Flow measurements isotropic

Conceptually similar results were demonstrated by Krutzer et al. [14], who measured the orthokinetic coagulation rate under laminar Couette flow and isotropic turbulent flow (as well as other flow conditions). Despite equal particle collision rates, significance differences were observed in the overall rates indicating different collision efficiencies (higher collision efficiencies were found under a turbulent flow regime). Thus, identical chemical properties of a dispersion do not determine a single collision efficiency the collision efficiency is indeed dependent upon the physical transport occurring in the system. 

The movement of the plate is coupled with a three-dimensional balancing flow. For isotropic liquids the influence of this flow can be taken into account by calibration with an isotropic liquid of known viscosity. For liquid crystals the influence is more complicated due to the fixed director orientation. The orientations of the velocity and the velocity gradient with respect to the director are different around the plate, and the effective viscosity also varies. Therefore, all viscosity coefficients contribute to the measured apparent viscosity. With a proper geometry the contribution of the unwanted viscosity coefficients can be minimized and the viscosity that is effective at the plate surface can be determined. 

In these model equations it is assumed that turbulence is isotropic, i.e. it has no favoured direction. The k-e model frequently offers a good compromise between computational economy and accuracy of the solution. It has been used successfully to model stirred tanks under turbulent conditions (Ranade, 1997). Manninen and Syrjanen (1998) modelled turbulent flow in stirred tanks and tested and compared different turbulence models. They found that the standard k-e model predicted the experimentally measured flow pattern best. 

Anisotropic material In an anisotropic material the properties vary, depending on the direction in which they are measured. There are various degrees of anisotropy, using different terms such as orthotropic or unidirectional, bidirectional, heterogeneous, and so on (Fig. 3-19). For example, cast plastics or metals tend to be reasonably isotropic. However, plastics that are extruded, injection molded, and rolled plastics and metals tend to develop an orientation in the processing flow direction (machined direction). Thus, they have different properties in the machine and transverse directions, particularly in the case of extruded or rolled materials (plastics, steels, etc.). 

The rotational diffusion coefficient Dr of a rodlike polymer in isotropic solutions can be measured by electric, flow, and magnetic birefringence, dynamic light scattering, and dielectric dispersion. However, if the polymer has some flexibility, its internal motion makes it difficult to extract Dr for the end-over-end rotation of the chain from data of these measurements. In other words, Dr can be measured only for nearly rodlike polymers. 

The work of Laufer (L3) indicates that eddy viscosity is not isotropic in shear flow. For this reason it is unlikely that eddy conductivity is isotropic in such flows. Therefore, uncertainties in the application of eddy conductivities must arise when it is assumed that this transport coefficient is isotropic. Until additional experimental information is available, it appears reasonable to consider eddy conductivity as isotropic except in circumstances when the vectorial nature (J4, R2) of the eddy viscosity may be estimated. Such an approximation appears acceptable since the measurements available described the conductivity normal to the axis of flow, which is the direction in which most detail is required in the prediction of temperature distribution in turbulently flowing streams. Throughout the remainder of this discussion all eddy properties will be treated as isotropic. Such a simplification is open to uncertainty, and further experimentation will be required in order to determine the error introduced by neglect of the vectorial characteristics of these macroscopic transport quantities. 

As discussed in section 7.1.6.4, semidilute solutions of rodlike polymers can be expected to follow the stress-optical rule as long as the concentration is sufficiently below the onset of the isotropic to nematic transition. Certainly, once such a system becomes nematic and anisotropic, the stress-optical rule cannot be expected to apply. This problem was studied in detail using an instrument capable of combined stress and birefringence measurements by Mead and Larson [109] on solutions of poly(y benzyl L-glutamate) in m-cresol. A pretransitional increase in the stress-optical coefficient was observed as the concentration approached the transition to a nematic state, in agreement of calculations based on the Doi model of polymer liquid crystals [63]. In addition to a dependence on concentration, the stress-optical coefficient was also seen to be dependent on shear rate, and on time for transient shear flows. 

