Particle contact angle

In processes where new powder feed has a much smaller particle size than the smallest granular product, the feed powder can be considered as a continuous phase which can nucleate to form new granules [Sastry Fuerstenau, Powder Tech., 7, 97 (1975)]. The size of the nuclei is then related to nucleation mechanism. In the case of nucleation by spray, the size of the nuclei is of the order of the droplet size and proportional to cos0, where 0 is binder fluid-particle contact angle (see Fig. 20-67 of Wetting section). 

A novel method for detennination of the particle contact angle at the fluid/fluid interface based on the excluded area concept revealed some serious difliculties connected with the exact quantitative particle deposition at the interface and with changes in the particulate contact angle upon binary monolayer compression. The comprehensive theoretical consideration of the contact angle behavior made for such system allowed considerable improvement of the proposed method that was then successfully proven by experimental data. 

FIGURE 5.51 Effect of adsorbed surfactant on the surface diffusivity, D, of a Brownian particle attached to a fluid interface (a) plot of Dp/D g vs. particle contact angle, 0, for various surface viscosities (see Equation 5.306) (b) plot of DpIDp, vs. the dimensionless surface viscosity, K= E, for various 0. 

Controlling particles contact angles at the interface is important as it determines their wettability (Fig. 7). Tailoringparticles contact angles via modification of chemical composition... 

For some types of wetting more than just the contact angle is involved in the basic mechanism of the action. This is true in the laying of dust and the wetting of a fabric since in these situations the liquid is required to penetrate between dust particles or between the fibers of the fabric. TTie phenomenon is related to that of capillary rise, where the driving force is the pressure difference across the curved surface of the meniscus. The relevant equation is then Eq. X-36,... 

The basic phenomenon involved is that particles of ore are carried upward and held in the froth by virtue of their being attached to an air bubble, as illustrated in the inset to Fig. XIII-4. Consider, for example, the gravity-free situation indicated in Fig. XIII-5 for the case of a spherical particle. The particle may be entirely in phase A or entirely in phase B. Alternatively, it may be located in the interface, in which case both 7sa nnd 7sb contribute to the total surface free energy of the system. Also, however, some liquid-liquid interface has been eliminated. It may be shown (see Problem XIII-12) that if there is a finite contact angle, 0sab> the stable position of the particle is at the interface, as shown in Fig. XIII-5Z>. Actual measured detachment forces are in the range of 5 to 20 dyn [60]. 

Clearly, it is important that there be a large contact angle at the solid particle-solution-air interface. Some minerals, such as graphite and sulfur, are naturally hydrophobic, but even with these it has been advantageous to add materials to the system that will adsorb to give a hydrophobic film on the solid surface. (Effects can be complicated—sulfur notability oscillates with the number of preadsoibed monolayers of hydrocarbons such as n-heptane [76].) The use of surface modifiers or collectors is, of course, essential in the case of naturally hydrophilic minerals such as silica. 

The cleaning process proceeds by one of three primary mechanisms solubilization, emulsification, and roll-up [229]. In solubilization the oily phase partitions into surfactant micelles that desorb from the solid surface and diffuse into the bulk. As mentioned above, there is a body of theoretical work on solubilization [146, 147] and numerous experimental studies by a variety of spectroscopic techniques [143-145,230]. Emulsification involves the formation and removal of an emulsion at the oil-water interface the removal step may involve hydrodynamic as well as surface chemical forces. Emulsion formation is covered in Chapter XIV. In roll-up the surfactant reduces the contact angle of the liquid soil or the surface free energy of a solid particle aiding its detachment and subsequent removal by hydrodynamic forces. Adam and Stevenson s beautiful photographs illustrate roll-up of lanoline on wood fibers [231]. In order to achieve roll-up, one requires the surface free energies for soil detachment illustrated in Fig. XIII-14 to obey... 

It was pointed out in Section XIII-4A that if the contact angle between a solid particle and two liquid phases is finite, a stable position for the particle is at the liquid-liquid interface. Coalescence is inhibited because it takes work to displace the particle from the interface. In addition, one can account for the type of emulsion that is formed, 0/W or W/O, simply in terms of the contact angle value. As illustrated in Fig. XIV-7, the bulk of the particle will lie in that liquid that most nearly wets it, and by what seems to be a correct application of the early oriented wedge" principle (see Ref. 48), this liquid should then constitute the outer phase. Furthermore, the action of surfactants should be predictable in terms of their effect on the contact angle. This was, indeed, found to be the case in a study by Schulman and Leja [49] on the stabilization of emulsions by barium sulfate. 

In the pendular state, shown in Figure la, particles ate held together by discrete lens-shaped rings at the points of contact or near-contact. For two uniformly sized spherical particles, the adhesive force in the pendular state for a wetting Hquid (contact angle zero degree) can be calculated (19,23) and substituted for H. in equation 1 to yield the foUowing, where y is the Hquid surface tension in N/m. 

CMC), reverses the effect that the surfactant has on contact angle at lower concentrations, and at or above the CMC there is no further lowering of surface tension. At the higher concentrations, the surfactant loses some of its beneficial effect on dewateriag, as shown ia Figure 5. The beneficial effects of surfactants on dewateriag are most pronounced ia cakes that have been partially deslimed or ia cakes of partially hydrophobic particles (eg, flotation concentrates) that are adsorbed onto each other. Surfactants at or above CMC have Httle practical effect on extremely fine cakes, where pores are small and the cake has no further opportunity to consoHdate. A number of filter cakes do not respond to surfactant addition at any level. 

Fig. 19. The energy to displace a particle from the interface into one phase strongly depends on the contact angle.

These values make it evident that the contact angles must be observed rather carefliUy to obtain a value close to 90°. The following experimental procedure is practical to obtain good stabiUty. A container with the particles is placed on the bottom of an ofl-filled vessel with parallel walls, and a drop of the aqueous phase is placed on the powder. The shape of the droplet decides the action to be taken. 

Increase adhesion tension. Maximize surface tension. Minimize contact angle. Alter surfactant concentration or type to maximize adhesion tension and minimize Marangoni effects. Precoat powder with wettahle monolayers, e.g., coatings or steam. Control impurity levels in particle formation. Alter crystal hahit in particle formation. Minimize surface roughness in milhng. 

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