Extensional viscosity

The extensional viscosity of semi-solid fat-based products such as butter, ice cream and some cheeses can be measured by lubricated squeezing flow rheometry (Campanella and Peleg, 2002 Gunasekaran and Ak, 2002). 

In the most suitable test configuration for foods, the sample initially completely fills the gap between two coaxial horizontal discs, one attached to the base and the other to the crosshead, of a UTM-type solids rheometer. Lubrication between the sample and disc surfaces is achieved by Teflon coating the surfaces and/or deliberately lubricating the surfaces with a suitable liquid of very low viscosity. 

The sample is subjected to compression by moving the crosshead downwards at a constant speed. The sample is extruded from between the two discs, undergoing elongational or biaxial flow the sample is stretched radially and azimuthally as it flows outwards between the approaching discs. Lubrication ensures that shear flow cannot occur. Elongational viscosity is calculated directly from the measured force-distance data, disc radius and crosshead speed no rheological model is required (Campanella and Peleg, 2002). 

Lubricated squeezing flow rheometry (and unlubricated squeezing flow rheometry, in which friction between the sample and discs results in radial shear flow) can be used also to measure Newtonian viscosity and the flow properties of non-Newtonian liquids (Campanella and Peleg, 2002). 

The theory of sqeezing flow rheometry assumes that the sample is nonelastic. Tests on viscoelastic samples should therefore be carried out at low strain rates, to minimize elastic response, and results should be reported as apparent elongational viscosity. 

The rotational instruments already discussed do not simulate this sort of condition. Nonetheless, a number of end-use environments exist where extensional flow is the predominant effect. Examples of this are listed below  

A value for the rate of extension can be considered as the equivalent to shear rate in flow environments. Actually devising methods which create conditions which can be firstly. 

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Extensional viscosity Extension cord External lubricant External plasticizers Exterol Exter press Exton... 

Film. By far the largest appHcation for LLDPE resins (over 60% in the United States) is film. Because LLDPE film has high tensile strength and puncture resistance, it is able to compete with HDPE film for many uses. The toughness and low temperature properties of LLDPE film also exceed those of conventional LDPE. Furthermore, because LLDPE resins exhibit relatively low strain hardening in the molten state and lower extensional viscosity, it can be produced at high rates with Httle risk of bubble breaks. 

Extensional Viscosity. In addition to the shear viscosity Tj, two other rheological constants can be defined for fluids the bulk viscosity, iC, and the extensional or elongational viscosity, Tj (34,49,100—107). The bulk viscosity relates the hydrostatic pressure to the rate of deformation of volume, whereas the extensional viscosity relates the tensile stress to the rate of extensional deformation of the fluid. Extensional viscosity is important in a number of industrial processes and problems (34,100,108—110). Shear properties alone are insufficient for the characterization of many fluids, particularly polymer melts (101,107,111,112). 

Extensional flows occur when fluid deformation is the result of a stretching motion. Extensional viscosity is related to the stress required for the stretching. This stress is necessary to increase the normalized distance between two material entities in the same plane when the separation is s and the relative velocity is ds/dt. The deformation rate is the extensional strain rate, which is given by equation 13 (108) ... 

Unlike shear viscosity, extensional viscosity has no meaning unless the type of deformation is specified. The three types of extensional viscosity identified and measured are uniaxial or simple, biaxial, and pure shear. Uniaxial viscosity is the only one used to characterize fluids. It has been employed mainly in the study of polymer melts, but also for other fluids. For a Newtonian fluid, the uniaxial extensional viscosity is three times the shear viscosity ... 

Fig. 14. Shear viscosity, Tj, and extensional viscosity, Tj as a function of deformation rate of a low density polyethylene (LDPE) at 150°C (111). To convert...

Extensional Viscosity. AH three types of extensional viscosity can be measured (101,103) uniaxial, biaxial, and pure shear. Only a few commercial instmments are available, however, and most measurements are made with improvised equipment. Extensional viscosity of polymer melts can be estimated from converging flow (entrance pressure) or from a melt strength drawdown test (208). 

Another type of experiment involves a fluid filament being drawn upward against gravity from a reservoir of the fluid (101,213,214), a phenomenon often called the tubeless siphon. The maximum height of the siphon is a measure of the spinnabiUty and extensional viscosity of the fluid. Mote quantitative measures of stress, strain, and strain rate can be determined from the pressure difference and filament diameter. A more recent filament stretching device ia which the specimen is held between two disks that move apart allows measurements ia low viscosity Hquids (215). AH of these methods are limited to spinnable fluids under small total strains and strain rates. High strain rates tend to break the column or filament. 

