Dispersion of solid particles in a fluid

For larger particle sizes, one may have to deal with pastes, particle beds and powder dispersions. In these situations, the volume fraction of particles is high 

The viscosity of a fluid is increased by the presence of dispersed particles as they tend to disturb the flow patterns. For dilute suspensions of spherical particles in a Newtonian fluid, the viscosity is described by Einstein s relation. 

For these cases, (empirical) non-linear versions of Eq. (5.38) are sometimes used to describe the variation of viscosity with particle volume fraction. 

As indicated earlier, unless particles are small enough to be held in suspension by Brownian motion they will undergo settling as a result of gravity. The force F on a sphere, radius a, moving slowly with a velocity v through a fluid of viscosity t) is given by 

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Sols arc dispersions of colloidal particles in a liquid. Colloids arc nanoscaled entities dispersed in a fluid. Gels are viscoelastic bodies that have interconnected pores of submicrometric dimensions. A gel typically consists of at Icasl two phases, a solid network that entraps a liquid phase. Sol-gel technology is the preparation of ceramic, glass, or composite materials by the preparation of a sol, gelation of the sol. and removal of the solvent. 

A simple unified model based on the concepts of universality and scaling for the shear viscosity of dispersions of solid particles in both non-Newtonian and Newtonian fluids was developed. This model was presented in the very broad context of a review article listing more than 200 references [42]. Highlights from this work are summarized below. 

Colloidal systems exist in both nature and industry and can consist of either solids or liquids dispersed in either fluids or gases. Blood is a dispersion of the red blood cells (which are similar to self-assembling colloids) in serum and emulsions or microemulsions (see Chapter 8) are dispersions of oil in water or water in oil. Fog, mist, and smoke are dispersions of small particles in gases, while pollution control deals with dispersions of solid particles in air. Foams (dispersion of liquid in a gas at relatively high volume fractions of liquid) are familiar from toothpastes to beer. Many industrial processes make use of colloidal dispersions of solid particles in fluids to tailor the hydrodynamic properties of the fluid or sometimes to produce a system with large amount of internal surface area for catalytic applications. 

Flocculation The formulation of clusters of pigment particles in a fluid medium which may occur after dispersion has been effected. The condition is usually reversible and the particle clusters can be broken up by the application of relatively weak mechanical forces or by a change in the physical forces at the interface between the liquid and the solid dispersed particles. Flocculation is often visible, as a Jack Frost pattern... 

FIG. 16-9 General scheme of adsorbent particles in a packed bed showing the locations of mass transfer and dispersive mechanisms. Numerals correspond to mimhered paragraphs in the text 1, pore diffusion 2, solid diffusion 3, reaction kinetics at phase boundary 4, external mass transfer 5, fluid mixing. 

Fluidised beds may be divided into two classes. In the first, there is a uniform dispersion of the particles within the fluid and the bed expands in a regular manner as the fluid velocity is increased. This behaviour, termed particulate fluidisation, is exhibited by most liquid-solids systems, the only important exceptions being those composed of fine particles of high density. This behaviour is also exhibited by certain gas-solids systems over a very small range of velocities just in excess of the minimum fluidising velocity—particularly where the particles are approximately spherical and have very low free-falling velocities. In particulate fluidisation the rate of movement of the particles is comparatively low, and the fluid is predominantly in piston-type flow with some back-mixing, particularly at low flowrates. Overall turbulence normally exists in the system. 

DISPERSANTS. Dispersants are materials that help maintain fine solid particles in a state of suspension, and inhibit their agglomeration or settling in a fluid medium. With the help of mechanical agitation, dispersants can also hit-.tk up agglomerates of particles to form particle suspensions. Another use of dispersants is to inhibit the growth of crystallites in a supersaturated solution. This characteristic is also known us precipitation... 

In the present study, two-dimensional Two-Fluid Eulerian model was used to describe the steady state, dilute phase flow of a wet dispersed phase (wet solid particles) in a continuous gas phase through a pneumatic dryer. The predictions of the numerical solutions were compared successfully with the results of other one-dimensional numerical solutions and experimental data of Baeyens et al. [5] and Rocha [13], Axial and the radial distributions of the characteristic properties were examined. 

