary, the liquid is sucked up past the upper calibration mark. With a stopwatch in hand, the suction is released and the liquid is allowed to flow under the force of gravity. The timing starts when the meniscus of the liquid hits the upper calibration mark. The timing ends when the meniscus of the liquid hits the lower calibration mark of the viscometer. The time elapsed between these two marks is the efflux time. 

The measurement of the size of the polymer is carried out in a capillary viscometer. The presence of polymer molecules in a solvent affects the relative motion of the solvent (i.e., solution viscosity). Even very dilute solutions of polymers are very viscous. When a dilute solution of a polymer travels along a capillary tube, as shown in Figure 7.5, there is a parabolic velocity gradient across the capillary tube with the maximum velocity at the center of the tube and a minimum velocity at the... 

Procedure Using a magnetic stirrer, dissolve 300 mg of sample in 200 mL of Tetrasodium Pyrophosphate Solution. When solution is complete, or after 30 min, whichever occurs first, transfer 10 mL of the solution into an Ostwald-Fenske viscometer, and determine the time, / , in seconds, required for the liquid to flow from the upper to the lower mark in the capillary tube. Calculate the viscosity, in centipoises, by the formula... 

Determine the viscosity in capillary tubes by measuring the amount of time it takes for a given volume of liquid to flow through a calibrated capillary tube. Calibrate the capillary tube by using liquids of known viscosity. The calibration may be supplied with the viscometer tube when purchased along with specific instructions for its use. Many types of capillary viscometer tubes are available, and exact procedures will vary... 

The time taken by this water to flow through the capillary tube DF is noted by means of a stop watch. Let it be ty The viscometer is dried and the same volume of the liquid under examination is taken into the bulb B (so that the pressure head remains the same) and the process repeated as before. Let the time of flow be t2. 

Some of the considerations in selecting a capillary/tube viscometer for viscosity measurement are shown in Figure 3-45. 

The opportunity to measure the dilute polymer solution viscosity in GPC came with the continuous capillary-type viscometers (single capillary or differential multicapillary detectors) coupled to the traditional chromatographic system before or after a concentration detector in series (see the entry Viscometric Detection in GPC-SEC). Because liquid continuously flows through the capillary tube, the detected pressure drop across the capillary provides the measure for the fluid viscosity according to the Poiseuille s equation for laminar flow of incompressible liquids [1], Most commercial on-line viscometers provide either relative or specific viscosities measured continuously across the entire polymer peak. These measurements produce a viscometry elution profile (chromatogram). Combined with a concentration-detector chromatogram (the concentration versus retention volume elution curve), this profile allows one to calculate the instantaneous intrinsic viscosity [17] of a polymer solution at each data point i (time slice) of a polymer distribution. Thus, if the differential refractometer is used as a concentration detector, then for each sample slice i. 

The use of these empirical procedures is being superseded by the more precise kinematic viscosity method (ASTM D-445, IP 71), in which a fixed volume of fuel flows through the capillary of a calibrated glass capillary viscometer under an accurately reproducible head and at a closely controlled temperature. The result is obtained from the product of the time taken for the fuel to flow between two etched marks on the capillary tube and the calibration factor of the viscometer and is reported in centistokes. Because the viscosity decreases with increasing temperature the temperature of test must also be reported if the viscosity value is to have any significance. For distillate fuel oils the usual test temperature is 38°C (100°F). 

Shear Viscosity. There are three main types of viscometers the rotational type, the flow-through-constriction type, and the flow-around-obstruction type. The concentric cylinder and the cone-and-plate are the two primary classes of rotational viscometers. The capillary tube is an example of the flow-through-constriction viscometers. Falling-ball or falling-needle viscometers are examples of the flow-around-obstruction type. 

FIGURE 10.23 Steady-shear-viscosity measurements for polyacrylamide (Separan AP-273) solutions from Weissenberg rheogoniometer and capillary-tube viscometer. tp is the characteristic time calculated from the Powell-Eyring model [37]. 

As shown in Sec. 1.5, the basic definition of viscosity is in terms of the sliding-plate experiment shown in Fig. 1.4. For newtonian fluids it was shown in Sec. 6.3 (Example 6.2) that the viscosity could be determined easily by a capillary-tube viscometer. It can be shown both theoretically and experimentally that the viscosity determined by such a viscometer for a newtonian liquid is exactly the same as the viscosity one would determine on a sliding-plate viscometer. Since capillary-tube viscometers are cheap and simple to operate, they are widely used in industry for newtonian fluids. 

For nonnewtonial fluids which are not time-dependent or viscoelastic, it is possible to convert capillary-tube viscometer measurements to the equivalent sliding-plate measurements, but this involves some mathematical manipulations. For time-dependent (e.g., thixotropic) fluids, this does not seem to be... 

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