Particle curve

In Fig. 9.24 the particle densities and the production rate are shown as functions of Yco- The phase transition at y disappears due to the effect of B desorption (which is equivalent to the effect of A-desorption at yf). The repulsive interaction of A particles (curve 2) smoothes the phase transition at 2/2- Eab = 1 (curve 3) shifts y2 to lower values of Yco- This comes from the fact that the A particles can easily adsorb on the free sites created by B-desorption. The increased number of A particles on the lattice leads to an increased B-desorption due to the repulsive A-B interaction (see Fig. 10 and 11). In curve 4 the repulsion between the A particles leads to to shift of 2/2 to larger values of kco- Smoothing of the phase transition (compare curve 2) can be observed only at the beginning of the phase transition. At larger values of Yco, CA increases abruptly. This can be explained by the... 

As shown in figure 5, the average compositions, using "solu-tionM reactivity ratios (0.13 and 0.34) and taking into account monomer contents within particles (curves 1 and 2), correspond well to experiments, and are quite different from the ones calculated from "emulsion reactivity ratios" (0.1 and 0.44)(curves 5 and 6). 

Fig. 1. Interaction potential between two colloidal particles as a function of the reduced centre-to-centre separation R = r/2a, where a is the radius of the particles. Curve 1, steric repulsion due to the adsorbed layer (Vs) curve 2, attraction due to the free polymer (Vd) curve 3, van dcr Waals attraction (X7.,) curve 4, sum of the contributions given by curves 1—3. System polvisobutene-stabilized silica particles and polystyrene (free polymer) in cyclohexane at 308 K. Molecular weight of the free polymer = 82,000, volume fraction of polystyrene, 0 = 0.02, a = 48 nm, thickness of the adsorbed layer 6 = 5 nm, x = 0.5 for polystyrene—cyclohexane, x, = 0.47 and xs = 0.10 for polyisobutene— cyclohexane, AjkT 4.54 and v = 0.10.

Between the fixed-bed and single-particle curves lies the region for fluidized solids. For ideal fluidization, the flow rate can be varied by one to two orders of magnitude without affecting the value of NuPr 1/3 or ShSc 1/3, thus lead-... 

Selected results on number concentrations are presented on Figure 1. Wersborg s results were obtained at = 3.0 and o = 50 cm/sec. The soot particles (curve a) refer to particles larger than about 15 A diameter, measured by electron microscopy. The charged fraction of particles (curve b) was determined by measuring particle number with and without an electric field applied across the beam to remove all charged particles. Measurement error was estimated to be below 20%. 

Figure 42. Differential scatter of left and right circularly polarized light by poly-L-glutamic acid particles. Curve a, mean residue rotation of PGA reference state plotted on right-hand ordinate. Curve b, contribution of differential scatter term only, (Asi. —Asr) 3300/Cl. Curve c, total change in mean residue ellipticity due to differential scatter, includes differential scatter component of the (Aol— 4or) term. Curve d, comparison of empirical lO " values with total differential scatter. Curve e, approxima-...

A last method to be mentioned here of simplifying the description of polyatomic interactions is a simple modification of the two-particle curve crossing model. The two-particle LZ cross section (13) is based upon the assumption that both crossings to be passed are completely equivalent, i.e. they are... 

Dry deposition velocity (A) and sedimentation velocity (B) of aerosol particles. Curve A refers to flow over grass (Hidy, 1973). (By courtesy of Plenum Press)... 

Fig. V-l 1. The coefficient as a function of kr for spherical particles (curve /), for nonconducting rod-like particles oriented parallel (curve 2) and perpendicular (curve 3) to the electric field, and for conducting rod-like particles oriented along the electric field (curve 4)...

Figure 23.1 Three types of radioactive emissions in an eiectric field. Positively charged ct particles curve toward the negative plate negatively charged (3 particles curve toward the positive plate. The curvature is greater for 3 particles because they have much lower mass. The y rays, uncharged high-energy photons, are unaffected by the field.

The behavior of these three emissions in an electric field is shown in Figure 23.1. Note that a particles curve to a small extent toward the negative plate, (3 particles curve to a great extent toward the positive plate, and y rays are not affected by the electric field. 

Fig. 16.9. The dependence of the critical concentration of free hydroxyethyl cellulose upon its molecular weight for the depletion flocculation of polystyrene latex particles curves 1, in the absence of anionic surfactant 2, in the presence of nonionic surfactant (after Sperry et al., 1981).

Because the detection of these particles is based on the condensation of a liquid, usually either water or butanol, surface effects come into play. The condensation process is the transfer of excess material in one of both phases gas or aerosol and is driven by evaporation/subUmation and condensation, which take place in parallel. Is the surface of an aerosol particle curved molecules can enter the gas phase more easily and the interaction between absorbed molecules is less in strength (Seinfeld and Pandis 2006). Therefore the saturation above a curved, i.e. smaller particle is larger and particles tend to evaporate. This effect is called Kelvin effect after Lord Kelvin, who figured out and explained the effect about 150 years ago. The second effect of relevance is the solution effect. Two different compounds with the potential to get dissolved in each other as for instance a salt in water, will stick to each other even at subsaturation because the evaporation/sublimation is drastically reduced (Raoult effect) (Friedlander 2000). 

