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1、Mass Transfer in BioreactorsMass transfer occurs in mixtures containing local concentration variablesMT plays a vital role in many reaction systemsIf, for example, the mass transfer of Oxygen from the bubbles in the fermentation broth is slow, then the rate of cell metabolism can become dependant on
2、 the rate of oxygen supply from the gas phase.So what drives MT?Molecular diffusion is the movement of molecules of a given substance from an area of high concentration of that given compound to one of lower concentration. The term concentration gradient is used to describe this difference in concen
3、tration and molecules will move in a direction which will eventually destroy the gradientWhat happens in Gas-Liquid Mass TransferGLMT is unusual as molecules have to move between different phases (i.e. the gas phase to the liquid phase) across a boundary or interface.Film theory attempts to explain
4、the process of diffusion of, lets say, Oxygen from the bubbles in the broth to the bulk liquid phase. Let us consider the mass transfer of Oxygen from gas to liquid across the bubble interface. Oxygen is in much higher concentration in the bubble (21% of the volume of the air is Oxygen) also Oxygen
5、is sparingly soluble in aqueous solutions. Therefore a considerable driving force exists to move O2 from gas to liquid.According to the film theory, the turbulence in each fluid dies away as you approach the interface. A thin film of stagnant fluid lies on each side of the interface. The only way th
6、rough for the Oxygen is molecular diffusion (normally in gasses or liquids we have convective mass transfer)The concentration of any compound at the interface differs across the interface, even though the fluids at ether side of the interface are supposed to be in equilibrium.This is simply due to t
7、he molecules relative solubility in each phase.As you move away from the interface, in either direction, the concentration of the molecule returns to the bulk liquid concentration which is regulated through convective mass transfer.CAGiCALiCALCAGGas-phasefilm resistanceLiquid-phasefilm resistanceBul
8、k gas phaseBulk liquid phaseFilm theory diagram reproduced from Doran - Figure 9.5Convective Mass TransferDefinition: Mass transfer occurring under the presence of bulk fluid motion.Rate of MT is directly proportional to the driving force for transfer, and the area available for the transfer process
9、.Transfer Rate (transfer area)x(driving force)The constant of proportionality is termed the Mass Transfer CoefficientLooking at film theory, the driving force for mass transfer from the bulk gas to the interface can be expressed as.(1)ahd the rate of transfer through the gas liquid boundary(2)where
10、kG is the gas phase MT coefficient and kL is the liquid phase MT coefficient. “a” is the interfacial area available for MT.It is important to eliminate and as they are impossible to measure. The first assumption we can make is that the interfacial gas concentration of the component in question is a
11、linear function of the interfacial liquid concentration of the component. I.e.(3)Where m is the distribution factorAt steady state, there can be no accumulation of the component at the interface, i.e. anything transported from the gas phase to the interface is subsequently moved from the interface i
12、nto the bulk liquid.(4)By manipulating the previous four equations, it is possible to eliminate all interface terms in the relationship(5)The overall liquid phase mass-transfer coefficient, KL is defined as:(6)Therefore we can simplify an expression to describe the transfer of a component from the g
13、as phase to the liquid phase to;(7) is often reffered to as , the concentration of component at the gas liquid interface that is in equilibrium with the gas phase concentration. A final representation of (7) can therefore be;(8)In the case of Oxygen transfer, the key element of this course, Oxygen i
14、s sparing soluble in aqueous solutions, greater resistance to mass transfer is provided by the liquid film over the gas film. kGa is going to be much larger than kLa, therefore from (6),(9)and(9)It is important to note that is the maximum attainable concentration of Oxygen in the liquid phase. Lets
15、see now what impacts on this value.Factors that impact on 1. Gas Pressure and Oxygen Partial Pressure in the gasThe equilibrium relationship between oxygen partial pressure in the gas phase (and therefore total air pressure) and the liquid saturation oxygen concentration, can be described by the following relationship.(10)What this equation means, is that the partial pressure of oxygen in the gas phase, , which is equivalent to the total pressure of the gas phase by the mole fraction of oxy
