Flocculation rate of locally densely distributed cohesive particles in Taylor–Green vortex flow

We employ the three-way coupled numerical simulations to investigate the flocculation of primary cohesive particles which are locally densely distributed in the Taylor–Green cellular vortex flow. The hydrodynamic and inertial forces as well as the direct contact, lubrication, and cohesion forces between particles during the growth, deformation, and breakup of flocs are captured in detail. The flocculation rate of the primary particles decreases gradually from its maximum value at the initial moment, then levels off during flocculation, yielding the flocculation and equilibrium stages. The flocculation rate is determined by the equilibrium floc size and a flocculation coefficient. A larger equilibrium floc size and a smaller value of the flocculation coefficient yield faster flocculation. An initially dense distribution of cohesive particles accelerates the growth of flocs during flocculation but has minor effects on the equilibrium floc size, compared to an initially dilute distribution. A larger particle-to-fluid density ratio, a smaller size ratio between the particle diameter and the Kolmogorov length scale, and stronger cohesion yield a larger equilibrium floc size and a higher flocculation coefficient. Their influence on the flocculation coefficient becomes more evident when the initial particle distribution becomes more concentrated, while their impact on the maximum flocculation rate is very limited. A simple new model is proposed to describe the flocculation process of unevenly distributed cohesive particles in turbulence.