A grafted layer of polymer of thickness L increases the effective size of a colloidal particle. In general, dispersions of these particles in good solvents behave as non-Newtonian fluids with low and high shear limiting relative viscosities (fj0 and rj ), and a dimensionless critical stress (a3aJkT) that depends on the effective volume fraction = (1 + L/a)3. The viscosities diverge at volume fractions m0 < for mo < fan < 4>moo> the dispersions yield and flow as pseudoplastic solids. 

Fog, which is a liquid aerosol, is formed when small liquid particles are dispersed in a gas. o Many paints are sols, a fluid colloidal system of fine solid particles in a liquid medium. Qlhe bagel has a coarse texure with lots of small holes throughout. These small holes are formed by a type of foam produced by yeast in the dough. 

Dispersed-Solids Leaching Equipment for batch leaching of fine solids in a liquid suspension is now confined mainly to batch tanks with rotating impellers. For a detailed discussion of all aspects of the suspension of solid particles in fluids, refer to agitation of particle suspensions at the beginning of this subsection. 

Definition of Suspension. The rheology of suspensions deals with how suspensions respond to an applied stress or strain. The term suspension refers, in general, to dispersions of solids in fluids, although the term aerosol is conventionally used to refer to dilute suspensions of fine particles in a gas and the term emulsion is used to identify (concentrated) suspensions of particles in a gas or liquid in the field of fluidization. However, emulsion is conventionally defined as the dispersion of a liquid in another (immiscible) liquid. In a broader sense, emulsions are also considered as suspensions. In this chapter, we deal mainly with suspen-... 

At the lower boundary its velocity would be v — RD. When a particle is present, this will no longer be the case. If there is no slip at the liquid/solid surface, the forces acting on the upper and lower hemispheres of the particle will cause it to rotate. However, this rotation will be resisted by viscous forces over the whole surface of the particle for example, there will be shears down and up, respectively, on the leading and trailing surfaces. Consequently the velocity of the liquid in contact with the top surface of the sphere will be lowered and that at the bottom increased. The velocity profile of the fluid round the perimeter of the particle will be distorted as indicated schematically in Figure 8.4(b). If the overall flow is to be kept constant, the stress must increase, i.e. the viscosity is increased by the presence of the particle. In a dispersion the total effect will be proportional to the concentration of particles and to their volume, leading to the relationship in equation (8.5). 

FIGURE 26.30 Snapshots from simulations of dispersion of coUoidal slab made of solid particles in DPD and FPM fluids in 2-D (a,b) and 3-D (c). The gravitational acceleration is directed downward. We can observe crystallization process along the mixing front (a) for a properly defined interparticle force. 

Emulsion pol)m erization is a complex process in which the radical addition polymerization proceeds in a heterogeneous system. This process involves emulsification of the relatively hydrophobic monomer in water by an oil-in-water emulsifier, followed by the initiation reaction with either a water-soluble or an oil-soluble free radical initiator. At the end of the pol)nnerization, a milky fluid called "latex", "synthetic latex" or "pol)rmer dispersion" is obtained. Latex is defined as "colloidal dispersion of polymer particles in an aqueous medium". The pol)nner may be organic or inorganic. In general, latexes contain 40-60 % pol)nner solids and comprise a large population of polymer particles dispersed in the continuous aqueous phase (about lO particles per mL of latex). The particles are within the size range 10 nm to 1000 run in a diameter and are generally spherical. A typical of particle is composed of 1-10000 macromolecules, and each macromolecule contains about lOO-lO " monomer units [10-16]. 

A turbulent flow is also capable of fragmenting bubbles or drops. We have presented in section 9.2.3, the model by Kolomogorov and by Hinze, which rely the maximum diameter of fluid particles in an emulsion to the rate of turbulent energy dissipation and to surface tensiom In the same way, indicated for the formation of clusters in a dispersion of solid particles, it is difficult to determine the bubble or drop size in a dispersion of fluid particles. We will not discuss this issue any further in this book, and hence refer the reader to more speciahzed volumes. ... 

Dispersion of solids is a physical process where solid particles or aggregates are suspended and dispersed by the action of an agitator in a fluid to achieve a... 

A suspension, or periuq>s more broadly a dispersion, consists of discrete particles randomly distributed in a fluid medium. Gen erally we divide suspensions into three categories solid particles in a liquid medium (often the word suspension is restricted to this meaning), liquid droplets in a liquid medium (or an emulsion), and gas in a liquid (or ifoam). All these categories have great practical importance, from biological materials like milk and blood to paint, ink, ceramics, and many other industrial dispersions. 

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