Skip to main content
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 9
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Maleki, A. and Frigaard, I.A. 2016. Axial dispersion in weakly turbulent flows of yield stress fluids. Journal of Non-Newtonian Fluid Mechanics, Vol. 235, p. 1.

    Aminian, Manuchehr Bernardi, Francesca Camassa, Roberto and McLaughlin, Richard M. 2015. Squaring the Circle: Geometric Skewness and Symmetry Breaking for Passive Scalar Transport in Ducts and Pipes. Physical Review Letters, Vol. 115, Issue. 15,

    Bhaumik, Soubhik Kumar Kannan, Aadithya and DasGupta, Sunando 2015. Taylor–Aris dispersion induced by axial variation in velocity profile in patterned microchannels. Chemical Engineering Science, Vol. 134, p. 251.

    Conway, A J Saadi, W M Sinatra, F L Kowalski, G Larson, D and Fiering, J 2014. Dispersion of a nanoliter bolus in microfluidic co-flow. Journal of Micromechanics and Microengineering, Vol. 24, Issue. 3, p. 034006.

    Dagdug, Leonardo Berezhkovskii, Alexander M. and Skvortsov, Alexei T. 2014. Aris-Taylor dispersion in tubes with dead ends. The Journal of Chemical Physics, Vol. 141, Issue. 2, p. 024705.

    Berezhkovskii, Alexander M. and Skvortsov, Alexei T. 2013. Aris-Taylor dispersion with drift and diffusion of particles on the tube wall. The Journal of Chemical Physics, Vol. 139, Issue. 8, p. 084101.

    Zhu, Yong Li, YiZeng Qin, KaiRong Tang, Hong and Qiu, TianShuang 2013. Transportation of dynamic biochemical signals in non-reversing oscillatory flows in blood vessels. Science China Physics, Mechanics and Astronomy, Vol. 56, Issue. 2, p. 322.

    Bruus, Henrik 2012. Acoustofluidics 10: Scaling laws in acoustophoresis. Lab on a Chip, Vol. 12, Issue. 9, p. 1578.

    Takikawa, Yoshinori and Orihara, Hiroshi 2012. Diffusion of Brownian Particles under Oscillatory Shear Flow. Journal of the Physical Society of Japan, Vol. 81, Issue. 12, p. 124001.

  • Journal of Fluid Mechanics, Volume 691
  • January 2012, pp. 95-122

Transient Taylor–Aris dispersion for time-dependent flows in straight channels

  • Søren Vedel (a1) and Henrik Bruus (a1)
  • DOI:
  • Published online: 02 December 2011

Taylor–Aris dispersion, the shear-induced enhancement of solute diffusion in the flow direction of the solvent, has been studied intensely in the past half century for the case of steady flow and single-frequency pulsating flows. Here, combining Aris’s method of moments with Dirac’s bra–ket formalism, we derive an expression for the effective solute diffusivity valid for transient Taylor–Aris dispersion in any given time-dependent, multi-frequency solvent flow through straight channels. Our theory shows that the solute dispersion may be greatly enhanced by the time-dependent parts of the flow, and it explicitly reveals how the dispersion coefficient depends on the external driving frequencies of the velocity field and the internal relaxation rates for mass and momentum diffusion. Although applicable to any type of fluid, we restrict the examples of our theory to Newtonian fluids, for which we both recover the known results for steady and single-frequency pulsating flows, and find new, richer structure of the dispersion as function of system parameters in multi-frequency systems. We show that the effective diffusivity is enhanced significantly by those parts of the time-dependent velocity field that have frequencies smaller than the fluid momentum diffusion rate and the solute diffusion rate.

Corresponding author
Email address for correspondence:
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

1.A. Ajdari , N. Bontoux & H. A. Stone 2006 Hydrodynamic dispersion in shallow microchannels: the effect of cross-sectional shape. Analyt. Chem. 78, 387392.

2.R. Aris 1956 On the dispersion of a solute in a fluid flowing through a tube. Proc. R. Soc. Lond. A Mat. 235 (1200), 6777.

3.R. Aris 1960 On the dispersion of solute in pulsating flow through a tube. Proc. R. Soc. Lond. A Mat. 259 (1298), 370376.

4.S. Bandyopadhyay & B. S. Mazumder 1999 Unsteady convective diffusion in a pulsatile flow through a channel. Acta Mechanica 134, 116.

