Liquid interlayer

Fig. 111-27. Formation of a liquid interlayer between grains in polycrystalline substance when the Gibbs-Smith condition is fulfilled...

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. 

Therefore, it is necessary to take into consideration surface roughness which determines the face of such particles. The resistance to thinning of the interfacial film can be drastically reduced if the angles between the faces are sufficiently sharp so that "intrusion" of the liquid interlayer by a sharpened section of the particle surface may take place. Such geometric conditions of the elementary flotation act also drastically facilitates motion against the disjoining pressure of the DL. 

The greater the equilihrium thickness of the liquid interlayer in a contactless flotation, the higher is the probability of detachment of particles from the Inibble and the more important is the decrease of the bubble size, which reduces the detaching forces. 

O.K St < 1 An inelastic inertia impact of particles on a bubble siuface is characteristic and, as will be shown below, a major portion of kinetic energy of the particles get lost both during the approach to the bubble and at the impact itself, when a liquid interlayer of liquid is formed between the surfaces of a particle and a bubble. 

Fig. 1 l.I. Diagram illustrating the impact of a spherical particle on a bubble surface with the formation of a liquid interlayer. 

The energy of the particle at the instant of liquid interlayer formation W] is given by... 

The length of the repetitive recoil 1, is smaller than the particle diameter. It measn that the particle and the surface oscillate together including the liquid interlayer. Eq. (11.55) has to be generalised to regard for this effect. These results differ essentially from the results given by Rulyovetal.(1987,1988). 

It was foimd that the degree of energy dissipation caused by viscous flow in the liquid interlayer approaches 100% at sufficiently small cone angle, which provides high rate of t.p.c. extension. Under these conditions, separation of particle from the bubble surface is prevented. The attachment is provided by first collision of particles with large diameter, i.e. 200pm. 

It is necessary to develop the theory of DAL for extending liquid interlayers. When the t.p.c. line moves, a transfer of surfactant fi-om the liquid/gas to the solid/liquid interface and vice versa is possible. Thus, there are changes in the interfacial energy and surface tension of the liquid in the region of the moving liquid meniscus which depend on the diffiision rate of surfactant molecules (Schulze 1992). Consequently, the movement of the liquid meniscus can also depend on the kinetics of the surfactant desorption-adsorption. Some additional remarks will be given in Section 12. 

The equations describe that stage of the particle movement when the liquid interlayer is thin and the distance between the centres of a particle and the bubble is equal to a. The rates of interlayer thinning and particle movement are identical and are controlled by the action of the pressing force F and the resistance force (product of Stokes drag coefficient and the... 

At St > St the inertial impact of a particle deforms the bubble surface, creates a thin water layer between the particle and bubble and makes the particle jump back from the bubble surface. This decreases the collision efficiency which otherwise rises with the particles size. For particles of subcritical diameter the collision efficiency increases with particle diameter. The proposed theory of inelastic collision unlike other theories describes the coupling of inertial bubble-particle interaction and water drainage from the liquid interlayer. 

We have described the theory of repetitive collision to show that the minimum thickness of the liquid interlayer during a second collision many times exceeds h . Thus, the attachment by a second collision is also impossible with particles with surfaces that are too smooth. The derived equation of the particle trajectory between the first and the second collision is restricted to Stokes numbers St < 1. Only one repetitive collision is possible under this condition. An additional restriction is given by the difference between St and St which must not be too small. 

The Liquid interlayer Stabilisation by Dynamic Adsorption Layers in Elementary Flotation Act... 

Fig. 12.1. Liquid interlayer stabilisation by a dynamic adsorption layer trajectory of a flat particle along the bubble surface (a), adsorption distribution (b), velocity v(r) in the interphase film (c), Jd is the diffusion flux (d)...

The flow forcing a particle to the bubble surface also causes excess pressure in the liquid interlayer 8p(r) which should compensate for F,... 

Fig. 12.2. Minimum thickness of the liquid interlayer h j for different bubble surface sections characterised by the angle 0, The region where the impossibility of deposition has not been proved, 0<0ci-.

Here z = 0 and z = h correspond to the surfaces of the liquid interlayer between the bubble and the solid particle. Two unknown constants which appear in the solution of Eq. (12.8) are determined by the boundary condition (12.9). Substitution of the expression for v(r,z) in Eq. (12.7) and integration gives a relation between pressure and adsorption distribution within the interphase film. 

Now, we use the dependence 0(t) which characterises the liquid interlayer and the particle transport along the bubble surface... 

The time of existence of the liquid interlayer (the time of the bubble motion with the adjacent particle surface section) is of the order of x,. The time of equalisation of the concentration in the liquid interlayer by diffusion is of the order of Tq. If Xp/Xb)) there is no time for diffusion to restore a concentration gradient. So, at large values of X[j/X, its influence on stabilisation is significant (cf. Eq. (12.23)). 

From Eq. (12.16) it can be seen that at 0->O the rate of surface motion and accordingly the particle with the liquid interlayer is reduced. Therefore, the closer the particle to the upper pole of the bubble, the less pronounced is the concentration gradient in the interphase film. Consequently, h, , is reduced with 0, given by Eq. (12.20), and the particle deposition is possible near the front pole. 

During the transition fi-om a plate-like particle to a spherical one a fast weakening of the liquid interlayer stabilisation effect is expected. With the same excessive pressure in the gap, caused by the pressing force, the film thinning would be more intensive, because the thickness of the liquid interlayer (in case of a sphere) is rapidly increased, directed from its centre. This supports the outflow of liquid. 

In the absence of the already mentioned phenomenon of liquid interlayer stabilisation the extreme trajectory is determined by the fact that a particle approaches the bubble at a distance of Her Integration results in... 

The theory of Dukhin (1981) was generalised by Listovnichiy Dukhin (1986) where the effect of stabilisation is considered under arbitrary hydrodynamic flow conditions around a bubble and the effect of convective transfer of surfactant into the adsorption layer was taken into account. Numerical estimations of 0, were carried out and it was shown that the effect of the liquid interlayer stabilisation by a DAL decreases the flotation efficiency over a wide range of system parameters by more than an order of magnitude. Numerical estimations also point to the fact that the effects under consideration have a much smaller influence on flotation of spherical particles than of disk-shaped particles. 

When drops or bubbles approach each other their diffusion layers overlap. This leads to local changes in the surface concentration and surface tension which causes liquid to flow into or out of the thick liquid interlayer. The dynamic adsorption layer and its diffusion layer deviate from electroneutrality and contain charges of opposite sign. The charged dynamic adsorption layer and the oppositely charges diffusion layer as a whole are electroneutral. This ensemble can be called the secondary electrical double layer. 

Dynamic adsorption layers (DAL) influence practically all sub-processes which manifest themselves in particle attachment to bubble surfaces by collision or sliding. Surface retardation by DAL affects the bubble velocity and the hydrodynamic field and consequently the bubble-particle inertial hydrodynamic interaction. It also affects the drainage and thereby the minimum thickness of the liquid interlayer achieved during a first or second collision or sliding. Thus elementary acts of microflotation and flotation is systematically considered in this book for the first time with accoimt of the role of DAL. Extreme cases of weakly and strongly retarded bubble surfaces are discussed which assists to clarify the influence of bubble and particles sizes on flotation processes. 

Knowing the relationship between n and H, as well as an approximate value of the width of the gap between the contiguous solids with the presence of a liquid interlayer [70-72], we can determine the value of . Calculations [73] show that, for the case of particle adhesion in a liquid medium, the actual values of n vary from 2 to 3, i.e., 2[Pg.59]

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