Applied Microbiology and Biotechnology

, Volume 29, Issue 2–3, pp 107–112

Estimation of oxygen penetration depth in immobilized cells

  • Ho Nam Chang
  • Murray Moo-Young


A simple method is proposed for calculating oxygen pentration depth in immobilized cells by assuming zero order kinetics in the presence of several external oxygen transport resistances. Calculations indicate that typical penetration depths of oxygen for immobilized microbial cells are in the range of 50–200 μ and those for immobilized or encapsulated animal and plant tissue culture are about 500–1000 μ. Based on calculations, oxygen transport in microencapsulation and microcarriers for tissue cultures are not transport-limited, but a slight limitation is expected for those in a hollow fiber reactor.



specific area of a support (cm)


Biot number

\(\frac{{k_{eff} d_p }}{{2D_{eff} }}\)



oxygen concentration in the bulk liquid (mM)


Cb*-Ccr (mM)


bulk oxygen concentration in equilibrium with air (mM)


critical oxygen concentration (mM)


oxygen concentration in the solid phase (mM)


diameter or thickness of a support (cm)


effective diffusivity of oxygen in the solid phase (cm2/s)


membrane permeability of oxygen (cm/s)




liquid phase mass transfer rate coefficient (1/s)


solid phase mass transfer rate coefficient (1/s)


volumetric oxygen uptake rate (mmol O2/l)


geometry parameter, p=0 for slab, p=1 for cylinder, p=2 for sphere


oxygen penetration depth (cm)


oxygen penetration depth in the absence of external diffusion limitation (cm)


volumetric oxygen uptake rate,\(Q_{O_2 } X\) (mmol O2/l·h)

\(Q_{O_2 } \)

specific oxygen uptake rate (mmol O2gm biomass (dry)·h)


length coordinate (cm)


oxygen penetration depth for sphere (cm)


rc in the absence of external diffusion limitation (cm)


oxygen penetration depth for cylinder (cm)


rc*in the absence of external diffusion limitation (cm)


combined mass transfer rate resistance (s)


location where Cs becomes zero or Ccr (cm)


radius of cylinder or sphere, half thickness of slab (cm)


superficial gas velocity (cm/s)


cell concentration (g/l)

Greek letters


Thiele modulus, dimensionless

φL, φs

liquid and solid phase volume fraction, respectively, dimensionless


effectiveness factor


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Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • Ho Nam Chang
    • 1
  • Murray Moo-Young
    • 1
  1. 1.Department of Chemical EngineeringUniversity of WaterlooWaterlooCanada

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