Question

2. Comparing sedimentation and flotation um spherical floc particles with a density of 1.15 g/cm3 pm spherical floc particles with a density of 1.15 g/cm Calculate the settling velocity of 12 in summer (T-20°C) and in winter (T 4°C). Calculate the rise velocity of the same floc particle after the attachment of a single air bubble of 40 um diameter for the same two temperatures. The density of air is 1.27 kg/m3 at 4°C and 1.19 kg/m3 at 20°C Comment on the results of the calculations in a and b with respect to sedimentation and DAF tank design a. b. c.

Answer 1

Basis: The fluid medium is air. The density of air is 1.27 kg/m³ at 4 ^oC and 1.19 kg/m³ at 20 ^oC.

For dilute suspensions, Stokes' law can be applied tp predict the settling velocity of small spheres in air, given as:

v = 2 (?_p -?_a).g.r²/9?

where v = settling velocity, ?_p = particle density (1.15 g/cm³ =1.15 x 10³ kg/m³), ?_{a =} density of air (1.27 kg/m³ at 4 ^oC and 1.19 kg/m³ at 20 ^oC), g = 9.8 m/s², r = 6 x 10^-6 m and ? = air visocity (1.7478 x 10^-5 kg/m.s at 4 ^oC1.8205 x 10^-5 kg/m.s at 20 ^oC)

Now substituting above data, the settling velocity are obatained as:

v (20 ^oC) = 4.947 x 10^-3 m/s or 0.4947 cm/s

v (4 ^oC) = 5.153 x 10^-3 m/s or 0.5153 cm/s

(b) When the bubble is attached with particle, the particle start moving up. The buoyant force will be opposite in direction with drag force and following relation can be applied:

v = 2 (?_p +?_a).g.R²/9?

where v = settling velocity, ?_p = particle density (1.15 g/cm³ =1.15 x 10³ kg/m³), ?_{a =} density of air (1.27 kg/m³ at 4 ^oC and 1.19 kg/m³ at 20 ^oC), g = 9.8 m/s², R =bubble radius 20 x 10^-6 m and ? = air visocity (1.7478 x 10^-5 kg/m.s at 4 ^oC1.8205 x 10^-5 kg/m.s at 20 ^oC)

Now substituting above data, the rise velocity of particle with bubble can be obatained as:

v (20 ^oC) = 0.12394m/s or 12.394 cm/s

v (4 ^oC) = 0.1291m/s or 12.91 cm/s

(c) It can be seen from above calculations that the rise velocity of particle with bubbles (part b) is much higher than the settling velocity of particle (part a).

So the rate of settling process will be lower than floation process.

The volume of sedimentation tank required will be much higher than DAF (dissolved air flotation) tank.