Transport stage

An analysis of DAL effect on microflotation is complicated as it has an effects both on the transport stage and the stage of attachment. It is advisable to consider first the regime at which... 

Effect of Dynamic Adsorption Layer on the Transport Stage of the Elementary Flotation Act... 

Influence of Surface Retardation by DAL on Transport Stage Qualitatjve Considerations... 

DAL Influence on Transport Stage of Microflotation and Level of Water Contamination... 

There are two regimes of DAL influence on the transport stage of microflotation. At sufficiently high level of water contamination the transport of a particle to the retarded surface of a bubble is the same as that of a solid sphere. Taking into account the results of Section... 

There is no specificity of the transport stage of microflotation at the condition (10.33) in comparison with a solid sphere. However let us emphasise that the surface retardation is caused by the dynamic state of the adsorption layer, i.e. by the change of the surface concentration and surface tension along the bubble surface. 

Due to rapid decrease of the retardation coefficient with increasing bubble dimension, a residual surface mobility remains for big bubbles. The transport stage for sufficiently small bubbles and solid spheres is identical. The characteristic bubble value which describes the boundary between the two ranges of bubble dimensions can be determined from Eq. (10.35) after substitution of Xb as a function of bubble radius, according to Eq. (8.106),... 

When the rear stagnant cap and the angle T increase, the collision efficiency decreases. Thus, at uniform surface retardation, i.e. under condition (8.71) and during the rear stagnant cap formation, the mechanisms of DAL effect on the transport stage differ qualitatively. In the former case, with increasing surfactant concentration, the normal component of velocity and, respectively, the flow of particles uniformly decrease over the leading surface. In the latter case, the area admissible for sedimentation of particles decreases. 

The consideration made is of semi-quantitative nature, and is justified both at moderate and large Reynolds numbers. At moderate Reynolds numbers, a refinement of the theory seems to be premature since the notion of the incomplete retardation of the surface is a hypothesis which needs an experimental check. At large Reynolds numbers, a quantitative consideration of the effect of DAL on the elementary flotation act will prove to be possible generally only after the quantitative theory of DAL has been developed. The given evaluations confirm that the effect of DAL on the transport stage of microflotation is high at large Reynolds munbers and, possibly, also at moderate values. 

In the preceding sections the possibility of the strong influence of the fi-ee surface zone near the front stagnant point on the transport stage of microflotation was emphasised. Eq. (10.40) enables us to estimate the critical condition of the appearance of an f.s.f.z. The parameters v and Re relate to the bubble with a completely retarded surface and can be described by equations derived for solid spheres. 

Role of r.s.c. in Transport Stage at Different Particle Attachment Mechanisms... 

In transient state the DAL has a slight effect on the transport stage if the rear stagnant cap covers a smaller part of the surface. If the rear stagnant cap is not too small and characterised by the angle 9 (cf Section 8.6) essentially less than 7t/2, the possibility of its effect depends substantially on the mechanism of fixation of particles on a bubble surface (see Appendix lOD). 

In conclusion of this section and in accordance with the results obtained in the preceding sections it can be recalled that in studies of DAL by microflotation methods it is necessary to provide attachment of particles on bubble surfaces. The results are then controlled only by the transport stage of the elementary flotation act. 

Dynamic Adsorption Layer and Optimisation of Transport Stage of Flotation... 

If flotation is not complicated by an energy barrier and h is not very small so that the approach of particles leads to a break of the film and a formation of three-phase contact (fulfilled for small particles), microflotation is perfected by controlling the transport stage. This question was considered in Section 10.4 and the control of microflotation reduces to the choice of an optimal bubble size. 

Through a recharge of the bubble surface not only the electrostatic barrier is removed, but also the near potential well becomes deeper, so that a subsequent detachment of particles becomes impossible. In this case microflotation perfection reduces to the control of the transport stage... 

The effect of the specific density of a particle and its radius on the combined effect of centrifugal forces is shown in Fig. 10.16. It can be expected that Sutherland s formula describes the transport stage of the elementary act also at Stokes number close to the critical one. It becomes clear from the results in Fig. 10.16, that it is applicable only at 0, close to 90°. This condition is not fulfilled over a wide range of 0, and Ap. 

The theory of the transport stage of elementary microflotation at strong surface retardation is confirmed by works of Reay Ratcliff (1975), Collins Jameson (1977) and Anfruns Kitchener (1976, 1977). Numerous confirmations of the possibility of contactless and collectorless microflotation, of the importance of overcoming or removing electrostatic barrier at microflotation and of the possibility of flotation even of hydrophilic particles through adsorption of cationic surfactant on bubble surface are presented in Section 10.5. 

Main propositions of the Derjaguin-Dukhin micro flotation theory (1961) are confirmed both with respect to the transport stage and to the attachment of small particles on bubble surfaces. This is demonstrated in Sections 10.1 and 10.5, in a monograph by Schulze (1984) and in reviews by Schulze (1989, 1991, 1993). At the same time, it should be pointed out that some propositions have been substantially changed in the process of development during the period of 30 years. Some of them are not so important as they seemed to be earlier others are still not understood. 

Water can contain impurities which immobilise the surface even of larger bubbles. In this situation to which insufficient attention was paid so far (Derjaguin et al., 1960- 1986) the peculiarity of the transport stage disappears and the problem of DAL loses its importance. At the same time it is important to underline that the loss of interest in the problem of DAL as applied to microflotation has no grounds and is fraught with serious losses for microflotation technology. 

Quite different measures are required when the experimentally determined kinetic constant of microflotation K is close to the calculated one. In this case it is necessary to intensify the transport stage either by arranging preliminary aggregation of particles or by applying two-stage microflotation (Section 10.9). 

Clearly if the depth of the primary energy minimum and cohesive forces in the aggregate are very small, a detachment can take place. To overcome electrostatic repulsion is a critical task in microflotation systems of such type as well as in the transport stage. 

Two possibilities are presented here. Bubbles with a completely or sufficiently strongly retarded surface can be used at Reynolds numbers less than 40. The second possibility is to use millimeter-size bubbles with less than completely-retarded surfaces. It follows from the estimate (10.50) that the transport stage proceeds in both cases with approximately equal intensity. Each variant has its advantages and disadvantages. 

Let us now dwell on the mechanism of electrolysis. The passage of current through an electrolytic cell may be considered as a special case of heterogeneous chemical reaction. As was already mentioned (see Section 6.1), a heterogeneous reaction consists of three stages 1) the transport stage, that is, the transport of... 

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