Particles may aggregate in water as a result of their hydrophobicity or Van der Waals attractions. Such aggregates are called flocs and the process is termed flocculation. (Aerosols also can flocculate.) The objective is to explore how this affects gravitational settling. Suppose that an individual particle is a sphere with diameter d = 10 μm and density ρ_o = 2000 kg/m³.

(a) Evaluate the terminal velocity u of an individual particle.

(b) Suppose that 1000 particles form a nearly spherical floc of diameter D. If the floc has a void fraction of ε = 0.50, what will D be?

(c) If the floc of part (b) behaves as an impermeable sphere, what will its terminal velocity U be? How does U compare with u?

(d) Whether water flow through the floc is actually negligible can be checked by viewing the floc as a miniature packed bed and estimating the superficial velocity. Predict k for the floc. To obtain v_s from Eq. (3.4-3), let L = D⁄2 and (because Re_p < 1) use the viscous pressure scale as an estimate for 

Is v_s ≪ U, as assumed in part (c)?