Mixing
Mixing time and degree of mixing: A) reactor without recirculation
Mixing time and degree of mixing: B) reactor with recirculation
van t Riet and van der Lans, in Comprehensive Biotechnol, 2nd ed. ( 2011), vol 2
Degree of Mixing (α) Degree of homogeneity or Degree of Mixing _ The extent to which homogenization has progressed compared to the initial nonhomogeneous state. Mixing time (t m ) is the time required to reach a given value of mixing (α)
Mechanically stirred reactors Standard Dimensions: D i /D T = 1/3 H L /D T : 2 to 4 Number of Baffles = 4 BW/D T = 1/10 (BW- baffle width) M Manuela R da Fonseca, DE
Mechanically stirred reactors D T _ Internal Tank Diameter D i, D A _ Impeller Diameter Dimensionless numbers Re A and N P ρ 2 N D A 3 5 Re A = Pot = N µ PρN D A Re A, Re I _ Impeller Reynolds number Pot Power dissipated by the impeller
Garcia-Ochoa et al., in Comprehensive Biotechnol, 2nd ed. ( 2011), vol 2
SCHEMATIC DIAGRAM OF RUSHTON TURBINE Aerated NEWTONIAN Fluids Side View Impeller Diameter, D i Top View: 6-Bladed Turbine
The flow in a Bubble Column is completely chaotic: Sieblist et al., in Comprehensive Biotechnol, 2nd ed. ( 2011), vol 2
The flow pattern in a STR is also chaotic, but some compartmentalization can be observed Sieblist et al., in Comprehensive Biotechnol, 2nd ed. ( 2011), vol 2
Flow Pattern produced by a radial-flow impeller in a baffled tank.
1. NEWTONIAN FLUID - UNGASSED
Newtonian Fluids
Newtonian Fluids Newton s law of viscosity τ = µ dv x dy dv x /dy γ _ velocity gradient or shear rate (s -1 ) µ _ (dynamic or absolute) viscosity (Pa.s) τ = F/A _ shear stress that results from the velocity gradient (Pa) A fluid has Newtonian behaviour when, under constant temperature, shows a viscosity that does not vary with shear rate the viscosity is constant with respect to the time of shearing Rheology of biological media
Shear can damage fragile cells in suspended cultures and cause: Cell death protozoa (relatively large) animal cells (sensitive cell membrane) plant cells (fragile cell wall) Fragmentation of hyphae In Bioreactors shear may be caused by - mechanical stirring (STRs!!) air flow (air-lift reactors!!) burst of bubbles at the liquid/head-space interface (in all reactors with gas injection)
N P vs. Re A Valid in a ungassed vessel with 4 baffles and a single impeller, containing a Newtonian fluid
TABELA 3.1 NÚMEROS DE POTÊNCIA DE VÁRIOS TIPOS DE AGITADOR. (fluxo turbulento) Agitador Tipo de circulação Nº de potência, N P Turbina Rushton Radial 5-5,5 Turbina Smith Radial 4 Turbina pás inclinadas Axial 1,5-2 Hydrofoil Prochem Maxflo Axial 1-1,6 Turbina Lightnin A310 Axial 0,3 Hydrofoil Chemineer HE3 Axial 0,3 Hélice de 3 pás Axial 0,23
Multiple impellers
2. Non-NEWTONIAN FLUID - UNGASSED
Newtonian and non-newtonian Fluids Bingham and Casson Yield stress Rheology of biological media M. Manuela da Fonseca, DEQB
Non-Newtonian Fluids Non-Newtonian behaviour may arise in at least 2 cases: Solutions of macromolecules (e.g. (bio)polymers) Suspensions of small particles - the 2 cases merge as particle diameters fall to the µm size and molecular diameters increase above 10-2 µm Rheology of biological media M. Manuela da Fonseca, DEQB
Non-Newtonian Fluids Power-law (or Ostwald - de Waele) model: n τ = Kγ n = 1 and K µ Newtonian n < 1 Pseudoplastic or shear thinning n > 1 Dilatant or shear thickening n - power-law index or flow behaviour index K - consistency index (Pa.s n ) The term viscosity has no meaning for a non-newtonian fluid unless it is related to a particular value of shear rate γ Rheology of biological media apparent viscosity µ a τ = n 1 = Kγ γ γ M. Manuela da Fonseca, DEQB
Non-NEWTONIAN FLUIDS - UNGASSED (µ a ) mean??? γ average = C.N (µ a ) mean = τ / γ average Thus an expression for a modified Re A is Re A 2 n ρ N D K C = n 1 2 A and N P can be estimated as for Newtonian fluids
Non-NEWTONIAN FLUIDS In Bioreactors non-newtonian behaviour may arise in at least 2 cases: Extra-cellular production of macromolecules (e.g. (bio)polymers) Cultivation of filamentous organisms
3. AERATED Bioreactors
Gas Cavities
Gas Cavities
Cavities behind impeller blades Low-pressure areas behind impeller blades attract gas bubbles, which then coalesce and form extended gas cavities in the culture. As the liquid must flow around the cavities, they practically change the impeller blade size and form. This usually results in a reduced flow resistance. In this way, cavities change the outflow characteristics of the impellers.
Sieblist et al., in Comprehensive Biotechnol, 2nd ed. ( 2011), vol 2
Gassed vs. ungassed Power Aeration number Fl or N A Fl = Q ND ar 3 A
Estimation of Gassed Power from Ungassed Power and Air Flow Rate For many foaming systems the following form of Michel & Miller s correlation applies: Pot G = 2 3 0.45 P ND 0 0 i.69 0.56 0 Q SI units Another correlation is Pharamond s:
3 NDA - Pumping flow of the turbine ( impeller) Aeration number Fl or N A Fl = Q ND ar 3 A
Multiple impellers J Vasconcelos, PhD thesis, 1993
Multiple impellers Sieblist et al., in Comprehensive Biotechnol, 2nd ed. ( 2011), vol 2 M Manuela R da da Fonseca, DEQB
Scaba Novel Impeller geometries for enhanced gas dispersion Lightnin A315 Prochem Maxflo
Oxygen transfer in Shaken Flasks
Oxygen transfer in Shaken Flasks
Oxygen transfer in Bioreactors Estimation of Kla K L a = χ Pot V G α u β G Pot G (W) is the stirring power, V (m 3 ) is the volume of liquid, u G (m s -1 ) is the linear gas velocity, α and β are empirical parameters Coalescent Liquids Non- Coalescent Liquids χ 0.026 0.0016 α 0.4 0.5 0.5 0.7 β 0.4 0.6 0.2 0.4 (SI) van t Riet (1979) Nielsen and Villadsen (1994)
Estimation of Kla In the presence of an organic phase: X o organic phase fraction (v/v) γ empirical parameter Nielsen et al., 2003
Power dissipated by the expansion of the injected air Assuming ideal behaviour, instant thermal equilibrium and isothermal expansion, the expansion energy is: (J) p i - air pressure at the bottom of reactor p o - air pressure in the headspace of reactor and the power communicated to the liquid will be: (1) - Gas molar flow (mol/s)
Power (heat!) from O 2 transfer Power communicated by the impeller (estimated on the basis of the power number) + Power dissipated by the expansion of the injected air (eq (1))
For multiple stirrers, a radial pumping stirrer in the lower compartment combined with axial pumping stirrers upper in the shaft, is a better configuration than radial pumping stirrers only.