Inertia force negative effects

Negative Effect of Inertia Forces on Flotation of Small Particles. Generalisation of Sutherland s Formula. Extension of Limits of Applicability of Microflotation Theory... 

If we take into account the negative effect of inertia forces on particle capture, it turns out that the grazing trajectory (Fig. 10.13) corresponds to values of b smaller than those in Sutherland s theory and the point of tangency moves from the equator towards the front pole. 

It is worth noticing that negative effects of inertia forces appear at subcritical values of Stokes numbers when a positive effect is practically absent (cf Section 10.1). The inertia-free approach of a particle and a bubble is caused by the radial particle velocity when its centre is located at a distance from the bubble surface approximately equal to a. When the particle radius tends to zero, this velocity also tends to zero and deposition depends on the finite size of the particle. 

Considering the negative effects of inertia forces, most important is the calculation of the point of tangency 0, where the radial component of the particle velocity at the time of contact with bubble surface becomes zero,... 

While neglecting the finite size of a particle at subcritical Stokes numbers excludes inertia forces at all, the situation changes with the consideration of a finite particle size. Inertia forces become essential at subcritical but not too small Stokes numbers. This effect can turn out to be negative. Thus, a critical Stokes number separates the regions of positive and negative effects of inertia forces on particle deposition. 

This theory enables to characterise quantitatively the conditions under which flotation proceeds inertia-free. It is simultaneously a generalisation of the theory of small particle flotation which not only allows to describe inertia-free flotation, but also flotation complicated by a negative effect of inertia forces. If flotation proceeds practically inertia-free at ap<3-10pm, the negative effect of inertia its quantitatively described over the range of bubble size from 10 to 30 pm. 

Unfortunately, up to now all quantitative investigations of collision efficiency have been performed under conditions which do not allow to check the validity of the present theory. In experiments by Anfhms Kitchener (1977), bubble surfaces were retarded to a large degree which strongly decreases the negative effect of inertia forces. 

A direct method for detection of negative inertia force effects on collision efficiency at St < St consists in performing experiments with particles of same size but with different and strongly varied density. 

Dynamic adsorption layers (DAL) cause bubble surface retardation and thus decrease the negative effect of inertia forces on microflotation. It is important to keep in mind the substantial qualitative distinctions of the DAL effect and the inertia forces at high (condition... 

Inertia reduces the measured normal forces and it only depends on the diameter of the system and the rotational speed for a given solution. In the case of a polymer solution with real but small normal forces (dilute or lower molar masses), even negative Nrvalues are simulated by this effect [85]. 

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