8.N. Bontoux , A. Pépin , Y. Chen , A. Ajdari & H. A. Stone 2006 Experimental characterization of hydrodynamic dispersion in shallow microchannels. Lab on a Chip 6, 930935.

9.H. Brenner & D. A. Edwards 1993 Macrotransport Processes. Butterworth–Heinemann.

11.H. Bruus & A. D. Stone 1994 Quantum chaos in a deformable billiard: applications to quantum dots. Phys. Rev. B 50 (24), 1827518287.

12.R. Camassa , Z. Lin & R. McLaughlin 2010 The exact evolution of scalar variance in pipe and channel flow. Commun. Math. Sci. 8 (2), 601626.

17.M. R. Doshi , P. M. Daiya & W. N. Gill 1978 Three dimensional laminar dispersion in open and closed rectangular conduits. Chem. Engng Sci. 33, 795804.

18.D. Dutta , A Ramachandran & D. T. Leighton 2006 Effect of channel geometry on solute dispersion in pressure-driven microfluidic systems. Microfluid Nanofluid 2, 275290.

20.L. T. Fan & C. B. Wang 1966 Dispersion of matter in non-Newtonian laminar flow through a circular tube. Proc. R. Soc. Lond. A Mat. 292 (1429), 203208.

21.J. P. Gleeson 2002 Electroosmotic flows with random zeta potential. J. Colloid Interface Sci. 249 (1), 217226.

22.J. D. Goddard 1993 The Green’s function for passive scalar diffusion in a homogeneously sheared continuum. Phys. Fluids A 5, 22952297.

23.H. G. Harris & S. L. Goren 1967 Axial diffusion in a cylinder with pulsed flow. Chem. Engng Sci. 22, 15711576.

24.K. M. Jansons 2006 On Taylor dispersion in oscillatory channel flows. Proc. R. Soc. Lond. A Mat. 462, 35013509.

29.R. F. Molloy & D. T. Leighton 1998 Binary oscillatory cross-flow electrophoresis: theory and experiments. J. Pharma. Sci. 87, 12701281.

30.N. A. Mortensen & H. Bruus 2006 Universal dynamics in the onset of a Hagen–Poiseuille flow. Phys. Rev. E 74 (1), 017301.

31.N. A. Mortensen , L. H. Olesen & H. Bruus 2006 Transport coefficients for electrolytes in arbitrarily shaped nano and micro-fluidic channels. New J. Phys. 8, 3751.

32.A. Mukherjee & B. S. Mazumder 1988 Dispersion of contaminant in oscillatory flows. Acta Mechanica 74, 107.

33.S. Paul & B. S. Mazumder 2008 Dispersion in unsteady Couette–Poiseuille flows. Intl J. Engng Sci. 46, 12031217.

34.R. F. Probstein 1994 Physicochemical Hydrodynamics. An Introduction, 2nd edn. John Wiley and Sons.

35.R. Sankarasubramanian & W. N. Gill 1973 Unsteady convective diffusion with interphase mass-transfer. Proc. R. Soc. Lond. A Mat. 333 (1592), 115132.

36.P. Skafte-Pedersen , D. Sabourin , M. Dufva & D. Snakenborg 2009 Multi-channel peristaltic pump for microfluidic applications featuring monolithic PDMS inlay. Lab on a Chip 9, 30033006.

37.G. I. Taylor 1953 Dispersion of soluble matter in solvent flowing slowly through a tube. Proc. R. Soc. Lond. A Mat. 219 (1137), 186.

38.H. M. Taylor & E. F. Leonard 1965 Axial dispersion during pulsating pipe flow. AIChE J. 11 (4), 686689.

39.A. M. Thomas & R. Narayanan 2001 Physics of oscillatory flow and its effect on the mass transfer and separation of species. Phys. Fluids 13 (4), 859866.

40.C. van den Broeck 1982 A stochastic description of longitudinal dispersion in uniaxial flows. Physica A 112, 343352.

41.S. Vedel , L. H. Olesen & H. Bruus 2010 Pulsatile microfluidics as an analytical tool for determining the dynamic characteristics of microfluidic systems. J. Micromech. Microengng 20, 035026.

42.A. Vikhansky & W. Wang 2011 Taylor dispersion in finite-length capillaries. Chem. Engng Sci. 66 (4), 642649.

44.J. R. Womersley 1955 Method for the calculation of velocity, rate of flow and viscous drag in arteries when the pressure gradient is known. J. Physiol. 127, 553563.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *