Newtonian fluids capillary viscometers

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. 

There are two main types of viscometer rotary instruments and tubular, often capillary, viscometers. When dealing with non-Newtonian fluids, it is desirable to use a viscometer that subjects the whole of the sample to the same shear rate and two such devices, the cone and plate viscometer and the narrow gap coaxial cylinders viscometer, will be considered first. With other instruments, which impose a non-uniform shear rate, the proper analysis of the measurements is more complicated. 

The membrane viscometer must use a membrane with a sufficiently well-defined pore so that the flow of isolated polymer molecules in solution can be analyzed as Poiseuille flow in a long capillary, whose length/diameter is j 10. As such the viscosity, T, of a Newtonian fluid can be determined by measuring the pressure drop across a single pore of the membrane, knowing in advance the thickness, L, and cross section. A, of the membrane, the radius of the pore, Rj., the flow rate per pore, Q,, and the number of pores per unit area. N. The viscosity, the maximum shear stress, cr. and the velocity gradient, y, can be calculated from laboratory measurements of the above instrumental parameters where Qj =... 

If one considers fluid flowing in a pipe, the situation is highly illustrative of the distinction between shear rate and flow rate. The flow rate is the volume of liquid discharged from the pipe over a period of time. The velocity of a Newtonian fluid in a pipe is a parabolic function of position. At the centerline the velocity is a maximum, while at the wall it is a minimum. The shear rate is effectively the slope of the parabolic function line, so it is a minimum at the centerline and a maximum at the wall. Because the shear rate in a pipe or capillary is a function of position, viscometers based around capillary flow are less useful for non-Newtonian materials. For this reason, rotational devices are often used in preference to capillary or tube viscometers. 

To successfully measure non-Newtonian fluids, a known shear field (preferably constant) must be generated in the instrument. Generally, this situation is known as steady simple shear. This precludes the use of most single-point viscometers and leaves only rotational and capillary devices. Of these, rotational devices are most commonly used. To meet the criterion of steady simple shear, cone and plate, parallel plates, or concentric cylinders are used (Figure HI. 1.1). 

This unit describes a method for measuring the viscosity (r ) of Newtonian fluids. For a Newtonian fluid, viscosity is a constant at a given temperature and pressure, as defined in unit hi. i common liquids under ordinary circumstances behave in this way. Examples include pure fluids and solutions. Liquids which have suspended matter of sufficient size and concentration may deviate from Newtonian behavior. Examples of liquids exhibiting non-Newtonian behavior (unit hi. i) include polymer suspensions, emulsions, and fruit juices. Glass capillary viscometers are useful for the measurement of fluids, with the appropriate choice of capillary dimensions, for Newtonian fluids of viscosity up to 10 Pascals (Newtons m/sec 2) or 100 Poise (dynes cm/sec 2). Traditionally, these viscometers have been used in the oil industry. However, they have been adapted for use in the food industry and are commonly used for molecular weight prediction of food polymers in very dilute solutions (Daubert and Foegeding, 1998). There are three common types of capillary viscometers including Ubelohde, Ostwald, and Cannon-Fenske. These viscometers are often referred to as U-tube viscometers because they resemble the letter U (see Fig. HI.3.1). 

Capillary viscometers are ideal for measuring the viscosity of Newtonian fluids. However, they are unsuitable for non-Newtonian fluids since variations in hydrostatic pressure during sample efflux results in variations in shear rate and thus viscosity. This unit contains protocols for measuring the viscosity of pure liquids and solutions (see Basic Protocol) and serums from fruit juices and pastes (see Alternate Protocol). 

Many modifications of the basic Ostwald geometry are employed in different situations. One example is the Cannon-Fenske routine viscometer (Fig. 6.37b) which is used in the oil industry for measuring kinematic viscosities of 0.02 m2/s and less(4<). As viscosity is sensitive to variations in temperature, these types of viscometer are always immersed in a constant temperature bath. They are not normally suitable for non-Newtonian fluids although FAROOQI and Richardson(47) have employed a capillary viscometer to characterise a power-law fluid. 

It is important that magnitudes of t and tgt are determined with care at a specific temperature, and that magnitude of viscosity of the standard fluid jst is reliable. Glass capillary viscometers are not suitable for liquids that deviate substantially from Newtonian flow or contain large size particles or a high concentration of suspended solids. In this case, the viscosity is directly proportional to the time of flow t. 

Equation 3B.16 is the basis for calculation of viscosity of a Newtonian fluid using glass capillary viscometer. Itshouldalso be recognized that(4g/jrro) = ilQ/nEf) gives the shear rate for Newtonian fluids but not for non-Newtonian fluids and it is called pseudo shear rate. Additional steps are required to obtain an expression for the true shear rate. 

Capillary viscometers have been widely used in determining the viscosity of Newtonian fluids. In these viscometers, the driving force is usually the hydrostatic head of the test liquid itself, although, application of external pressure is also used in order to increase the range of measurement and allow non-Newtonian behavior to be studied. In operation, the efflux time of a fixed volume of test liquid is measured, from which the kinematic viscosity is calculated. 

Polymer viscosity is strongly shear dependent. If we use the bulk viscosity measured at different shear rates to describe the flow behavior in porous media, our first task is to calculate the shear rate which is equivalent to that in the bulk viscometer. To do that, we start with the capillary flow of a non-Newtonian fluid. 

