Chapter 7 ( Dr. Ali Coşkun DALGIÇ )

FE 462 BIOCHEMICAL ENGINEERING
Agitation and Aeration
Introduction
BASIC MASS-TRANSFER CONCEPTS
The path of gaseous substrate from a gas bubble to an organelle in a microorganism can be divided into several steps as follows:

1. Transfer from bulk gas in a bubble to a relatively unmixed gas layer

2. Diffusion through the relatively unmixed gas layer

Molecular Diffusion in Liquids
When the concentration of a component varies from one point to another, the component has a tendency to flow in the direction that will reduce the local differences in concentration.
Molar flux of a component A relative to the average molal velocity of all constituent JA is proportional to the concentration gradient dCA/dz as
Diffusivity
The kinetic theory of liquids is much less advanced than that of gases. Therefore, the correlation for diffusivities in liquids is not as reliable as that for gases. Among several correlations reported, the Wilke-Chang correlation (Wilke and Chang, 1955) is the most widely used for dilute solutions of nonelectrolytes,
Example
Solution:

Equation 1 suggests that the quantity DABμ/T is constant for a given liquid system. Though this is an approximation, we may use it here to estimate the diffusivity at 40°C. Since the viscosity of water at 40°C is 6.529 X 10-4 kg/m s from the handbook,

Gas Sparging
Air under pressure is supplied through a tube end consists of an ‘O’ ring with very fine holes or orifices. The size of bubbles depends on the size of hole and type of sparger. For very fine bubbles with effective gas dispersion, a micro-sparger is used in the fermenter.
A micro-sparger is in fact a highly porous ceramic material and is used instead of a gas sparger. The size of bubbles affects the mass transfer process. Smaller bubble size provides more surface area for gas exposure, so a better oxygen transfer rate is obtained.
Gas Hold-up
Gas hold-up is one of the most important parameters characterizing the hydrodynamics in a fermenter. Gas hold-up depends mainly on the superficial gas velocity and the power consumption, and often is very sensitive to the physical properties of the liquid. Gas hold-up can be determined easily by measuring level of the aerated liquid during operation ZF and that of clear liquid ZL. Thus, the average fractional gas hold-up H is given as;
Power Consumption
Figure shows Power number-Reynolds number correlation in an agitator with four baffles (Rushton et al., 1950) for three different types of impellers. The power number decreases with an increase of the Reynolds number and reaches a constant value when the Reynolds number is larger than 10,000. At this point, the power number is independent of the Reynolds number.

The power required by an impeller in a gas sparged system Pm is usually less than the power required by the impeller operating at the same speed in a gas-free liquids Pmo. The Pm for the fIat-blade disk turbine can be calculated from Pmo (Nagata, 1975), as follows:

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