Diluting dispersions

To meter the two flows, a flow meter, a variable orifice meter or eddy current or sonic flow meter, for the water is generally used, and a metering pump, generally a progressive cavity pump, is used for the polymer. Unlike for solid polymer make-up. for dispersions the make-up plant is the same basic design for all sizes unless It is to be made up by hand, which is possible for small test runs. 

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For dilute dispersions of hard spheres, Einstein s viscosity equation predicts... 

Viscosity—Concentration Relationship for Dilute Dispersions. The viscosities of dilute dispersions have received considerable theoretical and experimental treatment, partly because of the similarity between polymer solutions and small particle dispersions at low concentration. Nondeformable spherical particles are usually assumed in the cases of molecules and particles. The key viscosity quantity for dispersions is the relative viscosity or viscosity ratio,... 

The relative viscosity of a dilute dispersion of rigid spherical particles is given by = 1 + ft0, where a is equal to [Tj], the limiting viscosity number (intrinsic viscosity) in terms of volume concentration, and ( ) is the volume fraction. Einstein has shown that, provided that the particle concentration is low enough and certain other conditions are met, [77] = 2.5, and the viscosity equation is then = 1 + 2.50. This expression is usually called the Einstein equation. 

Most metals are subject to erosion-corrosion in some specific environment. Soft metals, such as copper and some copper-base alloys, are especially susceptible. Erosion-corrosion is accelerated by, and frequently involves, a dilute dispersion of hard particles or gas bubbles entrained in the fluid. 

Although it is entirely possible for erosion-corrosion to occur in the absence of entrained particulate, it is common to find erosion-corrosion accelerated by a dilute dispersion of fine particulate matter (sand, silt, gas bubbles) entrained in the fluid. The character of the particulate, and even the fluid itself, substantially influences the effect. Eight major characteristics are influential particle shape, particle size, particle density, particle hardness, particle size distribution, angle of impact, impact velocity, and fluid viscosity. 

The problem in the solution of Tick s law when applied to dris problem lies in the difficulty in expressing analytically the A jx ratio for each pair of particles in the dispersion. Greenwood provided a limiting case solution to this problem by dealing only with a dilute dispersion in which each particle supplies or receives atoms from the sunounding average concentration solution. In such a dilute dispersion, each particle can be considered to be suiTounded only by... 

In this set of experiments, we avoided the formation of halloysite aggregates by working with diluted dispersions but microparticle formation through polycation bridging may also be useful for halloysite applications. 

Parker, F. L., Churchill, M. A., Andrew, R. W., Frederick, B. J., Carrigan, P. H. Jr., Cragwall, J. S. Jr., Jones, S. L., Struxness, E. G. and Morton, R. J. (1966). Dilution, dispersion and mass transport of radionuclides in the Clinch-Tennessee Rivers, page 35 in Disposal of Radioactive Wastes into Seas, Oceans and Surface Waters, IAEA Publication No. STI/PUB/126 (International Atomic Energy Agency, Vienna). 

Vincent et al.(3) used a simplified configurational entropy term Ass = -k ln(4>f /4>.). For a dilute dispersion, the In 4>d term is probably correct, but for the floe phase, with of the order of 0.5, a term In 4>f certainly can overestimate the entropy in the floe, because hard spheres with finite volume have at high concentration much less translational freedom than (volumeless) point... 

Critical Flocculation Electrolyte Concentration The critical flocculation electrolyte (Na2S0.) concentration was determined by following the average particle size of the dilute dispersion (where the particles were coated with PVA corresponding to the plateau adsorption) as a function of Na2S0 concentration, using a Coulters Nanosizer (Coulters Electronics Ltd) as described before (20). 

The CFC obtained with the dilute dispersion ( 10 %) using the Nanosizer was -0.28 mol dm, i.e. significantly larger than that for the concentrated dispersion. 

The difference observed between the CFC for the concentrated and dilute dispersions (0.22 and 0.28 mol dm 3, respectively) may be accounted for if one considers the actual electrolyte concentration in bulk solution. With dilute dispersions (4>s 10 ) there is no difference between the nominal... 

Gmin.in the free energy-particle separation curves. Since AS g is reduced in concentrated dispersions,the flocculation of the dispersion occurs at relatively lower Gm- n than that observed with dilute dispersions. Thus, this effect would result in a reduction of the CFC for concentrated dispersions. However, the net result of reduction of CFC may be due to a combination of this effect and depletion of electrolyte from the dense region of the adsorbed layers. 

The Euler Lagrangian approach is very common in the field of dilute dispersed two-phase flow. Already in the mid 1980s, a particle tracking routine was available in the commercial CFD-code FLUENT. In the Euler-Lagrangian approach, the dispersed phase is conceived as a collection of individual particles (solid particles, droplets, bubbles) for which the equations of motion can be solved individually. The particles are conceived as point particles which move... 

There are numerous equations in the literature describing the concentration dependence of the viscosity of dispersions. Some are from curve fitting whilst others are based on a model of the flow. A common theme is to start with a dilute dispersion, for which we may define the viscosity from the hydrodynamic analysis, and then to consider what occurs when more particles are added to replace some of the continuous phase. The best analysis of this situation is due to Dougherty and Krieger18 and the analysis presented here, due to Ball and Richmond,19 is particularly transparent and emphasises the problem of excluded volume. The starting point is the differentiation of Equation (3.42) to give the initial rate of change of viscosity with concentration ... 

In the case of spray towers it has been shown by Thornton 10 that ur is well represented by Hod — j) where u0 is the velocity of a single droplet relative to the continuous phase, and is termed the droplet characteristic velocity. The term (1 — j) is a correction to m0 which takes into account the way in which the characteristic velocity is modified when there is a finite population of droplets present, as opposed to a single droplet. It must be seen therefore that for very dilute dispersions, that is as j -> 0, w0(l — j) o- On the other hand, as the fractional hold-up increases, the relative velocity of the dispersed phase decreases due to interactions between the droplets. Substituting for ur, equation 13.32 may be written as ... 

A critical property of minimum protocells in the prebiotic environment would be their ability to sequester other molecules, including macromolecules. [142] In 1982, Deamer and Barchfeld [143] subjected phospholipid vesides to dehydration-rehydration cycles in the presence of either monomeric 6-carboxyfluorescein molecules or polymeric salmon sperm DNA molecules as extraneous solutes. The experiment modeled a prebiotic tidal pool containing dilute dispersions of phospholipids in the presence of external solutes, with the dehydration-rehydration cydes representing episodic dry and wet eras. They found that the vesides formed after rehydration... 

A. Biesheuvel and L. van Wijngaarden. Two-phase flow equations for a dilute dispersion of gas bubbles in liquid. J. Fluid Mech., 148 301-318, 1984. 

Fire protection systems achieve prevention of fire by operating until flammable vapor, gases, or hazardous materials dissolve, dilute, disperse, or cool. 

Chewable/Dispersible buffered tablets To provide adequate buffering, thoroughly chew at least 2 of the appropriate strength tablets, but no more than 4 tablets, or disperse in at least 1 ounce of water prior to consumption. To disperse tablets, add 2 tablets to at least 1 ounce of water. Stir until a uniform dispersion forms, and drink entire dispersion immediately. If additional flavoring is desired, the dispersion may be diluted with 1 ounce of clear apple juice. Stir the further diluted dispersion just prior to consumption. The dispersion with clear apple juice is stable at room temperature for up to 1 hour. 

As has already been indicated a dilute disperse system may be regarded as obeying the ordinary gas laws. If we imagine a small volume of the disperse system as separated from the bulk of the solution it will contain at any instant a certain number of particles n. Since these particles are agitated by Brownian movement the number of particles in the small volume will alter from moment to moment but always maintaining a mean value of n over long periods of time. If at any instant the number in the small volume be n< then the relative alteration from the mean value m will be... 

The different microstructures, shown in Fig. 3, are highly dynamic aggregates. They can be detected by well established scattering techniques, like X-ray, light or neutron scattering [ 13]. Beside scattering techniques, the transitions between the microstructures can be detected from the changes of the viscosity of w/o-micro emulsion. For a diluted dispersion of spherical droplets without interactions, the relative viscosity is expected to obey the Einstein-relation ... 

For dilute dispersions with a non-viscous dispersed phase where the viscous energy within a drop is negligible compared to the surface energy, the maximum stable drop diameter dmax is given by... 

In 1906 Albert Einstein (Nobel Prize, 1921) published his first derivation of an expression for the viscosity of a dilute dispersion of solid spheres. The initial theory contained errors that were corrected in a subsequent paper that appeared in 1911. It would be no mistake to infer from the historical existence of this error that the theory is complex. Therefore we restrict our discussion to an abbreviated description of the assumptions of the theory and some highlights of the derivation. Before examining the Einstein theory, let us qualitatively consider what effect the presence of dispersed particles is expected to have on the viscosity of a fluid. 

We have so far focused our attention on dilute systems so that we could avoid dealing with interference of scattering from different particles. The interference effects considered until now are restricted to interference due to scattering centers from within the same particle. When we have a fairly concentrated dispersion or even a dilute dispersion of charged particles that influence the position of each other through their interactions, the scattering data may have to be corrected for interparticle interference effects. Extending the previous discussion to mte/particle interference is not difficult, but the subsequent analysis of the information obtained is not trivial. We shall not go into the details of these here, but just make some brief remarks to establish the connection between interparticle effects and what we have described so far for dilute systems. 

For dilute dispersions, i.e., those in which the interparticle spacing is so large that there are no particle-particle interactions, DLS simply measures the intensity fluctuations due to single-... 

Even in the case of monodisperse systems, the observed decay rate of gi(s,td) (and hence the diffusion coefficient) in general depends on the angle at which the decay is measured if interparticle interference effects exist. In the case of dilute dispersions, in which interactions... 

Although the analysis becomes complex for more concentrated dispersions (or even for dilute dispersions of charged particles, which can interact over very large distances), some general observations on two limiting cases are useful ... 

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