Polymers that have been suggested for mobility control in oil reservoirs include polyacrylamides, hydroxy ethyl cellulose, and modified polysaccharides which are produced either by fermentation or by more conventional chemical processes. In this paper the solution properties of these polymers are presented and compared for tertiary oil recovery applications. Among the properties discussed are non-Newtonian character for different environmental conditions (electrolytes and temperature), filterability, and long term stability. The behavior of these water soluble polymers in solution can be correlated with the effective molecular size which can be measured by the intrinsic viscosity technique. A low-shear capillary viscometer with a high precision and a capability of covering low shear rates (such as 10 sec - - for a 10 cp fluid) has been designed to measure the viscosities. The measurement of viscosities at such slow flow conditions is necessitated... 

In a capillary viscometer, a piston of known weight presses the melt through a capillary with a specific diameter and length. The flow of a Newtonian fluid in a capillary obeys the Hagen-Poiseuille equation. 

In practical applications, flow of the material through an orifice is perhaps the most frequently encountered rheological phenomenon. It is then natural to be used for the viscosity measurement of suspensions (53-55). However, the flow through an orifice is not precise in terms of shear measurement because the shear rate is not well defined under such circumstances. To meet this objection, the orifice is in most cases extended to a tube. This leads to the capillary flow type of viscometers, the simplest, and for Newtonian fluids, the most accurate type, comprising the familiar Ostwald und Ubbelohde viscometers. The fully developed axial velocity in the laminar regime is given by... 

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. 

The most o.sed capillary viscometers are gravity-driven and coircspond to the Canon-Fenske, Ostwald. and Ubbelolide types Fig. 19 shows a scheme of an Ostwald capillary. In order to obtain viscosity, it is only necessary to measure the time / required for a given volume V of fluid to pa.ss between the two marks. L and f, . Thus, the Newtonian viscosity is... 

Viscosity of Newtonian liquids ean be measured by calibrated glass capillary viscometer. Kinematic (the resistance to flow of a fluid under gravity) and dynamic (the ratio between the applied shear stress and the rate of shear of a liqitid) viscosities can be calculated from measured time of flow using the following equations ... 

Flow properties of a fluid. In determining the flow properties of a time-independent non-Newtonian fluid, a capillary-tube viscometer is often used. The pressure drop AP N/m for a given flow rate q m s is measured in a straight tube of length L m and diameter D m. This is repeated for different flow rates or average velocities V m/s. If the fluid is time-independent, these flow data can be used to predict the flow in any other pipe size. 

Numerous methods for measuring fluid viscosity exist, for example, capillary tube flow methods (Ostwald viscometer), Zahn cup method, falling sphere methods, vibrational methods, and rotational methods. Rotational viscometers measure the torque required to turn an object immersed or in contact with a fluid this torque is related to the fluid s viscosity. A well-known example of this type of system is the Couette viscometer. However, it should be noted that as some CMP slurries may be non-Newtonian fluids, the viscosity may be a function of the rotation rate (shear rate). An example of this is the dilatant behavior (increasing viscosity unda increasing shear) of precipitated slurries that have symmetrical particles [33]. Furthermore, the CMP polisher can be thought of as a large rotational plate viscometer where shear rates can exceed 10 s and possibly affect changes to the apparoit viscosity. The reader can refer to the comprehensive review of viscosity measurement techniques in the book by Viswanath et aL [34]. 

Capillary viscometers, whilst best suited to the measurement of Newtonian fluids, can be used to provide some very useful information which is an accurate representation of the nature of the polymeric species when these are present as true solutions. 

The flow behavior of non-Newtonian fluids is usually described by expressing either shear rate or viscosity as a function of shear stress. Absolute viscometers, either capillary or rotational, are used to perform the necessary measurements. In the capillary viscometer, the flow rate is measured as a function of applied pressure. Apparent viscosities calculated by means of Poiseuille s relation [Eq. (9)], are converted to true viscosities using the Weissen-berg-Rabinowitsch correction... 

Once the length and radius of the capillary have been determined, the basic characteristics of the fluid must be determined. In addition to the use of experiments or correlations to determine the density and thermal properties, a conventional capillary viscometer such as a Cannon-Fenske viscometer is used to determine the viscosity of the fluid as a function of temperature in the Newtonian, low-shear, region. These viscosity measurements not only provide Information concerning the influence of temperature on the Newtonian viscosity of the polymer solution at low-shear rates, but the semi-em p i r ica1 correlation of So and Klaus (24) is utilized to estimate the influence of pressure on the viscosity from these data. 

Based on this approach, the apparent viscosity of the polymer solution, uapp corrected if the apparent viscosity of the corresponding hypothetical Newtonian fluid flowing in the same capillary with the same total pressure drop is known. There are two procedures to determine the apparent viscosity of such a Newtonian fluid. The direct experimental procedure is to measure the apparent viscosity of the appropriate Newtonian fluid in the high-shear capillary viscometer. This experimental calibration technique was employed by Graham and co-workers (20). Although this experimental technique is direct, in practice it is difficult to perform. It is difficult to find a Newtonian fluid with the identical rheological properties as exhibited by the polymer solution at low-shear rates. 

The use of capillary-like viscometers is complicated by the effective sUp of non-Newtonian fluid-suspended material, which tends to move away from the wall, leaving an attached layer of liquid. The result is a reduction in the measurements of effective viscosity. Therefore, it is often recommended to conduct such tests in a number of tubes of different diameters. 

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