Dispersion Newtonian flow

Dispersion of a soHd or Hquid in a Hquid affects the viscosity. In many cases Newtonian flow behavior is transformed into non-Newtonian flow behavior. Shear thinning results from the abiHty of the soHd particles or Hquid droplets to come together to form network stmctures when at rest or under low shear. With increasing shear the interlinked stmcture gradually breaks down, and the resistance to flow decreases. The viscosity of a dispersed system depends on hydrodynamic interactions between particles or droplets and the Hquid, particle—particle interactions (bumping), and interparticle attractions that promote the formation of aggregates, floes, and networks. 

Dispersion in the sensor volume resulting from Newtonian flow... 

The dispersion that takes place in an open tube, as discussed in chapter 8, results from the parabolic velocity profile that occurs under conditions of Newtonian flow (i.e., when the velocity is significantly below that which produces turbulence). Under condition of Newtonian flow, the distribution of fluid velocity across the tube... 

Dispersion in Detector Sensors Resulting from Newtonian Flow... 

Katz and Scott used equation (7) to calculate diffusivity data from measurements made on a specially arranged open tube. The equation that explicitly relates dispersion in an open tube to diffusivity (the Golay function) is only valid under condition of perfect Newtonian flow. That is, there must be no radial flow induced in the tube to enhance diffusion and, thus, the tube must be perfectly straight. This necessity, from a practical point of view, limits the length of tube that can be employed. 

This equation too is solved with the same boundary conditions as Eq. (148). A series of equations results when different combinations of fluids are used. There is no change for the first stage. All the terms of equation of motion remain the same except the force terms arising out of dispersed-phase and continuous-phase viscosities. The main information required for formulating the equations is the drag during the non-Newtonian flow around a sphere, which is available for a number of non-Newtonian models (A3, C6, FI, SI 3, SI 4, T2, W2). Drop formation in fluids of most of the non-Newtonian models still remains to be studied, so that whether the types of equations mentioned above can be applied to all the situations cannot now be determined. 

Mixing processes involved in the manufacture of disperse systems, whether suspensions or emulsions, are far more problematic than those employed in the blending of low-viscosity miscible liquids due to the multi-phasic character of the systems and deviations from Newtonian flow behavior. It is not uncommon for both laminar and turbulent flow to occur simultaneously in different regions of the system. In some regions, the flow regime may be in transition, i.e., neither laminar nor turbulent but somewhere in between. The implications of these flow regime variations for scale-up are considerable. Nonetheless, it should be noted that the mixing process is only completed when Brownian motion occurs sufficiently to achieve uniformity on a molecular scale. 

The electroviscous effects and the other effects discussed in Sections 4.7a-c lead to what is called non-Newtonian behavior in the flow of dispersions. In the next section, we begin with a brief review of the basic concepts concerning deviations from Newtonian flow behavior and then move on to consider how high particle concentrations and electroviscous effects affect the flow and viscosity. 

For convenience, this chapter has been divided into three sections in which the viscosity of dilute solutions and dispersions, non-Newtonian flow, and the viscoelastic properties of semi-solid systems are discussed. 

For most pure liquids and for many solutions and dispersions, t) is a well-defined quantity for a given temperature and pressure which is independent of other solutions and dispersions, especially if concentrated and if the particles are asymmetric and/or aggregated deviations from Newtonian flow are observed. The main causes of non-Newtonian flow are the formation of a structure throughout the system and orientation of asymmetric particles caused by the velocity gradient. 

The final chapter on applications of optical rheometric methods brings together examples of their use to solve a wide variety of physical problems. A partial list includes the use of birefringence to measure spatially resolved stress fields in non-Newtonian flows, the isolation of component dynamics in polymer/polymer blends using spectroscopic methods, the measurement of the structure factor in systems subject to field-induced phase separation, the measurement of structure in dense colloidal dispersions, and the dynamics of liquid crystals under flow. 

At 1-atm pressure in the surroundings, polysaccharide deformation and flow are normally initiated either by gravity or an applied shear rate (y) solvent (water) only flows under temperature (T) and concentration (c,) gradients. When T)i is constant or independent of the rate of shear (y in s 1) or stress (t), the flow is Newtonian. Very dilute polysaccharide dispersions are characterized mostly by Newtonian flow. At moderate concentrations, ti, may decrease (shear-thinning synonymous with pseudoplastic) or increase (shear-thickening synonymous with dilatant) nonlinearly with y for these dispersions, is replaced with (the apparent viscosity). Low DP and uniform distribution of substituents are conducive to tH high DP and nonuniform distribution are conducive to. A high T a is believed to elicit the human oral sensation of thickness. ... 

