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Abbreviations
- a:
-
gas/liquid interfacial area per unit liquid volume, m2/m3
- am :
-
liquid/cell interfacial area per unit liquid volume, m2/m3
- ap :
-
liquid/pellet interfacial area per unit liquid volume, m2/m3
- B:
-
width of baffle, m
- C:
-
concentration of dissolved oxygen or penetrating component, kg-moles/m3
- (C L) cr :
-
critical oxygen concentration in liquid, kg-moles/m3
- (C Li) cr :
-
critical oxygen concentration at liquid/cell or liquid/pellet interface, kg-moles/m3
- CL :
-
concentration of dissolved oxygen in bulk of liquid, kg-moles/m3
- (C L) i :
-
initial concentration of dissolved oxygen in bulk of liquid, kg-moles/m3
- CLi :
-
concentration of dissolved oxygen at liquid/cell or liquid/pellet interface, kg-moles/m3
- C*L :
-
oxygen concentration in equilibrium with air, kg-moles/m3
- C 0 :
-
concentration of dissolved oxygen at center of cell or pellet kg-moles/m3
- Cm :
-
dry cell weight per unit liquid volume, kg/m3
- D:
-
agitator diameter, m
- De :
-
effective diffusion coefficient of dissolved oxygen in mycelial pellet, m2/hr
- DL :
-
molecular diffusion coefficient of dissolved oxygen or transfer material in liquid m2/hr
- Dp :
-
molecular diffusion coefficient of dissolved oxygen in mycelial pellet, m2/hr
- dBM :
-
average diameter of bubble, m
- dp :
-
diameter of particle, m
- g:
-
acceleration due to gravity, m/hr2
- gc :
-
gravitational conversion factor, kg · m/Kg · hr2, where Kg indicates gravitational unit, while kg indicates mass unit
- H:
-
depth of medium in tank, m
- HG :
-
holdup of gas in tank
- HL :
-
holdup of liquid in tank
- h:
-
clearance from tank bottom to agitator, m
- kc :
-
specific respiration coefficient defined by Eq. (15)
- KL :
-
overall mass-transfer coefficient based on liquid film around gas bubbles, m/hr
- kL :
-
mass-transfer coefficient for liquid film around gas bubbles, m/hr
- Km :
-
apparent Michaelis constant for mycelia, kg-moles/m3
- K ′m :
-
apparent Michaelis constant for pellet, kg-moles/m3
- km :
-
mass-transfer coefficient for liquid film around cells or pellets defined by Eq. (2), m/hr
- kp :
-
oxygen-transfer coefficient for pellet defined by Eq. (27), m/hr
- kr :
-
specific oxygen-uptake rate per unit dry mycelial weight, kg-moles of oxygen/[(hr)(kg of dry cell)]
- (k r)max :
-
maximum specific oxygen-uptake rate per unit dry mycelial weight, kg-moles of oxygen/[(hr)(kg of dry cell)]
- l:
-
length of agitator blade, m
- N:
-
agitation speed, R.P.H. or R.P.M.
- NFr :
-
Froud number defined by DN 2/g
- Np :
-
Power number defined by P 0 g c/ρLN3 D 5
- NPe :
-
Peclet number defined by d PU/DL
- NRe :
-
Reynolds number defined by D 2NρL/μL
- (N Re) p :
-
Reynolds number for pellet defined by d PDNρL/μL
- Pg :
-
power consumption accompanied by aeration, Kg · m/hr
- P 0 :
-
power consumption without aeration, Kg · m/hr
- P max :
-
maximum power consumption without aeration, Kg · m/hr, where Kg indicates gravitational unit
- q:
-
volumetric flow rate of gas, m3/hr
- R:
-
radius of mycelial pellet, m
- r:
-
radial distance from center of cell or mycelial pellet, m
- rL :
-
radial distance from cell center to liquid bulk, m
- r 0 :
-
radius of cell, m
- T:
-
diameter of tank, m
- t 1/2 :
-
half-life time of oxygen concentration in liquid, min
- U:
-
relative velocity of particle and fluid, m/hr
- Ut :
-
terminal velocity of particle in free fall, m/hr
- V:
-
liquid volume in tank, m3
- Vr :
-
rapid oxygen-uptake rate per unit mycelial pellet, given by Eq. (21), kg-moles of oxygen/[(hr)(one pellet)]
- V ′r :
-
oxygen-uptake rate per unit mycelial pellet, kg-moles of oxygen/[(hr)(one pellet)]
- Vs :
-
superficial gas velocity based on cross section of tank, m/hr
- Vt :
-
terminal gas velocity in free rise, m/hr
- W:
-
agitator blade width, m
- x:
-
distance for penetration direction from interface, m
- ∈:
-
void fraction
- η:
-
effectiveness factor for oxygen consumption rate per unit mycelial pellet
- θ:
-
time, hr
- μL :
-
liquid viscosity, kg/m · hr
- ρ:
-
mycelial density in pellet, kg/m3
- ρL :
-
liquid density, kg/m3
- Δρ:
-
difference in density between dispersed and continuous phases, kg/m3
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Miura, Y. (1976). Transfer of oxygen and scale-up in submerged aerobic fermentation. In: Advances in Biochemical Engineering, Volume 4. Advances in Biochemical Engineering, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-07747-2_5
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DOI: https://doi.org/10.1007/3-540-07747-2_5
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