b reciprocal of the resistance to detachment
Bi Biot number
C 1 substrate concentration at reactor inlet, as soluble BOD 5 (mg.L−^1 )
C 2 substrate concentration at reactor outlet, as soluble BOD 5 (mg.L−^1 )
Df effective diffusion coefficient or effective diffusivity (m^2 .s−^1 )
(Df)ox effective diffusivity of the oxidant (m^2 .s−^1 )
(Df)red effective diffusivity of the reductant (m^2 .s−^1 )
Dw diffusion coefficient in water (m^2 .s−^1 )
dy element of thickness (m)
J substrate flux through the biofilm (kg.m−^2 .s−^1 )
Je external substrate flux (kg.m−^2 .s−^1 )
km external mass transfer coefficient (m.s−^1 )
Ks affinity (or saturation) constant of a suspended cell culture (kg.m−^3 )
knf rate constant for a reaction of order n.
KT observed removal rate constant at temperature T (m.s−^1 )
k0f zero order biofilm reaction rate (kg.m−^3 .s−^1 )
k1f first order biofilm reaction rate (s−^1 )
k1/2ap apparent half order constant (kg1/2.m−1/2.s−^1 )
Lf thickness of the microbial layer (m)
Md biofilm detachment flux (kg.m−^2 .s−^1 )
mf mass of attached biofilm per surface area (kg.m−^2 .s−^1 )
mf* maximum mass of biofilm at steady state
Mp biofilm production flux (kg.m−^2 .s−^1 )
n order of reaction
Nox/red stoichiometric ratio between the oxidant and reductant
Q volumetric flow rate (m−^3 .s−^1 )
rA reaction rate per unit area of biofilm or surface reaction rate (kg.m−^2 .s−^1 )
rf reaction rate inside the biofilm (kg.m−^3 .s−^1 )
(rf)max maximum reaction rate per unit volume of wet biofilm (kg.m−^3 .s−^1 )
rp radius of the bare carrier particles (m)
rpf radius of the biofilm-particles (m)
S bulk substrate concentration in the solution (kg.m−^3 )
Multiphase bioreactor design 320