Hydrodynamic pressing force

The important distinction is that in the case of large particles, thinning of a liquid interlayer is accomplished through an impact, while in the case of small particles it is due to the effect of hydrodynamic pressing forces. 

With very large particles the liquid interlayer thinning process is complicated by the deformation of the bubble surface by an inertia impact of the particle. It was shown by Derjaguin et al. (1977) and Dukhin Rulyov (1977) that in the inertia-free deposition of small particles on a bubble surface its deformation under the influence of the hydrodynamic pressing force is insignificant. This third important feature facilitates the development of a quantitative kinetic theory of flotation of small particles. 

The region of floatability due to hydrodynamic pressing forces were calculated for the Stokes (Fig. 10.7) and potential (Fig. 10.8) regimes and for several values of the product of surface potentials of the bubble, and the particle v /p. As could be expected, flotation can occur even... 

After the disjoining pressure of the double layer under the effect of hydrodynamic pressing forces (see Figs. 10.7 and 10.8) has been overcome, a subsequent detachment of the particle displaced to the rear pole of a bubble is hindered only at a sufficiently deep potential energy minimum. Even when the bubble is charged opposite to the particle, this minimum may be insufficiently deep if the a-film is thick enough (see Appendix lOD). The question about the depth of the primary minimum is very complex (cf Derjaguin Kudryavtseva 1964, Martynov Muller 1972, Overbeek 1977). 

Scheludko s (1970) statement that slow t.p.c expansion can control flotation kinetics may be important for large particles. Note that one of the decisive differences between flotation and microflotation also consists in the electrostatic barrier. In Section 10.5 it was shown that the weight and the hydrodynamic pressing force of micron particles, in contrast to large particles, are not sufficient to surmount the electrostatic barrier. Thus, electrostatic repulsion can exclude microflotation while it does not affect flotation, and the t.p.c. expansion rate can control flotation kinetics but has probably no influence on microflotation. 

Because of strong surface retardation and weak hydrodynamic pressing forces cationic surfactants are required. 

An evaluation of the possibility of overcoming the electrostatic barrier by hydrodynamic pressing forces in the transient hydrodynamic regime has not been carried out, but it is clear that the situation will be much better at strong surface retardation than in the Stokes regime (cf. Section 10.5.2). 

There is the possibility of non-reagent flotation. Because of non-retardation of surfaces and a high velocity of bubble rising, the normal component of the hydrodynamic field of bubbles is sufficiently large to provide hydrodynamic pressing forces to ensure the electrostatic barrier is overcome (cf Fig. 10.8). 

The use of millimeter bubbles is attractive because they are produced by existing technologies and because electrostatic repulsion can be overcome by hydrodynamic pressing forces. The latter advantage get lost if surfactant has to be added to modify the surface of the particle to prevent its detachment. 

Lamb, H., 1932. Hydrodynamics, 6th edn. Cambridge University Press, New York, Dover. 738 pp. Lass, H. U., 1988. A theoretical study of the barotropic water exchange between the North Sea and the Baltic and the sea level variations of the Baltic. Beitrage zur Meereskunde, Berlin, 58, 19-33. Lass, H. U., Matthaus, W., 1996. On temporal wind variations forcing salt water inflows into the Baltic... 

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