Estimation of oxygen penetration depth in immobilized cells

Summary 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 and those for immobilized or encapsulated animal and plant tissue culture are about 500–1000 . 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.Nomenclature a_s specific area of a support (cm) - Bi Biot number - dimensionless - C_b oxygen concentration in the bulk liquid (mM) - C_b C_b^*-C_cr (mM) - C_b^* bulk oxygen concentration in equilibrium with air (mM) - C_cr critical oxygen concentration (mM) - C_s oxygen concentration in the solid phase (mM) - d_p diameter or thickness of a support (cm) - D_eff effective diffusivity of oxygen in the solid phase (cm²/s) - k_m membrane permeability of oxygen (cm/s) - k_m^* D_eff/_m - k_La_L liquid phase mass transfer rate coefficient (1/s) - k_sa_s solid phase mass transfer rate coefficient (1/s) - (OUR)_v volumetric oxygen uptake rate (mmol O₂/l) - p geometry parameter, p=0 for slab, p=1 for cylinder, p=2 for sphere - P_d oxygen penetration depth (cm) - P_d oxygen penetration depth in the absence of external diffusion limitation (cm) - Q volumetric oxygen uptake rate, (mmol O₂/l·h) - specific oxygen uptake rate (mmol O₂gm biomass (dry)·h) - r length coordinate (cm) - r_c oxygen penetration depth for sphere (cm) - r_c r_c in the absence of external diffusion limitation (cm) - r_c^* oxygen penetration depth for cylinder (cm) - r_c^* r_c^*in the absence of external diffusion limitation (cm) - r_com combined mass transfer rate resistance (s) - r_d location where C_s becomes zero or C_cr (cm) - r_i radius of cylinder or sphere, half thickness of slab (cm) - U_sg superficial gas velocity (cm/s) - X cell concentration (g/l)Greek letters Thiele modulus, dimensionless - _L, _s liquid and solid phase volume fraction, respectively, dimensionless - effectiveness factorOn sabbatical leave from KAIST, Seoul, Korea