Determination of effective diffusivity of substrate in biological films and particles

Summary Particle supported biofilms of uniform thickness were generated in an aerobic fluidized-bed reactor with phenol as the carbon source. A method was developed for determining the effective diffusivities of oxygen and phenol using trypan blue, a vital stain as the tracer. The effective diffusivities of oxygen and phenol were found to be 2.72×10^–6 cm²/s and 1.12×10^–6 cm²/s respectively.Nomenclature C_i initial solute concentration in bulk, g/cm³ - C_t solute concentration in bulk at time t, g/cm³ - C bulk solute concentration at equilibrium, g/cm³ - D molecular diffusivity, cm²/s - D effective diffusivity, cm²/s - D_o D_p D_tb molecular diffusivity of oxygen, phenol and trypan blue, cm²/s - D_o, D_p, D_tb effective diffusivity of oxygen, phenol and trypan blue, cm²/s - D_s molecular diffusivity of substrate, cm²/s - D_s effective diffusivity of substrate, cm²/s - K partition coefficient - M_t amount of solute in the particle at time t, g - M amount of solute in the particle at equilibrium, g - r particle radius, cm - r_bp radius of the particle with biofilm, cm - S substrate concentration, g/cm³ - S_b substrate concentration in bulk, g/cm³ - S_i initial substrate concentration, g/cm³ - V₁ solute molar volume, cm³/g molGreek Symbols bf porosity of the biofilm - tortuosity factor