A method for measuring the uniaxial extensional viscosity of polymer soHds and melts uses a tensile tester in a Hquid oil bath to remove effects of gravity and provide temperature control cylindrical rods are used as specimens (218,219). The rod extmder may be part of the apparatus and may be combined with a device for clamping the extmded material (220). However, most of the mote recent versions use prepared rods, which are placed in the apparatus and heated to soften or melt the polymer (103,111,221—223). A constant stress or a constant strain rate is appHed, and the resultant extensional strain rate or stress, respectively, is measured. Similar techniques are used to study biaxial extension (101). 

Extensional viscosity that results purely from shear deformation seems to be of less interest, but has been measured (108). The theology of several different polymer melts in terms of shear viscosity and uniaxial and biaxial extensional viscosity has been compared (231). Additional information on the measurement of extensional viscosity are also available (105,238—240). 

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. 

Fig. 22. Schematic diagram of the opposite jets device with some of the associated streamlines (the x marks the location of the stagnation point). It has been determined that a ratio of d/(2 r0) w 1 — 1.4 constitutes the optimum geometry for extensional viscosity measurements [104]...

Extensional flow describes the situation where the large molecules in the fluid are being stretched without rotation or shearing [5]. Figure 4.3.3(b) illustrates a hypothetical situation where a polymer material is being stretched uniaxially with a velocity of v at both ends. Given the extensional strain rate e (= 2v/L0) for this configuration, the instantaneous extensional viscosity r e is related to the extensional stress difference (oxx-OyY), as... 

The ratio of extensional viscosity r e to shear viscosity r s is known as the Trouton ratio, which is three for Newtonian fluids in uniaxial extension and larger than three for non-Newtonian fluids. For a viscoelastic fluid such as a polymer in solution, the uniaxial extensional viscosity characterizes the resistance of the fluid... 

Fano columns are most easily formed in viscoelastic solutions where extensional viscosities exceed shear viscosities by several orders of magnitude. 

Compared to partially hydrolyzed polyacrylamide, xanthan gum is more expensive, more susceptible to bacterial degradation, and less stable at elevated temperatures (1). However, xanthan gum is more soluble in saline waters, particularly those containing divalent metal ions generally adsorbs less on rock surfaces and is substantially more resistant to shear degradation (1,34). The extensional viscosity of the semi-rigid xanthan molecule is less that that of the flexible polyacrylamide (263). 

Electrostatic repulsion of the anionic carboxylate groups elongates the polymer chain of partially hydrolyzed polyacrylamides increasing the hydrodynamic volume and solution viscosity. The extensional viscosity is responsible for increased resistance to flow at rapid flow rates in high permeability zones (313). The screen factor is primarily a measure of the extensional (elonga-tional) viscosity (314). The solution properties of polyacrylamides have been studied as a function of NaCl concentra-tion and the parameters of the Mark-Houwink-Sakaruda equation calculated... 

Oscillatory shear experiments are the preferred method to study the rheological behavior due to particle interactions because they directly probe these interactions without the influence of the external flow field as encountered in steady shear experiments. However, phenomena that arise due to the external flow, such as shear thickening, can only be investigated in steady shear experiments. Additionally, the analysis is complicated by the different response of the material to shear and extensional flow. For example, very strong deviations from Trouton s ratio (extensional viscosity is three times the shear viscosity) were found for suspensions [113]. 

However, this expression assumes that the total resistance to flow is due to the shear deformation of the fluid, as in a uniform pipe. In reality the resistance is a result of both shear and stretching (extensional) deformation as the fluid moves through the nonuniform converging-diverging flow cross section within the pores. The stretching resistance is the product of the extension (stretch) rate and the extensional viscosity. The extension rate in porous media is of the same order as the shear rate, and the extensional viscosity for a Newtonian fluid is three times the shear viscosity. Thus, in practice a value of 150-180 instead of 72 is in closer agreement with observations at low Reynolds numbers, i.e.,... 

Underwriters Laboratory UL 94 Standard for Safety, 11 457-458 Undifferentiated chemicals, 20 712 Undiscovered petroleum resources, 18 595 Unfilled tooth restorative resins, 8 333 Uniaxial extensional viscosity, measuring, 21 740... 

The first term on the left is the viscosity in extension, an extensional viscosity rje ... 

Figure 6.25 Plot of the normalised extensional viscosity of an 8% PVP solution with 320 mM sodium dodecyl sulphate. The data is plotted versus the reduced extension rate...

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