Fractal Dimension of Particle Aggregates in Magnetic Fields

REFERENCES

• Smoluchowski, M. Versuch einer mathematischen Theorie der Koagulationskinetic kolloider Lösungen. J. Physik. Chem. 1917, 92, 129–168.
   Google Scholar
• Elimelech, M.; Gregory, J.; Jia, X.; Williams, R. Particle Deposition and Aggregation—Measurement, Modeling and Simulation; Butterworth Heinemann: Oxford, 1995.
   Google Scholar
• Meakin, P. Diffusion-limited aggregation in three dimensions: results from a new cluster–cluster aggregation model. J. Colloid Interf. Sci. 1984, 102. 505–512.
   Web of Science ®Google Scholar
• Mandelbrot, B.B. Fractals: Form, Chance, and Dimension; Freeman: San Francisco, 1977.
   Google Scholar
• Mandelbrot, B.B. The Fractal Geometry of Nature; Freeman: San Francisco, 1982.
   Google Scholar
• Meakin, P. Simulations of aggregation processes. In The Fractal Approach to Heterogeneous Chemistry; Surfaces, Colloids, Polymers; Avnir, D., Ed.: John Wiley & Sons: Chichester, 1989; 131–160.
   Google Scholar
• Torres, F.E.; Russel, W.B.; Schowalter, W.R. Floc structure and growth kinetics for rapid shear coagulation of polystyrene colloids. J. Colloid Interf. Sci. 1991, 142, 554–574.
   Web of Science ®Google Scholar
• Li, X.; Logan, B.E. Permeability of fractal aggregates. Wat. Res. 2001, 35, 3373–3380.
   PubMed Web of Science ®Google Scholar
• Jiang, Q.; Logan, B.E. Fractal dimensions of aggregates determined from steady-state size distributions. Environ. Sci. Tech. 1991, 25, 2031–2038.
   Web of Science ®Google Scholar
• Witten, T.A.; Sander, L.M. Diffusion-limited aggregation, a kinetic critical phenomenon. Phys. Rev. Lett. 1981, 47, 1400–1403.
   Web of Science ®Google Scholar
• Lin, M.Y.; Lindsay, H.M.; Weitz, D.A.; Ball, R.C.; Klein, R.; Meakin, P. Universality in colloid aggregation. Nature 1989, 339, 360–362.
   Web of Science ®Google Scholar
• Ansell, G.C.; Dickinson, E. Aggregate structure and coagulation kinetics in a concentrated dispersion of interacting colloidal particles. Chem. Phys. Lett. 1985, 122, 594–598.
   Web of Science ®Google Scholar
• Wiesner, M.R. Kinetics of aggregate formation in rapid mix. Water Res. 1992, 26, 379–387.
   Web of Science ®Google Scholar
• Chin, C.J.; Yiacoumi, S.; Tsouris, C. Probing DLVO forces using interparticle magnetic forces: transition from secondary-minimum to primary-minimum aggregation. Langmuir 2001, 17, 6065–6071.
   Web of Science ®Google Scholar
• Helgesen, G.; Skjeitorp, A.T.; Mors, P.M.; Botet, R.; Jullien, R. Aggregation of magnetic microspheres: experiments and simulations. Phys. Rev. Lett. 1988, 61. 1737–1739.
   Web of Science ®Google Scholar
• Trohidou, K.N.; Blackman, J.A. Aggregation and segregation in a mixture of magnetic and nonmagnetic particles. Phys. Rev. B. 1995, 51, 11521–11526.
   Web of Science ®Google Scholar
• Tsouris, C.; Scott, T.C. Flocculation of paramagnetic particles in a magnetic field. J. Colloid Interf. Sci. 1995, 171, 319–330.
   Web of Science ®Google Scholar
• Valioulis, I.A.; List, E.J. Collision efficiency of diffusing spherical particles: hydrodynamic, van der Waals and electrostatic forces. Adv. Colloid Interf. Sci. 1984, 20, 1–20.
   Web of Science ®Google Scholar
• Chikazumi, S. Physics of Magnetism, Wiley: New York, 1964.
   Google Scholar
• Yiacoumi, S.; Rountree, D.A.; Tsouris, C. Mechanism of particle flocculation by magnetic seeding. J. Colloid Interf. Sci. 1996, 184, 477–488.
   PubMed Web of Science ®Google Scholar
• Bell, G.M.; Levine, S.; McCartney, L.N. Approximate methods of determining the double-layer free energy of interaction between two charged colloidal spheres. J. Colloid Interf. Sci. 1980, 33, 335–360.
   Google Scholar
• Hogg, R.; Healy, T.W.; Fuerstenau, D.W. Mutual coagulation of colloidal dispersions. Trans. Faraday Soc. 1966, 18, 1638–1651.
   Google Scholar
• Flanagan, D. Java in a Nutshell, O’Reilly & Associates Inc: Sebastopol, 1996.
   Google Scholar
• Hindmarch, A.C.; Byrne, G.D. EPISODE: An Effective Package for the Integration of System of Ordinary Differential Equations; 1976; Lawrence Livermore Laboratory Report UCID-30112.
   Google Scholar
• Chin, C.J.; Yiacoumi, S.; Tsouris, C. Shear-induced flocculation of colloidal particles in stirred tanks. J. Colloidal Interf. Sci. 1998, 206, 532–545.
   PubMed Web of Science ®Google Scholar
• Spicer, P.T.; Keller, W.; Pratsinis, S.E. The effect of impeller type on Hoc size and structure during shear-induced flocculation. J. Colloid Interf. Sci. 1996, 184, 112–122.
   PubMed Web of Science ®Google Scholar