Attachment of particles to a liquid surface (capillary theory of flotation)

Abstract

On the basis of the theory of capillarity, the process of formation of a wetting perimeter when a spherical particle touches a planar liquid surface is analysed taking into account the line energy of this perimeter. The minimum size of particle which can float is calculated and an accurate estimate is made for the minimum time of touching of particle and surface. The kinetic energy of collision between an air bubble and the particles is used to calculate the maximum size of particles which can remain attached for flotation. Flotation data suggest that a lower limit for the size of isolated particles which can be floated is of the order of 1 pm and a comparison of this radius with the theoretical limit gives a value of dyn for the line energy of the wetting perimeter. Predictions of the

Force measurements with the atomic force microscope: Technique, interpretation and applications

“…41c). The capillary force F cap acting on the particle is given by [880] F cap ¼ 2pRg sin a sinðu r À aÞ; (9.1) where R is the particle radius, g the surface tension of the liquid, a the immersion angle (see Fig. 42) and u r is the receding contact angle of the liquid on the sphere.…”

Detachment energies of spheroidal particles from fluid-fluid interfaces

“…The detachment energy of a single particle from a fluidfluid interface plays a vital role in our understanding of particle-stabilised emulsions and, for example, flotation processes, whereby particles selectively attach to bubbles depending on their contact angle, isolating the desired mineral. Previous detachment energy studies focussing on free energy differences between an equilibrated particle at an interface (buoyancy, gravity, and surface-tension forces interact to determine a particle's equilibrium position at an interface) [8][9][10][11][12][13][14][15] and in the bulk revealed a crucial dependence on particle shape: prolate and oblate spheroidal particles attach to interfaces more strongly because they reduce the interface area more than spherical particles for a given particle volume. [16][17][18][19][20][21] For a particle already adsorbed at an interface to detach itself, the particle must deform the interface and overcome the interface's resistive force: there is a free-energy barrier and an associated activation energy.…”

Geological Disposal of Nuclear Waste: Fate and Transport of Radioactive Materials

“…However, the gravity and buoyancy forces can be neglected for small particles with radii < 500 µm [57,58,64,70]. In experimental setup, when the liquid-gas interface moves in upward direction over the vertically mounted glass slide, the horizontal component of surface tension force (F γ ) is the detachment force (F det ) which is opposed by the DLVO force (F att ) ( Figure 6).…”

“…If capillary force dominates then the colloidal particles attracted towards the liquid-gas interface and if electrostatic dominates then the colloidal particles remain stay over the grain surface. The hydrodynamic forces may be neglected for the colloidal size particles [57,58,64]. Figure 6 shows the force balance between electrostatic force and the capillary force for hydrophilic and hydrophobic particle attached with the solid surface when liquid-gas interface moved in the upward direction.…”

“…In experimental setup, when the liquid-gas interface moves in upward direction over the vertically mounted glass slide, the horizontal component of surface tension force (F γ ) is the detachment force (F det ) which is opposed by the DLVO force (F att ) ( Figure 6). The detachment force (the maximum horizontal surface tension force) can be calculated by [45,57,58,64]:…”