**2. Flotation theory in brief**

Solids removal of the new process water treatment system VoxSton is based on centrifugal and screw separation. Separation and removal of soluble ingredients are based on OxTube separation, molecular activation, and flotation in tube and cell condition. Flotation bubbles are generated by OxTube in VoxFlot water intake and fed them to bottom of the cell. The design principles of the VoxFlot are based on the flotation theory that is preferred here in brief [1–3]. The OxTube treatment and VoxFlot flotation are described in Chapter 3.


#### **Table 1.**

*Conclusions on the comparison of the novel VoxSton and present industrial process water treatment systems of the same capacity.*

The mechanisms for the bubble-particle attachment are very complex and consists of three steps; collision, attachment (adsorption) and detachment (desorption). The collision is achieved by particles being within the collision tube of a bubble and this is affected by the velocity and radius of the bubble. The collision tube corresponds to the region in which a particle will collide with the bubble.

The attachment of the particle to the bubble is controlled by the induction time of the particle and bubble. The particle and bubble need to bind and this occurs if the time in which the particle and bubble are in contact with each other is larger than the required induction time. This induction time is affected by


The detachment of a particle and bubble occurs when the force exerted by the surface tension is exceeded by shear and gravitational forces. These forces are complex and vary within the cell. High shear will be experienced close to the impeller of a mechanical flotation cell and mostly gravitational force in the collection and cleaning zone of a flotation column.

The attachment of the bubbles to the surface is determined by the interfacial energies between the solid, liquid, and gas phases. This is determined by the Young-Duprè equation [1]

$$\mathbf{'}\mathbf{'}\mathbf{'}\_{l\nu}\mathbf{cos}\mathbf{6} = \left(\mathbf{'}\mathbf{'}\_{w} - \mathbf{'}\mathbf{'}\_{d}\right) \tag{1}$$

where:


A common quantity used to describe the collection efficiency of a flotation process is *flotation recovery R*. This quantity incorporates the probabilities of collision and attachment of particles to gas flotation bubbles [2, 3].

$$R = \frac{N\_c}{\left(\frac{\pi}{4}\right) \left(d\_p + d\_b\right)^2 H\_C} \tag{2}$$

where:

