Energy detachment

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]. 

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... 

Orbital energies and sizes go hand-in-hand small tight orbitals have large electron binding energies (i.e., low energies relative to a detached electron). For orbitals on... 

Atoms of elements that are characterized by a valence greater than four, eg, phosphoms or arsenic (valence = 5), are one type of dopant. These high valence dopants contribute free electrons to the crystal and are cabed donor dopants. If one donor atom is incorporated in the lattice, four of the five valence electrons of donor dopants are covalentiy bonded, but the fifth electron is very weakly bound and can be detached by only ca 0.03 eV of energy. Once it is detached, it is available as a free electron, ie, a carrier of electric current. A sibcon crystal with added donor dopants has excess electron carriers and is cabed n-ty e (negative) sibcon (Fig. Ic). 

The depth of this potential minimum will play a part similar to that of the depth of the minimum in Fig. 8a. The energy represented by the vertical arrow in Fig. 9a is the work required to detach a positive atomic core from the surface of the metallic lattice and to leave it at rest in a vacuum. No name for this quantity has come into general use. We shall denote it by Y, c, corresponding to the D of Fig. 8a. 

The elementary process of growth is treated as the attaching or detaching of one repeating unit on the surface. There are two possible ways in which a unit may add to a nucleus, which are shown in Fig. 3.20 (from Ref. [146]). A unit may diffuse from the liquid to the side of the nucleus with a small activation energy compared with kT. However, it is very difficult for a new unit from the liquid to add directly onto the fold surface, and the thickening of the nucleus is due to the... 

Anion photoelectron spectroscopy [37, 38] amd photodetachment techniques [39] provide accurate information on electron detachment energies of negative ions. Ten closed-shell ainions considered here exhibit sharp peaks, indicative of minor or vanishing final-state nuclear rearrangements, in their photoelectron spectra. Comparisons between theory and experiment are straiightforward, for differences between vertical and adiabatic electron detachment energies (VEDEs and AEDEs, respectively) are small. 

Notice that the carbon black hller reduces the rate of cut growth, but has only a small effect on the power index. Generally, it appears that abrasion occurs mainly in the third region, except when the abrasive track is very sharp. In this case the number of cycles to detach a small piece of rubber becomes small and the abrasion is proportional to the reciprocal of the energy density at break of the rubber compound. 

If these large energy concentrations meet a flaw in the rubber, the resulting tearing energy will increase the flaw at each pass until a rubber particle is detached. This is essentially the mechanical basis of the abrasion process. 

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