Hydrodynamic and Mechanical Factors

Variation in the Adhesion of Particles with the Conditions of Depositing Dust on Surfaces, 

Fuks [59] directed attention to the dependence of the adhesion on the period of contact between the particles and the surface on settling in the liquid. At the initial instant the adhesion of the particles is a minimum (Fig. IV.3), but with increasing contact time adhesion becomes stronger, the rise ceasing some 60-90 min after the particle first came into contact with the surface. This phenomenon has become known as aging. Fuks [59] studied the effect of contact time on adhesion specifically for the case of the liquid settling of particles. 

Thus at the initial instant (in our own experiments after a 2-min period of contact between particles and the substrate in the liquid) the adhesion for air dusting is always greater than the adhesion for liquid settling. 

An analogous law holds for molar and centimolar solutions of KCl and CaCl2 however, the equilibrium value of the adhesion numbers for the same detaching force moves upward in the first case and downward in the second. 

The increase in adhesion in distilled water (Fig. IV.5) for liquid settling (lower branches of curves 1 and 2) depends less on the time spent by the substrate in the liquid than in electrolyte lutions (see Fig. IV.4). The adhesion of glass particles to a glass surface in distilled water is greater (Fig. IV.5, curve 1) than to a surface painted with perchlorvinyl enamel (curve 2). 

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The Reynolds number for a particle Rep of supercritical size, deposited on the surface of a sufficiently large bubble (for which a potential distribution of the liquid velocity field is valid), is much larger than imity. In this case, the hydrodynamic resistance is expressed by a resistance coefficient. In aerosol mechanics a technique is used (Fuks, 1961) in which the non-linearity from the resistance term is displaced by the inertia term. As a result, a factor appears in the Stokes number which, taking into account Eq. (11.20), can be reduced to (l + Rep /b). This allows us to find the upper and the lower limits of the effect by introducing K instead of K " into Eq. (10.47) and the factor X in the third term. 

Because the hydrodynamic thickening mechanism of conventional ASTs (ASE and ASNE) is also present in the associative ASTs (HASE and HASNE), common factors affecting the thickening behavior of both types of thickeners would be expected, and are indeed observed. In a previously unpublished study (DeSoto, Inc. internal report), Brizgys and Shay examined the effect of the nonassociative hydrophobic comonomer on the thickening behavior of urethane-functional HASE thickeners prepared under identical conditions of semicontinuous emulsion polymerization. The results (Table I) obtained with respect to Tg and water solubility of the hydrophobic comonomer were generally similar to those observed for conventional ASTs by others cited earlier in this chapter. 

There is a large literature on the influence of additives on particle-filled elastomers and thermoplastics. Many particle-additive systems are marketed to produce polymer compounds containing small particles, which have strong interparticle forces. Small molecule additives are used in compounds with very small polar particles. Larger particles (i.e., particles greater in size than 5 pm) generally do not require associated additives because their flow behavior is dominated by hydrodynamic factors as described in Section 2.3. Some small nonpolar particles do not have suitable additives. Carbon black has relatively weak interparticle forces (Section 2.4.3), and additives have not been found to significantly modify the flow and mechanical characteristics of its compounds. 

Since the absolute thickness of the effective hydrodynamic boundary layer is very small, below a particular size range minimum, no hydrodynamic effects are perceived experimentally with varying agitation. This, however, does not mean, that there are no such influences Further, the mechanisms of mass transfer and dissolution may change for very small particles depending on a number of factors, such as the fluid viscosity, the Sherwood number (the ratio of mass diffusivity to molecular diffusivity), and the power input per unit mass of fluid. 

In general, when the system is subject to stirring by mechanical means or by density or temperature variations during absorption, Ri is difficult to calculate from fundamental principles, and each system has to be considered separately. Among the complicating factors is spontaneous surface instability which may reduce Ri by as much as five times and, before discussing the relation of Ri to the external hydrodynamics, we shall outline the conditions under which spontaneous surface turbulence may occur during mass transfer. 

Although HETP is a useful concept, it is an empirical factor. Since plate theory does not explain the mechanism that determines these factors, we must use a more sophisticated approach, the rate theory, to explain chromatographic behavior. Rate theory is based on such parameters as rate of mass transfer between stationary and mobile phases, diffusion rate of solute along the column, carrier gas flowrate, and the hydrodynamics of the mobile phase. 

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