An aqueous suspension of cassiterite (SnO 2 ), galena (PbS) and gold (Au) sphere

Question

An aqueous suspension of cassiterite (SnO2), galena (PbS) and gold (Au) spheres is poured and thoroughly mixed into a cylindrical vessel and allowed to settle. The liquid is water. The original suspension contains 10 wt% each of all three solid components. Particle diameters are 5 micron cassiterite, 25 micron galena and 20 micron gold. The vessel is 200 cm high. The solids are initially completely dispersed throughout the vessel. After settling for one hour, what is the weight fraction of cassiterite to galena to gold in the sediment at the bottom of the vessel? Assume the particles reach a terminal settling velocity instantaneously after being placed in suspension.

Explanation / Answer

For same qty of intial particles,

Terminal velocity is proportional to (Particle size)^.5

Number of Particle is proportional to 1/(Particle size)^3

Mass of Particle settled is proportional to multiplication of Number of Particles and Terminal velocity

=> Mass of Particle settled is proportional to (Particle size)^(.5-3)= (Particle size)^(-2.5)

=>Ratio of SnO2:PbS:Au=(5)^-2.5:(25)^-2.5:20^-2.5

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