Advances in Water Treatment and Enviromental Management

170 WATER TREATMENT4–3 Analytical expression for collection efficiencyWe consider that all the flow rate Q flows through Region II. The variation dC of theconcentration of the light dispersion between two cross sections separated by dx can bewritten:(5)Fig. 6 Swirl decay—— Formula (4), K=2.2Exp, points: o Q=10,8m3/h;Ue:7m/s. Q=7,7m3/h;Ue:5m/sW is the migration velocity of the droplet at the boundary between region II and region I(r=RO/2) and can be written according to Stokes law: 2(6)∆δ being the density difference between the water and the suspension, u the viscosity ofwater, d the diameter of the droplets and b a correction factor depending of the size of thedroplet. We can take, according to Ref.4:Re being the Reynolds number of the droplet.According to section 3, we can calculate the acceleration “a” in a given cross section from themean value of the velocity between the wall and the boundary r=RO/2,that is:(7)We know from section 3 that V(r=RO/2) is constant all along the separation chamber and canbe written V=1.6 Vs, which leads, according to Eq (4),to:(8)whereas(9) vo(x) = vo /(1+K.X)Combination of Eq. (5) to (9) gives the equation governing the variation of the light dispersionconcentration along the separation chamber, which is: