The Normal Stress Pump

In Section 6.1 we noted that the term V x in the equation of motion is an important source of pressurization. We have further pointed out that this source may be related either to viscosity or to the normal stress difference coefficient. We discuss the latter case in this section. 

In the normal stress extruder we first want to evaluate the pressure at the center as a function of disk outer radius, frequency of rotation, and rheological properties. We do this in the absence of radial flow (i.e., for a closed discharge condition), which will give us the 

The first centripetal pump resulting from non-Newtonian properties of liquids was suggested by Marcus Reiner in the 1950s. 

To determine what stresses are generated in the torsional disk flow of a CEF fluid, we assume that its flow field is that of a pure viscous fluid then we calculate the tensor quantities Vv, y, co, y y, co y, and v Vy that appear in the CEF equation. Obtaining these quantities, we substitute them in the constitutive equation to find out which are the nonzero stress components. 

Assuming that the flow kinematics of CEF and Newtonian fluids are identical, the velocity profile in steady torsional disk flow is 

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Fig. 6.29 Flow rate versus disk gap separation in normal stress pump. The polymer used was polyacrylamide solution at 28°C. Smooth curves indicate calculated values. The die was 0.482 cm long and had a diameter of 0.244 cm. [Data replotted from P. A. Good, A. J. Swartz, and C. W. Macosko, AIChE 20, 67(1974).]...

Wang et al. (2004a) reported that excessive eccentric sucker-rod wear with beam pumps occurred when the produced fluid contained more than 100 mg/L polymer. The service life of rods was approximately only half a year, a 75% reduction compared to the rod life in waterflooding (waterflood producers with beam pumps had a service life of approximately 2 years). Wang et al. (2004c) also reported that based on the statistical data in the year 2000, 880 wells had been eccentrically worn in 2,365 rod-pumped wells, producing fluids containing polymer. Compared to the wells with no polymer before the year 1997, the number of wells with eccentric wear had increased by 840. Thirty-six percent of wells suffered the eccentric wear. The pump service work wells had also increased from 3.2% in 1997 to 27.1% in 2000 because of eccentric wear in rod-pumped wells. The main cause of eccentric wear on sucker rods was the normal stress of polymer solution, as explained next. 

Many years of experience with sliding plate rheometers have revealed several phenomena that limit their utility under certain conditions. First, the normal stress differences create a pressure gradient in the sample that tends to pump melt in from the ends of the sample and out toward the edges. [ 147-149]. This flow can be prevented by the use of fluorocarbon side- rails. More serious limitations are imposed by slip, cavitation and rupture, which interrupt experiments at sufficiently high strains and strain rates. At the same time, however, sliding plate rheometers have been found to be useful tools for the study of melt slip [150]. Elastomers are particularly resistant to shearing deformations and even the use of deep grooves in the plates does not ensure their adherence [146]. 

The melt-spinning process used to convert mesophase pitch into fiber form is similar to that employed for many thermoplastic polymers. Normally, an extruder melts the pitch and pumps it into the spin pack. Typically, the molten pitch is filtered before being extruded through a multi-holed spinnerette. The pitch is subjected to high extensional and shear stresses as it approaches and flows through the spinnerette capillaries. The associated torques tend to orient the liquid crystalline pitch in a regular transverse pattern. Upon emerging from the... 

The dissipation is calculated for barrel rotation in the screw pump device in a similar manner. For this case, the velocities Vozl, and are used for the calculations, and they are provided by Eqs. 7.21,7.23, and 7.27, respectively. The rate of work input for barrel rotation tv, is obtained by multiplying the normal shear stress for the barrel surface by the velocity of the barrel surface integrated over the barrel surface area. The traditional method for calculation of dissipation for barrel rotation is as follows ... 

Major modifications were made to the fluid-supply system to solve the vibration problem. The most important one was to increase the diameter of the main flow line. Consequently, the fluid velocity in the main line was practically zero, and the extension viscosity and normal-stress difference at the inlet of the fluid-supply line were also practically zero. There was sufficient time for the gas bubbles to rise to the top of the main line and be discharged before entering the pump inlet. The vibration was decreased after the modification. With lower vibration, the service life of the pumps was greatly increased. Before the modifications, two or three pumps per injection well were required to maintain continuous injection of polymer solution. Only one pump (no standby pump)... 

The Na -K ATPase Pump. The Na -K" " adenosine triphosphatase (ATPase) transport system is the primary active transport process that maintains the normal chemical gradients for Na" " and K" " in cells of both vertebrates and invertebrates. Although the concern of this article is with neuronal tissue, it should be stressed that the Na -K ATPase pump... 

Hypertension is usually a temporary adjustment to emotional stress or trauma, but after sustained hypertension, the condition perpetuates itself, becoming essential hypertension. The left ventricle of the heart, challenged by the need to pump blood against pressure higher than normal, develops a thickened muscular wall, called cardiac hypertrophy. The extra muscular mass requires additional oxygen, and any decrease in coronary blood flow has more serious consequences in hypertensive patients than in normal individuals. Myocardial infarction (muscle cells die due to lack of oxygen) is therefore more of a threat in hypertensive patients than in normals. Even with the implantation of a replacement heart, the underlying causes of the heart failure have not been eliminated, and the cycle is likely to repeat. 

As the polymer is sheared, normal stresses will generate a centripetal pumping action. Thus, the polymer can be extruded through the central opening in the stationary plate in a continuous fashion. Because normal stresses generate the pumping action, this machine is sometimes referred to as a normal stress extruder. 

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