Advection‐dispersion in symmetric field‐flow fractionation channels

  • S.A. Suslov
  • A.J. Roberts
Article

Abstract

We model the evolution of the concentration field of macromolecules in a symmetric field‐flow fractionation (FFF) channel by a one‐dimensional advection–diffusion equation. The coefficients are precisely determined from the fluid dynamics. This model gives quantitative predictions of the time of elution of the molecules and the width in time of the concentration pulse. The model is rigorously supported by centre manifold theory. Errors of the derived model are quantified for improved predictions if necessary. The advection–diffusion equation is used to find that the optimal condition in a symmetric FFF for the separation of two species of molecules with similar diffusivities involves a high rate of cross‐flow.

References

  1. [1]
    J. Carr, Applications Of Centre Manifold Theory, Applied Math. Sci., Vol. 35 (Springer-Verlag, Berlin, 1981).Google Scholar
  2. [2]
    J. Carr and R.G. Muncaster, The application of centre manifold theory to amplitude expansions. I. Ordinary differential equations, J. Differential Equations 50 (1983) 260–279.CrossRefGoogle Scholar
  3. [3]
    J. Carr and R.G. Muncaster, The application of centre manifold theory to amplitude expansions. II. Infinite dimensional problems, J. Differential Equations 50 (1983) 280–288.CrossRefGoogle Scholar
  4. [4]
    P.H. Coullet and E.A. Spiegel, Amplitude equations for systems with competing instabilities, SIAM J. Appl. Math. 43 (1983) 776–821.CrossRefGoogle Scholar
  5. [5]
    J.C. Giddings, Crossflow gradients in thin channels for separation by hyperlayer FFF, SPLIT cells, elutriation, and related methods, Separation Science and Technology 21(8) (1986) 831–843.Google Scholar
  6. [6]
    A. Litzén and K.-G. Wahlund, Zone broadening and dilution in rectangular and trapezoidal asymmetrical flow field-flow fractionation channels, Anal. Chem. 62 (1990) 1001–1007.Google Scholar
  7. [7]
    A. Litzén, Separation speed, retention, and dispersion in asymmetrical flow field-flow fractionation as functions of channel dimensions and flow rates, Anal. Chem. 65 (1993) 461–470.CrossRefGoogle Scholar
  8. [8]
    G.N. Mercer and A.J. Roberts, A centre manifold description of contaminant dispersion in channels with varying flow properties, SIAM J. Appl. Math. 50 (1990) 1547–1565.CrossRefGoogle Scholar
  9. [9]
    G.N. Mercer and A.J. Roberts, A complete model of shear dispersion in pipes, Jap. J. Indust. Appl. Math. 11 (1994) 499–521.CrossRefGoogle Scholar
  10. [10]
    A.J. Roberts, The application of centre manifold theory to the evolution of systems which vary slowly in space, J. Austral. Math. Soc. B 29 (1997) 480–500.Google Scholar
  11. [11]
    A.J. Roberts, Low-dimensional modelling of dynamical systems, Preprint, University of Southern Queensland, Australia (1997).Google Scholar
  12. [12]
    A.J. Roberts, Low-dimensional modelling of dynamics via computer algebra, Comput. Phys. Comm. 100 (1997) 215–230.CrossRefGoogle Scholar
  13. [13]
    M.R. Schure, B.N. Barman and J.C. Giddings, Deconvolution of nonequilibrium band broadening effects for accurate particle size distributions by sedimentation field-flow fractionation, Anal. Chem. 61 (1989) 2735–2743.CrossRefGoogle Scholar
  14. [14]
    K.-G. Wahlund and J.G. Giddings, Properties of an asymmetrical flow field-flow fractionation channel having one permeable wall, Anal. Chem. 59 (1987) 1332–1339.CrossRefGoogle Scholar
  15. [15]
    S.D. Watt and A.J. Roberts, The construction of zonal models of dispersion in channels via matching centre manifolds, J. Austral. Math. Soc. B 38 (1994) 101–125.CrossRefGoogle Scholar
  16. [16]
    S.D. Watt and A.J. Roberts, The accurate dynamic modelling of contaminant dispersion in channels, SIAM J. Appl. Math. 55(4) (1995) 1016–1038.CrossRefGoogle Scholar
  17. [17]
    P.G. Wyatt, Submicrometer particle sizing by multiangle light scattering following fractionation, J. Colloid and Interface Sci. 197 (1998) 9–20.CrossRefGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • S.A. Suslov
    • 1
  • A.J. Roberts
    • 1
  1. 1.Department of Mathematics and ComputingUniversity of Southern Queensland, ToowoombaQueenslandAustralia E-mail:

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