Floc cohesive force in reversible aggregation: a Couette laminar flow investigation.
A simple theoretical model is proposed to describe the limiting size of aggregates attained at steady state under given shear conditions. The stable size is assumed to be the result of a dynamic equilibrium between simultaneous aggregate growth and breakup that are represented as first-order processes. The theory establishes that the evolution of steady-state aggregate size versus shear rate is written as the sum of two exponential laws. The validity of the model is verified by direct observation of the coagulation behavior of latex particles in the stagnant plane of a counter-rotating Couette reactor. The influence of latex elementary particle size, initial particle volume fraction, and inner gap spacing of Couette reactor, are investigated. In all cases, the model shows good agreement with the experimental results. Aggregate growth proceeds with a monomodal size distribution that exhibits a scaling behavior. Such monomodal distribution evolves toward broad and even bimodal steady-state distributions at both low and high shear rates, whereas a narrow monomodal pattern is observed at intermediate shear gradients. The aggregate cohesive force F(C) can be calculated from the critical shear rate of dislocation defined by the model. In contrast to the broadly accepted view that larger flocs should be more fragile than smaller aggregates, we find that F(C) scales as D(3/2) where D is the aggregate characteristic diameter. The latter relationship may be derived by assuming linear elasticity of aggregates.
Nancy University-LEM-ENSG/INPL-CNRS, BP 40 54501 Vandoeuvre Cedex, France.
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