In flow through a tube, therefore, the measured effective viscosity, which is defined to be proportional to the pressure drop, depends on the Ericksen number. Note that the Ericksen number is proportional to Vh, the velocity times the tube diameter, where we take h = 2R. Since the velocity V is proportional to QfR, Vh is proportional to Q/R. Thus, the data for various tube radii in Fig. 10-11a collapse onto a single line when plotted against AQfjtR (see Fig. 10-1 lb). This shows that the effective viscosity is a function of the Ericksen number, which is proportional to the velocity times the tube diameter. (For shear-thinning isotropic liquids, on the other hand, the viscosity depends on y ff, which is the velocity divided by the tube diameter.) Because of the orientation-dependence of the viscosity (illustrated in Fig. 10-9a), the wall layer is much more viscous than the core fluid and since the thickness 5 of the wall layer scales as it follows... 

The flow properties of cholesterics have scarcely been studied at all. Figure 10-26 shows one of the few sets of measurements of the viscosity of a cholesteric-forming small-molecule material, cholesteryl myristate, as a function of shear rate in flow through a eapillaiy at various temperatures (Sakamoto et al. 1969). As the temperature is lowered, cholesteryl myristate passes through isotropic, chiral nematir smectic, and nrystalline phases Figure... 

In addition, measurements of orientation after cessation of shearing show that flow-induced orientation decreases after cessation of shearing toward an isotropic state of orientation, and the dynamic moduli increase with time (Hongladarom et al. 1994). This behavior is seen in PBLG solutions only under conditions where a pronounced Region I is seen for lower concentrations where only Region II is present, the orientation increases after cessation of shearing (Walker et al. 1995). 

Detector flow cells are the link between the chromatographic system and the detector system. The cell cuvettes are made of quartz, with either cylindrical or square shapes and volumes between 5 and 20 /tL. The sensitivity is directly proportional to the volume. However, resolution decreases with increasing volume. Fluorescence is normally measured at an angle perpendicular to the incident light. An angle of 90° has the lowest scatter of incident light. However, fluorescence from the flow cell is isotropic and can be collected from the entire 360°. 

For isotropic polymer fluids, stress relaxation upon cessation of flow reflects the relaxation time scales during the previous flow. As the relaxation spectrum is determined by the microstructure such measurements can be used to probe the effect of shear on the structure. This turns out to be a rather insensitive technique in polymer fluids because of changes which already occur during the relaxation (161. 

System assumptions that should be valid for such applications include fluid flow in the porous media is isotropic and adsorption is fast, reversible, and linear (cf. Freeze and Cherry 1979). Given these constraints, the comparative transport of a conserved (nonadsorbed) tracer, such as Br , and an adsorbed or retarded species, such as Am, can be described as shown in Fig. 10.29. A comparison of migration distances of the two species after time t, is made at concentrations where C(measured)/Co(initial) = 0.5 for the conserved and adsorbed species. The migration distance X of the conserved species after time r is a measure of the average groundwater velocity (U), or X = vt. Similarly, the migration distance of the adsorbed species (X,) i related to its velocity of movement (v ) by Xf = vj. The retardation factor (/tj for the adsorbed species is then given by... 

There have been few experimental tests of the theoretical predictions of turbulent coagulation under controlled conditions. Delichaisios and Probstein (1975) measured rates of coagulation of 0.6-mm latex particles suspended in an aqueous solution in turbulent pipe flow. The Reynolds numbers ranged from 17,000 to 51,000 for flow through a 1-in. (l.D.) smooth-walled pipe. For the core of the pipe flow, the turbulence was approximately isotropic. The energy dissipation per unit mass was calculated from the relation... 

Broad-line nuclear magnetic resonance has been used to study melting in stearic acid and a mesomorphic crystalline to waxy) phase transition in lithium stearate. Extensive motion, liquidlike, though less extensive than that in an isotropic free-flowing liquid, takes place within the system below the melting point of stearic acid or the crystalline to waxy phase transition of lithium stearate. The amount of liquid-like character, as measured by the intensity of a narrow component in the NMR spectrum relative to the total intensity of the whole spectrum, depends on the presence of impurities in the system and even more significantly on whether and how many times the sample has been melted. 

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