Journal of Applied Electrochemistry

, Volume 24, Issue 8, pp 737–744 | Cite as

Turbulent mass transfer in small radius ratio annuli

  • J. Legrand
  • S. A. Martemyanov


Mass transfer in annuli for both fully developed laminar and turbulent flow conditions has been studied with respect to available experimental data. It is shown that prediction of the Sherwood number for the inner annular wall based on the hypothesis of coincidence of the zero shear stress position for laminar and turbulent flows leads to serious error in the case of small radius ratio. Also it is shown that in contrast with plain tubes the curvature in small radius ratio annuli should be taken into account for the case of small Reynolds numbers. In consequence, the well-known Leveque equation can be used for the calculation of the mass transfer coefficient in annuli only under certain conditions. Possibilities of electrodiffusion diagnostics for the precise determination of the zero shear stress position in annuli are discussed.


Experimental Data Shear Stress Mass Transfer Reynolds Number Transfer Coefficient 
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List of symbols


cross-section flow area (m2)

a =r1/r2

annular radius ratio (−)

\(\bar c,c',c_0 \)

mean fluctuation and bulk concentration (mol m−3)


molecular diffusivity (m2s−1)


hydraulic diameter (m)


overall, inner and outer wall friction factors (−)

fτ = τ1

near wall velocity gradient (s−1)

\(\bar \iota \)

pressure drop per unit of length (Pam−1)


average mass transfer coefficient (ms−1 )

k =r0/r0,L

ratio of zero shear stress position in turbulent and laminar flows (−)


mass transfer surface length (m)


diffusion ‘leading edge’ length (m)


diffusion entrance length (m)


wetted perimeter (m)

Re =Uavdh

Reynolds number (−)


radial distance from conduit axis (m)


radial distance of zero shear stress position in turbulent and laminar flows (m)


radius of inner and outer annular cylinders (m)

Sc = ν/D

molecular Schmidt number (−)

Sh =KLdh/D

Sherwood number (−)


average liquid velocity (ms−1)


mean and fluctuation axial velocity (ms−1)

υ, υ′

mean and fluctuation radial velocity (ms−1)

y = r − r1

distance from the inner wall (m)

yτ = ν(ρ/τ1)1/2

dynamic length (m)


distance in direction of the flow (m)

Greek symbols


diffusion layer thickness (m)


dynamic viscosity (Pa s)


kinematic viscosity (m2s−1)


density (kgm−3)


shear stress (Pa)


wall shear stress for tube and plate channel (Pa)

τ1, τ2

wall shear stress for inner and outer annular cylinders (Pa)


Geometrical factor with respect to k-function (−)

ϕR, ϕK

geometrical factor with respect to Rothfus or Kays-Leung equations (−)


ratio of radial distance of zero shear stress position to outer radius in laminar flow (−)


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Copyright information

© Chapman & Hall 1994

Authors and Affiliations

  • J. Legrand
    • 1
  • S. A. Martemyanov
    • 2
  1. 1.Laboratoire de Génie des ProcédésSaint-Nazaire CedexFrance
  2. 2.A.N. Frumkin Institute of Electrochemistry, Russian Academy of SciencesMoscowRussia

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