Figure 3Jxi-l Mass transfer between a fluid and a bed of particles. Curve I Gamson et al. [3], Wilke and Hougen [4]. Curve 2 Taecker and Hougen [5]. Curve 3 McCune and Wilhelm [6]. Curve 4 Ishino and Otake [7]. Curve 5 Bar Ilan and Resnick [8]. Curve 6 De Acetis and Thodos [9]. Curve 7 Bradshaw and Bennett [10]. Curved Hougen [11], Yoshida, Ramaswami, and Hougen [12] spheres e = 0.37). 

In Fig. VI.2, the variation of adhesion is shown for spherical gold particles (3-jLim diameter) in an aqueous medium. With primary deposition of the particles (curve 2), the same as in our experiments (see curve 1 in Fig. VI. 1), the adhesion of the particles was greater than with secondary deposition (curves 3 and 4 in Fig. V1.2 and curve 2 in Fig. VI.1). Results obtained on particle adhesion in air (curve 1 in Fig. VI.2) are shown for comparison. 

The influence of C or, for that matter, O on the viscosity may be analyzed on the basis of a plot of rjjed versus C, as shown in Figure 17.10. Curve 1 represents nonsolvated particles that do not interact. For interacting particles curve 2 is obtained and the departure from curve 1 is determined by the third and higher terms on the right-hand side of Equation 17.8. If the effective volume fraction =Clpf) of... 

Fig. 1. The concentration of human serum albumin adsorbed to hydroxyapatite particles versus bulk protein concentration along several concentration trajectories. Curve A a gradual increase in bulk protein concentration via flow of 0.066 g/L protein solution into chamber of particles. Curve B a gradual decrease in bulk protein concentration via flow of buffer solution without protein. Curve C a protein concentration of 0.695 g/L for 30 min followed by a gradual decrease in bulk protein concentration via flow of buffer solution. Curve D a protein concentration of 0.858 g/L for 8 h followed by a gradual decrease in bulk protein concentration via flow of buffer solution. Curve I Protein concentrations corresponding to the horizontal axis for 8 h. Taken with permission from Ref 77.

FIG. 14-14. Bulk moduli at three temperatures as indicated for a polyurethane rubber containing sodium chloride particles with sharp size distributions in the ranges shown, plotted against volume fraction of particles.Curves calculated from the theory of van der Poel. ... 

Figure 2. Fluorescence spectrum of a colloidal particle composed of poly(viny] acetate) [PVAc] and poly(2 ethylhexyl methacrylate) labelled with phenanthrene in the PVAc phase, curve a. Curve b is the fluorescence spectrum of an identical unlabelled particle. Curve c is obtained by subtracting b from a. The excitation wavelength was 290 nm.

Despite the direct visualization of nanocomposite structure TEM allows also for quantitative understanding of its internal structure as well as for observation of spatial distribution and quantity of various phases. Proper evaluation of all those features requires exploitation of a representative cross-section of the sample, which often means that many pictures have to be taken [64, 65]. Figure 21.39 presents the microphotograph which was used by Vermogen et al. [66] to define the particle curved length (L), thickness (t), and the interparticular distance in the... 

FIGURE 6.6 Dry deposition velocity of ammonium sulfate particles to a smooth water surface for a windspeed of 2 m/s, T = 20°C, relative humidity at 1 m = 75%, and initial particle height = 1 m. Curve A is the baseline case without any hygroscopic growth, while Curve B is for growth to equUibrium. Curve C is for partial growth of metastable liquid particles. Curve D is for partial growth of particles that deliquesce from solid crystals to become liquid. [Adapted from ZufaU, M.J. et al., Environ. Sci. Technol., 1998, 32(5), 584—590.]... 

The dates of Figures 2 and 3 about the dynamic viscosity of 1-8% solutions of chitosan, shows the viscosity increase with the introduction of alcohol, more than have more maintenance of alcohol and chitosan. They also consistent with the known views on the impact of solvent quality on the properties of the solutions. However, the introduction of ethanol visually observed decrease in turbidity and increase the homogeneity of concentrated (6-8%) solutions chitosan in dilute acetic acid. The decrease of turbidity for 1% solutions is confirmed by calculation (curve 1 in Figure 4). The calculations also showed a significant reduction in the number of scattering particles (curve 2) and some increase in their average sizes (curve 3) with the introduction of ethanol, apparently due to dissolution micro and nanosized helices. 

A decrease in the size of droplets (the right-hand side of the graph in Figure 2.38) makes the profiles of solid particles (curve 3) and droplets (curve 1) approach one another. In the central part of the contact region, the flat interlayer region reduces, whereas the differences from the profile of the flat interlayers (curve 2) increases. A further decrease in the droplet radius causes a still greater approach of the profiles of the fluid and the solid particles to one another and a disappearance of the flat portion of the interlayer. As already shown, at R R, the known solutions for the interaction of solid spheres may be used. 

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