Particles in water

Using the conditions of the Langmuir approximation for the double-layer repulsion, calculate for what size particles in water at 25°C the double-layer repulsion energy should equal kT if the particles are 40 A apart. 

Table C2.6.5 Rapid coagulation half-life time for particles in water at 7 =300 K (equation (C2.6.16)).

A preparation of reduced and carboxymethylated protein particles in water reached sedimentation equilibrium after 40 hr at 12,590 rpm. When the data are plotted as suggested by Eq. (9.103), two distinctly linear portions are observed in the graph. The following pairs of points are taken from these two regions ... 

Mixing. In method 1, a suspension of colloidal powders, or sol, is formed by mechanical mixing of colloidal particles in water at a pH that prevents precipitation (step A in Fig. 1) (8). In method 2 or 3, a Hquid alkoxide precursor such as Si(OR)4, where R is CH (TMOS), C2H (TEOS), or C Hy, is hydrolyzed by mixing with water (eq. 2). 

Consider an alchemical transformation of a particle in water, where the particle s charge is changed from 0 to i) (e.g., neon sodium q = ). Let the transformation be performed first with the particle in a spherical water droplet of radius R (formed of explicit water molecules), and let the droplet then be transferred into bulk continuum water. From dielectric continuum theory, the transfer free energy is just the Born free energy to transfer a spherical ion of charge q and radius R into a continuum with the dielectric constant e of water ... 

SBR latices are high-solids dispersions of rubber particles in water, the viscosity and rheology of which are, in general, independent of the polymer properties, unlike solutions. They offer a wide range of molecular weight and glass transition temperature. Three classes of SBR latices are available in the market. 

Calculate the settling velocity of coal particles in water at 20 C. The average size of the particles is 225 /tm. 

Determine the settling velocity of spherical quartz particles in water (d = 0.9 mm) using the dimensionless plot of the Lyachshenko and Reynolds numbers versus the Archimedes number in the figure above. The Lyashenko number is the same as the dimensionless settling number. The specific weight of the quartz is 2650 kg/m and the temperature of the water is 20° C. 

This prediction is drawn according to the following model. Figure 5 illustrates that in the latex state the grafting PVA protects hydrophobic PVAc particles in water by concentrating on the surfaces of PVAc particles, but in the porous film after acetone extraction, the insoluble grafting PVAc conversely exists as an important component on the inner surface of spherical cells of PVA. 

Figure 4-8. Terminal settling velocity of particles in water. By permission, Lapple, C. E., Fluid and Particle Mechanics, 1st Ed., University of Delaware, Newark, 1954.

Figure 27.1 A soap micelle solubilizing a grease particle in water. An electrostatic potential map of a fatty acid carboxylate shows how the negative charge is located in the head group.

Latex Also called emulsion. It is an aqueous dispersion of natural or synthetic elastomeric rubbers and plastics (dispersions of plastic particles in water). 

The layers of opposite charges formed on the surface of individual electrically-charged particles in water, causing mutual repulsion. 

Additionally, the sequestering ability of polyphosphoric acid and phosphonic acid derivatives as well is a valuable property for their use as dispersants. The main task of dispersants is to suspend solid particles in water or organic solvents and avoid their coalescence and precipitation. This complex plays an important role in many processes and as a result dispersants are used in many technical fields. 

The terminal falling velocity of the sand particles in water may be taken as 0.0239 m/s. This value may be confirmed using the method given in Volume 2. 

Pirie, R. L. Ph D. Thesis, University of Wales (1990). Transport of coarse particles in water and shearthinning suspensions in horizontal pipes. 

Rubber is a polymer of isoprene (15). Natural rubber is obtained from the bark of the rubber tree as a milky white liquid, which is called latex (Fig. 19.8) and consists of a suspension of rubber particles in water. The rubber itself is a soft white solid that becomes even softer when warm. It is used for pencil erasers and was once used as crepe rubber for the soles of shoes. 

In practice, the catal5Tic layers are prepared by brushing or spraying catalyst ink (a suspension of the catalyst particles in water and/or an organic solvent with addition of ionomer) either onto diffusion media (carbon paper or carbon cloth, also referred to as substrates), resulting in so-called catalyst-coated substrates (CCS), or directly onto... 

A slurry of acrylic polymer particles in water is held in storage tanks prior to filtering and drying. Plain carbon steel would be a suitable material for the tanks, but it is essential that the polymer does not become contaminated with iron in storage. Suggest some alternative materials of construction for the tanks. 

Classifiers that depend on the difference in the settling rates of different size particles in water are frequently used for separating fine particles, in the 50 to 300 /im range. Various designs are used. The principal ones used in the chemical process industries are described below. 

Higher levels of lead in soil can be measured near roadways. This accumulation came from car exhaust in the past. Once lead falls onto soil, it usually sticks to soil particles. Small amounts of lead may enter rivers, lakes, and streams when soil particles are moved by rainwater. Lead may remain stuck to soil particles in water for many years. Movement of lead from soil particles into underground water or drinking water is unlikely unless the water is acidic or "soft." Movement of lead from soil will also depend on the type of lead salt or compound and on the physical and chemical characteristics of the soil. 

We begin by considering a spherical particle in water. We introduce the solute-solvent interactions gradually, through a coupling parameter A that varies from zero to one... 

Figure 41. Traj ectories of single resin particle in water computed from the equation on p. 548 (particle diameter 0.435 mm, amplitude 2 cm, asymmetric factor 1.2). (Deng, and Kw auk, 1990.)...

Wash the carboxylated particles at least 3 times with DMF by centrifugation. Resuspend in water and wash 3 times with water to remove DMF. Store the particles in water or a suitable buffer at neutral or slightly acidic pH. 

Radical polymerization of styrene was carried out in the presence of bare silica particles, and of the HPC-coated silica particles in water by using potassium persulfate as an initiator. Table 2 gives the typical ingredients used for these polymerizations. The HPC-coated silica particles were prepared under the same conditions as in the adsorption experiments. The polymerization temperature was kept at 1+5 °C to protect the adsorption layer of HPC, and polymerized for 2l+ hrs in the same manner as that... 

The force-distance profiles Al, A2 appear to show the relaxed, or quasi-equilibrium limit for the interaction between the mica plates bearing the PEO in the good solvent conditions of the present study. The adsorbed layer thicknesses 6 are then about half the value of D at which onset of repulsion (A curves) is first noted. 6 thus corresponds to some 3Rg for both polymers in the present investigation, a value comparable to that obtained for hydrodynamic layer thickness of PEO absorbed on latex particles in water, for similar molecular weights, from light scattering studies. 

Figure 3 is a graph of H vs. particle radius (a) for carbon particles in oil where tfte Hamaker constant is relatively high (Ai2i=2.8xl0 13ergs), for polystyrene particles in water... 

Using the nomenclature of Chapter 3 in Volume 2, a force balance on the particle in water gives ... 

Richardson and Zaki (1954) showed that in the Reynolds number range Rep<0.2, the velocity uc of a suspension of coarse spherical particles in water relative to a fixed horizontal plane is given by the equation... 

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