Rotating viscometers, laminar flow

The main requirement for exact and reproducible results is that the sample undergoes laminar flow during testing. Laminar flow appears as streamlined with a velocity profile of parabolic shape when monitored in a tube viscometer. For a Newtonian sample, shear stress and shear strain rate are at a maximum in close proximity to the walls of the test tube, and zero in the center. Shear thinning samples show truncated flow patterns, and the tendency to plug flow increases with a decrease in the power law index. In rotational viscometers laminar flow is the movement of the sample in concentric circles around the axis of rotation of the instrument. 

This second method does not lend itself to the development of quantitative correlations which are based solely on true physical properties of the fluids and which, therefore, can be measured in the laboratory. The prediction of heat transfer coefficients for a new suspension, for example, might require pilot-plant-scale turbulent-flow viscosity measurements, which could just as easily be extended to include experimental measurement of the desired heat transfer coefficient directly. These remarks may best be summarized by saying that both types of measurements would have been desirable in some of the research work, in order to compare the results. For a significant number of suspensions (four) this has been done by Miller (M13), who found no difference between laboratory viscosities measured with a rotational viscometer and those obtained from turbulent-flow pressure-drop measurements, assuming, for suspensions, the validity of the conventional friction-factor—Reynolds-number plot.11 It is accordingly concluded here that use of either type of measurement is satisfactory use of a viscometer such as that described by Orr (05) is recommended on the basis that fundamental fluid properties are more readily determined under laminar-flow conditions, and a means is provided whereby heat transfer characteristics of a new suspension may be predicted without pilot-plant-scale studies. 

For practical reasons some rotational viscometers are fitted with bobs of complex geometry. For one of these an empirical method has been presented (M10) which enables use of the instrument for the sizing of pipe lines. It would appear likely that this same method could be extended to other geometries provided that the flow of the fluid around the viscometer bob is laminar. 

The unsuitable nature of many commercial instruments which are in common use clearly illustrates the confusion prevalent in the field of viscometric measurements. Many instruments measure some combination of properties which depend only partly on the fluid consistency since the flow is not laminar. In others the shear rates are indeterminate and the data cannot be interpreted completely. Examples of such units include rotational viscometers with inserted baffles, as in the modified Stormer instruments in which the fluid flows through an orifice, as in the Saybolt or Engler viscometers instruments in which a ball, disk, or cylinder falls through the fluid, as in the Gardiner mobilometer. Recently even the use of a vibrating reed has been claimed to be useful for measurement of non-Newtonian viscosities (M14, W10), although theoretical studies (R6, W10) show that true physical properties are obviously not obtainable in these instruments for such fluids. These various instru-... 

The samples were sheared using a rotational viscometer with a coaxial cylinder system, based on the Searle-type, where the inner cylinder (connected to a sensor system) rotates while the outer cylinder remains stationary. The outer cylinder surrounding the inner one was jacketed, allowing good temperature control, and the annular gap was of constant width. The sensor system used was the NV type, with a rotor with a recommended viscosity range of 2x10 mPa, a maximum recommended shear stress of 178 Pa, and a maximum recommended shear strain rate of 2700 s this rotor could work with volumes from 10-50 ml. Flow was laminar. 

Departures from laminar flow, which are attributed to inertia and/or viscoelasticity, result in turbulences, i.e., an uneven flow pattern with locally clear deviations from the flow direction. In the extreme, the flowing sample can start to circulate locally, which is known as Taylor vortices and mainly observed in concentric cylinder instruments, where the inner cylinder rotates,i.e., in cup and bob viscometers. ... 

In most cases viscosity is measured by capillary viscometers or rotating viscometers. In a capillary viscometer one measures the pressure drop by means of constant laminar flow in a capillary the constant flow can be achieved by a pump and the pressure drop is obtained by a differential pressure transmitter whose plus and minus sides are connected to the capillary. The pressure drop is then directly proportional to the viscosity according to the Hagen-Poiseuille law [4, 11] [Eq. (30), where p is the viscosity, r is the capillary radius, I is the capillary length, Ap is the pressure drop, and is the mass flow rate]. The capillary viscometer may also be employed in-line for monitoring of molecular weight in polymerizations, as described in Ref. 14. 

For the impeller ribbon viscometer technique, the power number of an impeller is inversely proportional to the impeller Reynolds number (Eq. 1). As the impeller rotational speed increases, the flow will gradually change from laminar to turbulent, passing through a transition region. Parameter c can be obtained from the calibration fluids. If the same value for c is assumed to apply to a non-Newtonian fluid, then Eq. 4 can be used to calculate the apparent viscosity of that fluid. The range of the impeller method is determined by the minimum and maximum torques that can be measured (5). 

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