A mixture containing two types of particles, “flotsam” and “jetsam”, is to be separated into these two components, Singapore

QUESTION 1 Answer BOTH parts (a) and (b)

A mixture containing two types of particles, “flotsam” and “jetsam”, is to be separated into these two components by flowing the particles upwards through a 0.1 m vertical pipe with water. The ranges of particle size and particle density for the two types of particles are as shown in the following table. The mixture may be considered sufficiently dilute such that multiple particle effects are negligible. Stokes’ law may be assumed to be valid throughout this question. The density and viscosity of water are 1000 kg m-3
and 1.0  10-3 Pa·s respectively. Particle type Range of particle size (m) Range of particle density (kg m-3)
Flotsam 1 – 10 1200 – 2400
Jetsam 15 – 20 1500 – 3000

(a) Determine the time taken for the last flotsam particle and the first jetsam particle to exit the 0.1 m vertical pipe if the flow velocity of water is 0.5 mm s-1. Hence, explain briefly whether a perfect separation of the mixture into the two components is possible.

(b) The fluid used in the vertical pipe is to be changed to allow the above separation to be achieved. Design a set of material properties (density and viscosity) for the new fluid that will allow perfect separation between flotsam and jetsam particles. Explain briefly when the collection of each type of particles should be performed.

QUESTION 2 Answer BOTH parts (a) and (b)

The results of a batch settling test are shown in the following table:
Solid concentration, C Superficial particle velocity,
Ups (mm s-1)
0.05 0.023
0.10 0.036
0.15 0.043
0.20 0.046
0.25 0.039
0.30 0.035
where solid concentration, C, is defined to be (1 – ) and  is the voidage of the suspension.

(a)  If a single particle from the above suspension was allowed to settle under gravity through the same liquid, deduce which region (Stokes’ law region, Intermediate region or Newton’s law region) the motion of the particle will belong to. Justify your answer with appropriate calculations and a brief explanation. The liquid may be assumed to be water and particle
density may be taken to be 2000 kg m-3.

(b)  Based on the above information, a liquid fluidized bed containing the same particles and liquid is to be designed. The initial height and voidage of the packed bed of particles to be
fluidized are 10 cm and 0.45 respectively. The height of the fluidized bed required during actual operation is 30 cm. Determine the inlet superficial velocity of the liquid that needs to be applied to achieve this requirement. (10 marks)