Biochemical Engineering Fundamentals, Part 1 - Bailey J., Ollis D. 1989

Transport Processes in Biotechnological Systems
Mass Transfer by Forced Convection
General Principles and Basic Similarity Criteria

To achieve economically viable rates of biomass growth, substrate utilization, or cellular product formation, efficient mixing of the Water-air disperse system is often required. This section will focus primarily on the relationships between the relevant variables that determine the mass transfer coefficient k_l and/or a or a', i.e., The ratio of the interfacial area to the corresponding volume.

* Richards J. W., Prog. Ind. Microbiol., 3, 143 (1961).

The primary objective of mechanical agitation is to enhance (sometimes very significantly) The rate of phase mixing compared to natural convection driven by the movement of particles in a freely rising or settling dispersed phase. This objective can be achieved through the following effects:

1. High dynamic pressure near the tip of the impeller blade or other mixing device leads to The formation of small bubbles, thereby increasing local a' values. Unless the rate of coalescence throughout the bulk liquid phase increases correspondingly, this results in an increase in the average volumetric value of a'.

2. The culture medium may contain a suspension of a solid or another liquid phase, which leads to phase Separation (settling) in the Reactor. Mechanical agitation ensures more uniform dispersion of these phases within the continuous liquid phase. In the case of hydrocarbon emulsions, the equation for k_l includes a term proportional to the cube ROOT of the phase density difference (р_н2о — p_нс)^1/3 [see Eq. (8.38)]; the resulting low mass transfer coefficient is typical for microbiological processes limited by a hydrocarbon substrate and can be enhanced by agitation.

3. When gas bubbles of a certain diameter are in an effectively agitated reactor, k_l does not change significantly with an increase or decrease in the power input to the reactor, since the relative velocity of gas bubbles or liquid droplets is primarily determined by the density difference. (Explain why.) At the same time, the turbulence induced by agitation reduces the bubble diameter D and thus increases a' at a given gas holdup; furthermore, The change in D will also affect the value of k_l.

4. Agitation can help reduce the maximum particle size of loose mycelium, microbial slime layers, and mold clumps, which leads to a decrease in the Thiele modulus of the microorganisms (Sec. 4.4), as well as a more uniform DISTRIBUTION OF MICROORGANISMS in the liquid phase. On the other hand, there are known cases where relatively high agitation rates led to a decrease in the yield of desired cellular products due to the disruption of cellular or extracellular Enzymes, The Effect of agitation on morphological development and Cell Differentiation, etc.

5. A cell suspension in a liquid can be so viscous that only mechanical agitation can achieve any significant gas dispersion in the liquid medium (we will discuss this issue in more detail in Sec. 8.8).

Under forced agitation, the action of applied mechanical forces establishes a characteristic velocity against which the scales of other motions in the system can be evaluated. In the case of impeller agitation, There are two scales: the root-mean-square fluid velocity fluctuation u_rms and the impeller tip speed u_i, which is proportional to N_iD_i, where N_i is the impeller rotational speed in revolutions per unit time, and D_i is the impeller diameter.

If u_rms is used as the characteristic velocity, the material balance equations for the entire system, its individual components, and the momentum balance can be expressed in terms of the following dimensionless parameters (similarity criteria):

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In an alternative approach, the impeller diameter D_i can be taken as the characteristic parameter of the agitated systems; the characteristic velocity will then be its tip speed N_iD_i. The subscript i indicates that, in this case, the basis for scaling is the impeller rotational speed rather than the parameters of the gaseous, liquid, or solid Components of the disperse system. In this case, the corresponding Reynolds and Froude numbers are expressed by the equations

The Froude number has other Structure/97.html">Definitions as well. For instance, for mass transfer in a suspension of "neutrally buoyant" particles, the following expression has been proposed:

where L is the reactor height. Since the Froude number reflects the dependence of free surface dynamics on mechanical agitation, it must also account for the distance from The surface of the disperse system to the bottom of the reactor. If there are two phases (continuous and dispersed) with different densities in the agitated system, such as a hydrocarbon emulsion in an aqueous medium, another modified Definition of the Froude number may be useful:

Obviously, in all cases when working with literature data, close attention must be paid to both the form of the equations themselves and the definitions of the similarity criteria used in them; an equation should not be used or cited without defining all the similarity criteria it contains.