Analysis of particle trajectories of small particles in flotation when the particles and bubbles are both charged

Abstract

The trajectory of a small particle moving to a bubble surface was analyzed by taking into account the effects of surface charges of the bubble and particle and the short range hydrodynamic interaction near the bubble surface, in a flotation process. The particle trajectories obtained theoretically were in good agreement with those obtained by direct observation. Even if the signs of the surface charges of the bubble and particle were the same, the particle adhered to the bubble surface when the net surface force, that is, the sum of the electrostatic force and the van der Waals force, was attractive. Particle capture efficiency, vs, per bubble was estimated by trajectory analysis and the flotation efficiency, qT, was calculated. The values of q calculated by the particle trajectory analysis were in reasonable agreement with those obtained experimentally. The dependence of particle diameter on q T was also examined by the particle trajectory analysis.~~ ~~~~ ~. . . ~~ ~~~~ On a analyse la trajectoire d'une petite particule se dtplaFant vers la surface d'une bulle en tenant compte des effets des charges de surface de la bulle et de la particule ainsi que de I'interaction hydrodynamique h courte distance pres de la surface de la bulle, dans un processus de flottaison. Les trajectoires de particules obtenues de maniere thdorique montrent un bon accord avec celles obtenues par observation directe. M&me si les signes des charges de surface de la bulle et de la particule sont identiques, la particule adhere B la surface de la bulle lorsque la force de surface nette, a savoir la somrne de la force Clectrostatique et la force de van der Waals, est attractive. L'efficacitt de capture des particules, q5, par bulle, a CtC estimCe par l'analyse de la trajectoire et I'efticacite de la tlottaison, v T , a CtC calculee.Les valeurs de q r , calculee par I'analyse de la trajectoire des particules, concordent raisonnablement avec celles obtenues expkrimentalement. La dipendance du diametre de particule sur q a Cgalement Ctt examinCe par l'analyse de la trajectoire des particules.

Trajectory Analysis and Collision Efficiency during Microbubble Flotation

“…In Eqs. [9] and [10] above, A is the Hamaker constant. Since the van der Waals force is the net result of induced dipoledipole interactions between the molecules comprising spheres 1 and 2, the Hamaker constant depends on the composition of the two spheres and on the medium between the two spheres.…”

“…Experiments by Collins and Jameson (18,19) and others (20 -22) have shown that collision efficiencies can be dramatically altered by changing the electrical properties of the bubble and particle surfaces and of the surrounding fluid. The experiments by Okada et al (10) have also shown that the relative trajectories of particles around bubbles can be strongly effected by electrostatic forces. In this paper the influence of electrostatic forces (which were neglected in (7)) and van der Waals forces will be included in a mathematical model of the interaction of a rising bubble and a solid spherical particle in microbubble flotation.…”

“…The use of both Eqs. [9] and [10] to calculate the van der Waals potential is required in order to account for retardation effects. At short separation distances (h Ӷ L where h ϭ r Ϫ a 1 Ϫ a 2 ) the electromagnetic waves of the induced dipole-dipole interactions can be regarded as instantaneous (unretarded), while at large separation distance (h ӷ L ) the finite propagation time of the waves result in retarded van der Waals forces.…”

Strategy for selection of methods for separation of bioparticles from particle mixtures

“…For two spherical particles with zeta-potentials between À60 mV and 60 mV (Hogg et al, 1965) the electrostatic interaction force can be approximated with the following equation (Hogg et al, 1965;Okada et al, 1990a):…”

“…In order to calculate the interaction force between a surface and a spherical particle at close distances the diameter of one of the two spheres can again be chosen much larger than the other. This results in the following approximation (Hogg et al, 1965;Okada et al, 1990a):…”