Turbulent disruption of flocs in small particle size suspensions

Abstract

Abstract In the absence of turbulent fluctuations the main effect of a velocity gradient on the floc properties is a rearrangement of particles within the floc producing a more dense floc structure. When the suspension is sufficiently dilute that floc‐floc collisions are negligible, the limits on the floc diameter are (1 + α) 5/3 < ( D f / D p ) ⩽ (1 + α) 2 , where α is the ratio of the volume of fluid immobilized in the floc structure to volume of solids in the floc structure as determined from hindred‐settling measurements. These results set an upper limit on the floc size. Under turbulent flow conditions the principle mechanism leading to floc rupture is pressure differences on opposite sides of the floc which cause bulgy deformation and rupture. The breakup of the floc is resisted by the yield stress τ y and is promoted by an increase in the energy dissipation per unit mass of fluid ϵ. Because the energy dissipation per unit mass is at a maximum near the pipe wall, the floc size is at a minimum in this same region. By application of the concepts of local isotropy, the floc size is found to be proportional to (τ y 9 /ϵ 5 ) 1/2 once the turbulent intensity is sufficient to overcome the yield stress. In the wall region the floc diameter is proportional to ( du / dr ) 3 (τ y 9 /ϵ 8 ) 1/2 .