Dispersion from Newtonian flow

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

Dispersion in Detector Sensors Resulting from Newtonian Flow... 

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 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 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... 

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. 

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... 

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. 

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 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). 

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