Viscosity variable

Variable viscosity in laminar tube flows is an example of the coupling of mass, energy, and momentum transport in a reactor design problem of practical significance. Elaborate computer codes are being devised that recognize this... 

Consider axisymmetric flow in a circular tube so that Vg = 0. Two additional assumptions are needed to treat the variable-viscosity problem in its simplest form ... 

Practical applications to laminar flow reactors are still mainly in the research literature. The first good treatment of a variable-viscosity reactor is... 

Such an approach is conceptually different from the continuum description of momentum transport in a fluid in terms of the NS equations. It can be demonstrated, however, that, with a proper choice of the lattice (viz. its symmetry properties), with the collision rules, and with the proper redistribution of particle mass over the (discrete) velocity directions, the NS equations are obeyed at least in the incompressible limit. It is all about translating the above characteristic LB features into the physical concepts momentum, density, and viscosity. The collision rules can be translated into the common variable viscosity, since colliding particles lead to viscous behavior indeed. The reader interested in more details is referred to Succi (2001). 

Foam viscosities measured after one min were essentially the same at flour concentrations of 2 to 10%, increased at the 12% flour level, declined slightly at the 14 and 16% levels, then increased as the flour concentration was increased to 23 and 30% (Figure 5). Changes in foam viscosities after 60 min were more variable viscosities were highest at the 30% flour level, intermediate at the 6 to 8% levels, and lowest at the 16% flour 1 evel. 

Bird et al. (Bll), 1960 Brief theoretical treatments of various cases of film flow (on cone, with variable viscosity, non-Newtonian liquids, etc.) and of heat and mass transfer to films. 

APPENDIX 13.2 VARIABLE-VISCOSITY MODEL FOR A POLYCONDENSATION IN A TUBULAR REACTOR... 

Yang, K.T., Laminar Forced Convection of Liquids in Tubes with Variable Viscosity , J. Heat Transfer, Vol. 84, pp. 353-362, 1962. 

Many substances, such as gums, have a variable viscosity, and most of them are less resistant to flow at higher flow (more correctly, shear) rates. In such cases, select a given set of conditions for measurement, and consider the measurement obtained to be an apparent viscosity. Since a change in the conditions of measurement would yield a different value for the apparent viscosity of such substances, the operator must closely adhere to the instrument dimensions and conditions for measurement. 

The behaviour of a foam at deformation can be described also by the Newton s law but then the rheological properties would be characterised by a variable viscosity [20]... 

The stomach empties liquids faster than solids. The rate of transfer of gastric contents to the small intestine is retarded by the activity of receptors sensitive to acid, fat, osmotic pressure and amino acids in the duodenum and the small intestine and stimulated by material that has arrived from the stomach. Gastric emptying is a simple exponential or square-root function of the volume of a test meal - a pattern that holds for meals of variable viscosity. To explain the effect of a large range of substances on emptying, an osmoreceptor has been postulated which, like a red blood cell, shrinks in hypertonic solutions and swells in hypotonic solutions. 

The internal standard method can compensate for several types of errors that can be caused by sample matrix. Systematic errors due to matrix effects can sometimes be avoided. The internal standard method can also correct for fluctuations in experimental conditions amount of sample analysed, sample introduction, emission source temperature assuming that the signal analyte and internal standard are influenced to the same extent. The main advantage of the internal method over usual calibration methods is that it can provide excellent accuracy and precision and at the same time correct for variable viscosity affects. The method is limited by the availability of a suitable reference element that behaves almost as close to the analyte under test in terms of ionisation energy, solubility, low memory effects, etc. 

Calculation of the Inlet Pressure in the Case of a Variable Viscosity.266... 

Variable viscosity, depending upon shear rate (non-Newtonian fluid) Calculating averages ... 

It is difficult to study the rheological properties of a foam since, on deformation, its properties are changed. The most convenient geometry to measure foam rheology is to use a parallel plate. The rheological properties could be characterised by a variable viscosity [4],... 

The effect of osmotic pressure in macromolecular ultraflltra-tlon has not been analyzed in detail although many similarities between this process and reverse osmosis may be drawn. An excellent review of reverse osmosis research has been given by Gill et al. (1971). It is generally found, however, that the simple linear osmotic pressure-concentration relationship used in reverse osmosis studies cannot be applied to ultrafiltration where the concentration dependency of macromolecular solutions is more complex. It is also reasonable to assume that variable viscosity effects may be more pronounced In macromolecular ultra-filtration as opposed to reverse osmosis. Similarly, because of the relatively low diffuslvlty of macromolecules conqiared to typical reverse osmosis solutes (by a factor of 100), concentration polarization effects are more severe in ultrafiltration. 

The resulting average velocities for constant (Eq. [38]) and variable viscosity (Eq. [40]) become indistinguishable for liquid films thicker than about 10 nm. We therefore use the simpler expression in Eq. [38] for films thicker than 10 nm, and the more complex Eq. [40] for flow in very thin films. 

The earliest studies related to thermophysieal property variation in tube flow conducted by Deissler [51] and Oskay and Kakac [52], who studied the variation of viscosity with temperature in a tube in macroscale flow. The concept seems to be well-understood for the macroscale heat transfer problem, but how it affects microscale heat transfer is an ongoing research area. Experimental and numerical studies point out to the non-negligible effects of the variation of especially viscosity with temperature. For example, Nusselt numbers may differ up to 30% as a result of thermophysieal property variation in microchannels [53]. Variable property effects have been analyzed with the traditional no-slip/no-temperature jump boundary conditions in microchannels for three-dimensional thermally-developing flow [22] and two-dimensional simultaneously developing flow [23, 26], where the effect of viscous dissipation was neglected. Another study includes the viscous dissipation effect and suggests a correlation for the Nusselt number and the variation of properties [24]. In contrast to the abovementioned studies, the slip velocity boundary condition was considered only recently, where variable viscosity and viscous dissipation effects on pressure drop and the friction factor were analyzed in microchannels [25]. 

Elaborate computer codes that recognize this coupling in complex flow geometries have been devised and verified. The present examples are representative of a general class of single-phase, variable-viscosity, variable-density problems yet avoid undue complications in mathematical or numerical analysis. 

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