Measurements of effective sizes and diffusivities of nano-colloids and micro-particles

Jaeweon Cho, Young Jun Park, Hyang Sun, Suhan Kim, Yeomin Yoon

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


A theoretical diffusivity equation was proposed by Einstein [A. Einstein, Investigations of the Theory of the Brownian Movement, Dover Publication Inc., New York, 1956]; thermodynamic and drag (i.e., resistance or mobility relation) forces were compared at equilibrium. The diffusivity relationship, the ratio of the thermodynamic and drag forces, was combined with steady-state convection and diffusion equations to finally give a relationship between the retention times from flow field-flow fractionation (fl-FFF) and the diffusivity of a particle. An asymmetric fl-FFF system equipped with a regenerated cellulose membrane with molecular weight cutoff of 1000 and a micro channel employing both laminar channel and cross flows, was used to obtain chromatograms, using UV detection. A wide range of nano-colloids and micro-particles were measured with respect to their effective sizes and diffusivities. The classical FFF theory was incorporated with two different diffusion estimation relations: the Brownian and shear-induced diffusivities. It was found that the fl-FFF system provided similar and much lower sizes compared to absolute sizes provided by the manufacturer, for the smaller colloids (30, 60 nm), and the larger nano-colloids (90 nm and 0.2, 0.3, 0.43 and 0.5 μm) and micro-particles (0.5, 0.701, 0.993, 2, 3.1, and 8 μm), respectively. This was due to the larger nano-colloids and micro-particles being influenced by both the Brownian (the normal FFF mode) and shear-induced (the hyperlayer FFF mode) diffusions under the channel laminar and crossing flows condition within the micro channel of the fl-FFF system, which provided effective colloids and particles sizes. For all the nano-colloids and micro-particles, the fl-FFF system was able to determine the effective diffusion coefficients, irrespective of their size. For the micro-particles, the dimensionless diffusion coefficient was suggested to depend on the particle size, rather than that obtained by different methods suggested in previous works [E.C. Eckstein, D.G. Bailey, A.H. Shapiro, Self-diffusion of particles in shear flow of a suspension, J. Fluid Mech. 79 (Part 1) (1977) 191-208; D. Leighton, A. Acrivos, Measurement of shear-induced self-diffusion in concentrated suspensions of spheres, J. Fluid Mech. 177 (1987) 109-131].

Original languageEnglish
Pages (from-to)43-47
Number of pages5
JournalColloids and Surfaces A: Physicochemical and Engineering Aspects
Issue number1-3
StatePublished - 15 Feb 2006

Bibliographical note

Funding Information:
This work was supported by a grant (code 4-1-2) from Sustainable Water Resources Research Center of 21st Century Frontier Research Program through Water Reuse Technology Center (WRTC) at GIST, and also supported by the Center for Massive Distributed Sensor Network (MDSN) at GIST.


  • Diffusivity
  • Effective size
  • Flow field-flow fractionation
  • Micro-particles
  • Nano-colloids


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