Aggregation kinetics of small particles in agitated vessels

Rapid coagulation by turbulence in stirred tanks was studied for particles and aggregates smaller than the Kolmogorov microscale. The coagulation kinetics are determined by the floc structure and by the hydrodynamic and colloidal interactions between the colliding particles. The collision efficiency for doublet formation in the heterogeneous shear field of a stirred tank follows from particle trajectory analysis of solid particles in simple shear flow, provided the simple shear rate is made to correspond to the residence time weighted turbulent shear rate. Experimentally, the resulting aggregates proved to be fractal-like with their porosity increasing with aggregate size. Porosity within the aggregates results in penetration of the floc surface by the fluid flow, giving rise to enhanced collision efficiencies compared to solid particles. The collision efficiencies between porous flocs may be estimated by a model that pictures a porous floc as consisting of an impermeable core and a completely permeable shell. With the collision efficiencies from this shell-core model the aggregate growth could be described adequately.

[1]  W. R. Schowalter,et al.  The effect of Brownian diffusion on shear-induced coagulation of colloidal dispersions , 1983, Journal of Fluid Mechanics.

[2]  Bruce E. Logan,et al.  Fractal dimensions of aggregates determined from steady-state size distributions , 1991 .

[3]  E. Ruckenstein,et al.  Similarity solutions of population balances , 1974 .

[4]  P. Latimer Experimental tests of a theoretical method for predicting light scattering by aggregates. , 1985, Applied optics.

[5]  J. Visser On Hamaker constants: A comparison between Hamaker constants and Lifshitz-van der Waals constants , 1972 .

[6]  P. Adler Heterocoagulation in shear flow , 1981 .

[7]  R. J. Hunter,et al.  Flow properties of coagulated colloidal suspensions: I. Energy dissipation in the flow units , 1976 .

[8]  R Hogg,et al.  Effects of flocculation conditions on agglomerate structure , 1986 .

[9]  K. Higashitani,et al.  Turbulent coagulation of particles dispersed in a viscous fluid. , 1983 .

[10]  R. West,et al.  Optical properties of aggregate particles whose outer diameter is comparable to the wavelength. , 1991, Applied optics.

[11]  John Happel,et al.  Viscous flow in multiparticle systems: Slow motion of fluids relative to beds of spherical particles , 1958 .

[12]  U. Baltensperger,et al.  Scaling behaviour of physical parameters describing agglomerates , 1990 .

[13]  Uhlherr Peter Heinz Theodore,et al.  Flocculation in stired tanks , 1984 .

[14]  Karel Antonius Kusters,et al.  The influence of turbulence on aggregation of small particles in agitated vessels , 1991 .

[15]  P. Saffman,et al.  On the collision of drops in turbulent clouds , 1956, Journal of Fluid Mechanics.

[16]  Norihito Tambo,et al.  Physical characteristics of flocs—I. The floc density function and aluminium floc , 1979 .

[17]  K. Higashitani,et al.  Kinetic theory of shear coagulation for particles in a viscous fluid. , 1982 .

[18]  D. Thoenes,et al.  Coagulation in turbulent flow. Part II , 1989 .

[19]  H. V. Hulst Light Scattering by Small Particles , 1957 .

[20]  W. R. Schowalter,et al.  Stability and Coagulation of Colloids in Shear Fields , 1984 .

[21]  S. G. Mason,et al.  Orthokinetic collisions of hard spheres in simple shear flow , 1976 .

[22]  B. Dobiáš,et al.  Coagulation and flocculation : theory and applications , 1993 .

[23]  M. Smoluchowski Versuch einer mathematischen Theorie der Koagulationskinetik kolloider Lösungen , 1918 .

[24]  D. Thoenes,et al.  Particle sizing by laser diffraction spectrometry in the anomalous regime. , 1991, Applied optics.

[25]  Gordon P. Treweek,et al.  Size distributions of flocculated particles: application of electronic particle counters , 1977 .

[26]  L. Brakalov A connection between the orthokinetic coagulation capture efficiency of aggregates and their maximum size , 1987 .

[27]  V. Oles Shear-induced aggregation and breakup of polystyrene latex particles , 1992 .

[28]  J. Gregory Flocculation in laminar tube flow , 1981 .

[29]  P. Adler Streamlines in and around porous particles , 1981 .

[30]  W. Russel,et al.  Structure and breakup of flocs subjected to fluid stresses: I. Shear experiments , 1986 .

[31]  G. D. Boer Coagulation in stirred tanks , 1987 .

[32]  S. Bruckenstein Physicochemical hydrodynamics , 1977, Nature.

[33]  W. Saarloos On the hydrodynamic radius of fractal aggregates , 1987 .

[34]  W. Russel,et al.  SIMULATIONS OF COAGULATION IN VISCOUS FLOWS , 1991 .

[35]  C F Bohren,et al.  Forward-scattering corrected extinction by nonspherical particles. , 1985, Applied optics.

[36]  D. Thoenes,et al.  Numerical particle tracking in a turbine agitated vessel , 1992 .

[37]  S. G. Mason,et al.  The microrheology of colloidal dispersions VII. Orthokinetic doublet formation of spheres , 1977 .

[38]  P. Adler Interaction of unequal spheres , 1981 .

[39]  S. Friedlander,et al.  The coagulation of hydrosols by brownian motion and laminar shear flow , 1964 .

[40]  H Gomi Multiple scattering correction in the measurement of particle size and number density by the diffraction method. , 1986, Applied optics.

[41]  Modelling shear-flocculation by population balances , 1987 .

[42]  W. Russel,et al.  Structure and breakup of flocs subjected to fluid stresses: II. Theory , 1987 .

[43]  W. Russel,et al.  Floc structure and growth kinetics for rapid shear coagulation of polystyrene colloids , 1991 .