Characterization of materials by Hallimond tube flotation, Part 3. Maximumsize of floating and interacting particles

The tests carried out with solids of different hydrophobicities and densiti es, floated individually and as a collection of particles in the monobubble Hallimond tube, allowed to characterize flotation in this small-scale labo ratory flotation device and determine the maximum size of entrained particl es, maximum size of floating particles, particle hydrophobicity, increase o f the apparent density of the particle in contact with air bubble due to ag gregation with other particles, and flotometric equations interrelating the se parameters. Hydrophilic particles do not float in the Hallimond tube but there is some mechanical entrainment governed by the equations: a(max)(rho (p) - rho(w))/rho(w) = 0.023 +/- 0.002 valid for particles with density gre ater than 2 g/cm(3) and a(max)((rho(p) - rho(w))/rho(w))(0.75) = 0.0225 +/- 0.0025 (cm) applicable for less dense particles, where a(max) is the maxim um size of entrained particles (in cm), rho(p) is the particle density, and rho(w) denotes density of the aqueous phase (in g/cm(3)). Hydrophobic part icles tend to form aggregates and float as a cluster but no interaction was detected for contact angles (theta(s)) below 20 degrees. Thus, for theta(s ) < 20 degrees the flotation of a collection of particles can be characteri zed by the same equations as for flotation of individual particles includin g the simplified formula of Scheludko D-max(2)(rho(p) - rho(w)) = 6 sigma g (-1) sin(2)(theta(s)/2) in which g is the acceleration due to gravity, sigm a stands for the surface tension of water, and D-max is the maximum size of floating particles. Hydrophobic interactions between particles become sign ificant for theta(s) > 20 degrees. When 20 degrees > theta(s) > 55 degrees and the number of particles in the cluster is greater than 1, the flotation of an ensemble of particles is given either by: d(max)(2)n(rho(p) - rho(w) ) = 6 sigma g(-1) sin(2)(theta(s)/2) or by: d(max)(rho(p) - rho(w)) = k sin (2)(theta(s)/2) (g/cm(2)), where n is defined as (D-max/d(max))(2) and the term n(rho(p) - rho(w)) represents a new apparent density of the particle i n contact with air due to aggregation with other particles which do not tou ch the bubble, d(max) is the maximum size of floating and interacting parti cles, and k is a constant equal to 2.08 g/cm(3). It was established that th e clustering does not occur sharply at theta(s) = 20 degrees but it depends on the density of particles and that for less dense particles occurs at hi gher hydrophobicity. For theta(s) > 55 degrees the flotation of a cluster o f particles is not influenced by hydrophobicity and the equation: d(max)(rh o(p) - rho(w)) = 0.40 +/- 0.05 (g/cm(2)) is valid. (C) 1999 Elsevier Scienc e B.V. All rights reserved.