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Parameter
Greek Symbol
Units
Explanation of parameters
alpha
α
[-] Factor that describes the ratio of kLa in the media as compared to the kLa in water/air under identical conditions of power and gas flow rate.
beta
&beta
[-] Factor that describes the ratio of dissolved oxygen saturation in deactivated media as compared to that of water/air under identical conditions of temperature and pressure. In a fermentation, the microorganisms must be disabled for this determination.
Deflection near bottom
δSHAFT.BOT
 mm Deflection in the shaft near the bottom of the reactor, tank, vessel, or fermenter.
Shaft deflection near top
δSHAFT.TOP
 mm Deflection in the shaft near the top of the reactor, tank, vessel, or fermenter.
Tank deflection at side
δTANK.SIDE
 mm Deflection in the side wall of the reactor, tank, vessel, or fermenter. This is a sign that the tank wobbles.
Baffle thickness
ΔBAF
 mm Thickness of the baffles.
thickness(i)
Δi,BLADES
 mm Thickness of the the blades of the i-impeller.
Top head thickness
ΔTOP
 mm Thickness of the top dish. Often found on data describing the ASME pressure testing of the tank.
Longitude relative to front ΦBAF deg Position of the first baffle from the front in CCW-direction. If the baffles are not placed symmetrically around the tank, list their positions separately.
Longitude relative to front ΦCOIL deg Position of first coil or bundle from the front. List them if not symmetrical. Irrelevant for helical coils.
Longitude relative to front ΦSP deg Position of the sparge pipe relative to the front in degrees.
Avg Shear Rate γ·i,AVG 1/s Average impeller shear rate for the i-impeller.
Max Shear Rate γ·i,MAX 1/s Maximum impeller shear rate for the i-impeller.
Newtonian Viscosity η cPs or mPas Although most fluids and slurries exhibit non-Newtonian flow characteristics, this is a characteristic viscosity that a company has used to date to describe the viscosity of their fluids.
Viscosity factor ηF Factor that reduces the kLa as viscosity increases. It is a constant for viscosity < 25 mPas.
Rotational direction φ   Rotational direction of the shaft, either clockwise (CW) or counter clockwise (CCW) as seen from the top-down.
kLa Impeller Factor κF   Ratio that describes how well an impeller system is, based on kLa as compared to a standard single impeller system at the same P/V and Qg. All single impeller systems have the same kL a at the same P/V and Qg.
Theta θ   Constant that describes the deviation of kLa based on different temperatures. The standard temperature is 20oC. Most reported Theta-values vary between 1.016 and 1.047.
Henzler's ThetaMix(95%) θ1i,MIX,HENZLER [-] Henzler’s ThetaMix number (95%) for a single mixer in a standard tank for the i-impeller.
Henzler's Mult-Imp ThetaMix(95%) θMi,MIX,HENZLER [-] Modified Henzler’s ThetaMix number (95%) for multiple impellers in a tank for the i-impeller for the i-impeller.
Recirculation Time θRECIRC,i s Recirculation Time. Time for the average packet of fluid to return to the place it started from for the i-impeller.
Unaerated Density ρ kg/m3 Density of the media without any gas pockets. This should be the density at the operating temperature.
Density of unaerated water at temperature ρH2O kg/m3 Density of water at the operating temperature.
Average gassed density of the media ρLIQ,G kg/m3 Density of media at the operating temperature taking the entire gassed volume into account.
Total MixTime(95%) for all impellers τMIX,95 s Mixing time based on 95% degree of blending.
95% Blend Time for bottom impeller τMIX,B,95 s Mixing time based on 95% degree of blending for just the bottom impeller (or single impeller).
95.0% Blend Time for bottom impeller τMIX,B,x s Mixing time based on the degree of blending,ξ, for just the bottom impeller (or single impeller).
Total MixTime(95.0%) for all impellers τMIX,x s Total mixing time based on the degree of blending, ξ , and the εAVG.
Degree of mixing (blending) desired ξ % Point at which the reactor, tank, vessel, or fermenter is considered mixed. 100% would take indefinitely long by definition. Typical values are 90%, 95% or 99% mixed.


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