Pressure-Driven Flow Viscometers

PRESSURE-DRIVEN FLOW VISCOMETERS Capillary/Tube Viscometer 

Entrance region Fully developed flow region Exit effect region 

An outline of the steps involved to derive the equations for shear rate and shear stress for fully developed flow in a tube is given in Appendix 3-B. The shear stress (ctw) is given by Equation (3.34) and the shear rate by Equation 3.35, where the subscript w is used to emphasize that the values obtained are those at the pipe wall. 

If one can determine accurately the minimum pressure required, Apmin, to cause flow in a horizontal tube, then the yield stress of the material can be estimated from  

In a highly elastic material with a high first normal stress difference, cth — 022, the material expands to a larger diameter, known as die swell or jet expansion. The diameter of the expanded jet, Dy, may be estimated from an equation developed by 

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The capillary viscometer. The most common and simplest device for measuring viscosity is the capillary viscometer. Its main component is a straight tube or capillary, and it was first used to measure the viscosity of water by Hagen [28] and Poiseuille [60], A capillary rheometer has a pressure driven flow for which the velocity gradient or strain rate and also the shear rate will be maximum at the wall and zero at the center of the flow, making it a non-homogeneous flow. 

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). 

Since pressure driven viscometers employ non-homogeneous flows, they can only measure steady shear functions such as viscosity, 77(7). However, they are widely used because they are relatively inexpensive to build and simple to operate. Despite their simplicity, long capillary viscometers give the most accurate viscosity data available. Another major advantage is that the capillary rheometer has no free surfaces in the test region, unlike other types of rheometers such as the cone and plate rheometers, which we will discuss in the next section. When the strain rate dependent viscosity of polymer melts is measured, capillary rheometers may provide the only satisfactory method of obtaining such data at shear rates... 

Pressure-driven devices include capillary viscometers and slit-die viscometers, in both of which the flow is driven by pressure. In the case of the capillary viscometer the pressure is generated by an upstream piston, and in the case of the slit-die viscometer flow is generated by an extruder. In both cases, measurements of pressure drop and flow rate are used to determine the viscosity. Both techniques have the inherent problem of pressure drop, which may result in phase separation. For this reason, the techniques are suitable for low-pressure measurements, which may mean that the polymer has not reached equilibrated CO2 concentrations. 

The measured viscosities and first normal stress differences for Tsang and Dealy s two polyethylenes are shown in Figure 9.7. The data at shear rates up to 1 s were obtained in a torsional flow between a cone and plate, while the data at higher shear rates were obtained from the pressure drop in a capillary. The high- and low-shear rate data appear to be consistent, but it is difficult to obtain overlap with a commercial piston-driven capillary viscometer because of the importance of frictional losses at very low rates. These data are typical of many commercial polymers. 

An automated gas-driven cap-ilkny viscometer. A pressure transducer (not shown) records the head. Valve A opens the head to sample t B. Jacket C controls temperature. is a ball valve, which opens flow to capillary E. Balance F (not shown) records the flow rate. From Grankvist and Sandas (1990 Giadek Ab, Kauni-ainen, Finland). 

A capillary viscometer is a device in which the fluid under investigation is forced from a reservoir through a cylindrical capillary tube. They are operated with either flow rate or pressure as the independent variable. In the former case, the fluid is usually driven by a piston advancing through a cylindrical reservoir at a known constant rate with the force on the piston recorded in the latter case, regulated gas pressure drives the fluid and the volumetric flow rate is measured. 

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