## Direct Contact of a Particle with a Bubble

In this collection process, a particle encounters a bubble, either by relative motion or the turbulence in a flotation system. The probability of the particle being captured by the bubble (P) can be expressed as:

where Pc, Pa and Pd are the probability of bubble/particle collision, attachment and detachment, respectively. For a hydrophobic particle, bubble/particle collision determines the particle collection rate governed by hydrodynamic conditions. Hydrodynamic analysis showed that the collision probability between a descending particle with an ascending bubble is given by:

where parameters a and n are a strong function of hydrodynamic characteristics of the system. Eqn [2] shows that the probability of particle-bubble collision is proportional to the nth (n > 1) power of the solid particle size (dp) and inversely proportional to the same power of the bubble size (db). For fine particles, small bubbles have to be used to obtain sufficient particle-bubble collisions. The direct contact was analysed between a descending fine particle of dp = 10 |im and a rising swarm of bubbles in a flotation column. A collection zone as tall as 10 m was determined to be essential to ensure at least one collision of the particle with a bubble. This implies an inefficient collection process under conventional column flotation conditions.

To increase the particle-bubble contact frequency, a relatively high turbulence or energy dissipation rate is required, as in mechanical flotation machines. The number of particle-bubble collisions per unit volume and time in a highly turbulent flowing fluid (Zpb) can be expressed as:

where Np and Nb are the number concentrations of particles and bubbles in the pulp. Vp and Vb are the mean relative velocities of the particles and bubbles (with reference to fluid), which are given collectively by:

In eqn [4], subscript i refers to bubble or particle, s is the specific energy dissipation rate, Ap is the difference in densities of particle i and liquid medium, p is the medium density, and v is the kinematic viscosity. This equation shows that a high energy dissipation rate favours particle-bubble collision. However, vigorous agitation as in mechanical flotation machines may break particle-bubble aggregates, thereby increasing the probability of particle detachment from bubbles and hence decreasing the overall collection rate. In addition, the back mixing (or liquid circulation) caused by increased turbulence may hinder the transport of bubble-particle aggregates out of the turbulent zone, contributing to low flotation kinetics. The incentive to separate the two functions of a flotation machine, i.e. aeration and separation, is evident, as reflected in the reactor-separator design.

## Solar Panel Basics

Global warming is a huge problem which will significantly affect every country in the world. Many people all over the world are trying to do whatever they can to help combat the effects of global warming. One of the ways that people can fight global warming is to reduce their dependence on non-renewable energy sources like oil and petroleum based products.

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