This report brings to completion our work on the kinetics and structure of floes grown in shear flows at dilute concentrations. The first phase of the work consisted of detailed measurements of floe structure and growth kinetics for rapid, irreversible flocculation in a simple shear flow with minimal effect of Brownian motion. We employed polystyrene latices of 0.1um diameter in glycerol-water mixtures at 1.0 M NaCl at a volume fraction of lo4 with dynamic light scattering detecting the hydrodynamic radius and static light scattering probing the internal structure of the floes.
Comparison of the results for sheared dispersions with data for Brownian flocculation revealed a similar structure, i.e. floes having characteristics of fractals with dimension d=1.8+0.1 and an equal number of nearest neighbors. Of course, the kinetics differ substantially with shear accelerating the rate in proportion to the Peclet number, which gauges the ratio of shear to Brownian collisions, As the floe size approached lpm, however, the growth rate decreased significantly, suggesting that viscous forces impose a maximum for these tenuous structures. Straightforward calculations -- assuming Smoluchowski kinetics with weak hydrodynamic interactions, adhesion of particles upon contact, and a maximum size estimated by comparing the dispersion attraction to the viscous force -- reproduced the data within the experimental uncertainty.
In the second phase we addressed the evolution of the structure, seeking to understand the similarity between the results for the shear and Brownian modes. This involved hierarchical simulations performed by combining N particles into N/2 doublets, colliding those doublets to form quadruplets, etc., until only a single N-particle floe remained. At each step two aggregates at randomly chosen initial positions and orientations were translated along streamlines of the undisturbed velocity field and rotated with the local vorticity until two particles made contact. There the particles were assumed to stick, forming rigid bonds. The structure was characterized statistically through particle-particle correlation functions within the floes, the variation of the radius of gyration with number of particles, the asymmetry of the shape, and the corresponding light scattering spectrum.
Remarkably, the simulations produce floes with light scattering spectra indistinguishable from those studied experimentally and with no detectable difference between Brownian, shear, and extensional collisions processes. Hence, we conclude that irreversible flocculation, with no subsequent rearrangement or breakup, generates fractals of low dimension (d= 1.8) essentially independent of the kinematics of the collision process. A corollary is that creating compact, uniform floes with d=3.0 must require substantial rearrangement and/or breakup, processes that probably depend on many collisions. Thus future work along these lines must deal with concentrated dispersions and longer shearing times than examined here.