The dimensionless product c[k]] is defined as the coil overlap parameter it provides information about the changing nature of the interactions in a dispersion (Blanshard and Mitchell, 1979 Morris et al., 1981). For dilute dispersions, i.e., below c, the slope of log( qsp/cI) vs log(c[T ]) universally approximates 1.4. At the upper practical extreme, with exceptions (especially the galactomannans Morris et al., 1981), the slope increases sharply to 3.3, illustrating wide deviations from Newtonian flow in the segment approaching elasticity. The deviations are significant when 5 < < 10 (Barnes... 

Colloidal systems, because of their large number of dispersed particles, show non-Newtonian flow behavior. For a highly dilute dispersion of spherical particles, the following equation has been proposed by Einstein ... 

In this equation, viscosity is independent of the degree of dispersion. As soon as the ratio of disperse and continuous phases increases to the point where particles start to interact, the flow behavior becomes more complex. The effect of increasing the concentration of the disperse phase on the flow behavior of a disperse system is shown in Figure 8-41. The disperse phase, as well as the low solids dispersion (curves 1 and 2), shows Newtonian flow behavior. As the solids content increases, the flow behavior becomes non-Newtonian (curves 3 and 4). Especially with anisotropic particles, interaction between them will result in the formation of three-dimensional network structures. These network structures usually show non-Newtonian flow behavior and viscoelastic properties and often have a yield value. Network structure formation may occur in emulsions (Figure 8-42) as well as in particulate systems. The forces between particles that result in the formation of networks may be... 

The dispersion that takes place in an open tube results from the parabolic velocity profile that occurs under conditions of Newtonian flow, i.e. when the velocity is significantly below that which produces turbulence. Under condition of Newtonian flow, the distribution of fluid velocity across the tube adopts a parabolic profile, the velocity at the walls being virtually zero and that at the center a maximum. This situation is depicted diagramatically in Figure 6A. Due to the relatively high velocity at the center of the tube and the very low velocity at the walls, the center of the band of solute passing down the tube will move ahead of that situated at the walls. This dispersive effect is depicted in figure 6B. 

The first attempt to produce low dispersion tubing was by Halasz et al. [14], who crimped and bent the tube into different shapes to interrupt the Newtonian flow and introduce radial flow within the tube. His devices had limited success and the tubes had a tendency to block very easily. 

The viscosity of microemulsions has been studied several times in order to determine hydration and interactions between the dispersed droplets. It was found that an increase in hydration of the surfactant molecules resulted in rheological behavior more similar to that of suspensions containing solid particles in low concentrations. In any case, the microemulsions showed Newtonian flow characteristics. 

The viscosity of the mixed oils is higher than that of the bagasse and the PR individually. This is due to the formation of con Iex three component emulsions (biooil, PR-derived hydrocarbons and water) with dispersed solid particles. As expected, the mixed oils exhibit non-Newtonian flow behaviour (herein not shown). The con lex emulsion obtained seems to be more stable than the one obtained by mixing die oils produced separately from bagasse and PR. The oils from bagasse, PR and the mixed oils were also observed by microscopy. The existence of three liquid emulsions was confirmed by microscopic analysis (Figure 4). 

Aqueous pectin dispersions show flow behavior similar to many other polysaccharide solutions. Flow curves of specific viscosity rpp vs. shear rate have a Newtonian plateau (constant r sp) at low shear rates, followed by a shear thinning region at moderate shear rates (Morris et al., 1981). Most pectin solutions have relatively low viscosity compared to some other commercial polysaccharides, such as guar gum, mainly because of the lower MW. Consequently, pectin has limited use as a thickener. 

Our main concern here is to present the mass transfer enhancement in several rate-controlled separation processes and how they are affected by the flow instabilities. These processes include membrane processes of reverse osmosis, ultra/microfiltration, gas permeation, and chromatography. In the following section, the different types of flow instabilities are classified and discussed. The axial dispersion in curved tubes is also discussed to understand the dispersion in the biological systems and radial mass transport in the chromatographic columns. Several experimental and theoretical studies have been reported on dispersion of solute in curved and coiled tubes under various laminar Newtonian and non-Newtonian flow conditions. The prior literature on dispersion in the laminar flow of Newtonian and non-Newtonian fluids through... 

The movement of a liquid, when in contact with a charged surface, situated in a strong electric field is called electro-endosmosis. The flow of liquid through a silica tube under electro-endosmosis is of plug form, and does not exhibit the parabolic velocity profile that normally occurs in Newtonian flow. As a result of this, there is little, or no, resistance to mass transfer similar to that in open tubular columns. It follows, that there is very little band dispersion when the flow is electrosmotically driven and consequently extremely high efficiencies can be attained. 

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