Liquid-cell mass transfer

There is a singular lack of information on this aspect of mass transfer in bioreactors. Fignre 7B.18 shows that oxygen dissolved in the bulk liquid must diffuse across the liquid-cell film before it is taken np by the cell. Although there is no literature information 

STIRRED TANK REACTORS FOR CELL CULTURE TECHNOLOGY 

These cells are relatively very small ( 20 pm) and have density only slightly higher than the broth. Therefore, most investigators have implicitly assumed that the suspension of these cells under normal conditions of agitation (adequate power input) is undeniable. For these relatively very small cells, the characteristic Reynolds number is likely to be 1 (Nienow 2006). Under these conditions, the Ranz and Marshall equation (Eq. 6.4 in Chapter 6) predicts that the particle Sherwood number is given by the limiting value  

Knowledge of and allows calculation of The suspension viscosities are similar to that of water (Nienow, 2006), which gives D 2x 10 mVs. This yields an estimate of around 2.5 x 10 m/s, which is approximately the same as that for small particles at the state of just suspension (N=N ) in a conventional stirred reactor for chemical systems (Section 7A.7). 

Microcarriers have a relatively large size (150-300 pm). For this situation, the value of can be calculated by the universal correlation proposed by Pangarkar et al. 

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The gas-liquid and liquid-cell mass transfer steps are in series. The last step in the growth/differentiation of the cell is the biological uptake of oxygen by the cell. This... 

Liquid-solid mass transfer has also been studied, on a limited basis. Application to systems with catalytic surfaces or electrodes would benefit from such studies. The theoretical equations have been proposed based on film-flow theory (32) and surface-renewal theory (39). Using an electrochemical cell with rotating screen disks, liquid-solid mass transfer was shown to increase with rotor speed and increased spacing between disks but to decrease with the addition of more disks (39). Water flow over naphthalene pellets provided 4-6 times higher volumetric mass transfer coefficients compared to gravity flow and similar superficial liquid velocities (17). 

The optimal design of liquid-junction photovoltaic cells shares constraints with solid-state photovoltaic cells.25 209 Current collectors cast shadows and can reduce the amount of sunlight absorbed in the semiconductor. A constraint unique to the liquid-junction cell is the placement of the counterelectrode relative to the semiconductor-electrolyte interface. Shadows, which reduce efficiency and cause local currents in solid-state photovoltaic cells, may lead to localized corrosion in photoelectrochemical cells. Mass-transfer and kinetic limitations at the counterelectrode and resistance of the electrolyte can play important roles in the optimal design of the liquid-junction photovoltaic cell. These considerations are treated qualitatively by Parkinson.210... 

A schematic diagram of the unit cell for a vapor-Uquid-porous catalyst system is shown in Fig. 9.9. Each cell is modeled essentially using the NEQ model for heterogeneous systems described above. The bulk fluid phases are assumed to be completely mixed. Mass-transfer resistances are located in films near the vapor-liquid and liquid-solid interfaces, and the Maxwell-Stefan equations are used for calculation of the mass-transfer rates through each film. Thermodynamic equilibrium is assumed only at the vapor-liquid interface. Mass transfer inside the porous catalyst may be described with the dusty fluid model described above. 

Bulk Liquid Membranes (BLM). This is the simplest type of liquid membrane (2-8) and is utilized for fundamental studies of certain aspects of liquid membrane transport processes. In one such process, a beaker-in-a-beaker cell (Figure 1) consists of inner and outer compartments which contain the aqueous feed (F) and strip (S) solutions, respectively. The inner beaker contains the stripping solution and is surroimded by the feed solution. Both aqueous solutions contact the upper organic layer, which is the liquid membrane. Mass transfer takes place from the feed solution through the liquid membrane and into the strip solution. Bartsch et aL studied the transport of alkali metal cations across bulk liquid membranes in which a crown ether carboxylic acid in the organic layer served as the carrier (2,3). 

FIG. 18-28 Usually, the gas-liquid mass-transfer coefficient, K, is reduced with increased viscosity. This shows the effect of increased concentration of microbial cells in a fermentation process. 

There is always a limit to the liquid phase oxygen transfer for high cell density because mass transfer is limited. Actual cases are ... 

The simplest theory involved in mass transfer across an interface is film theory, as shown in Figure 3.10. In this model, the gas (CO) is transferred from the gas phase into the liquid phase and it must reach the surface of the growing cells. The rate equation for this case is similar to the slurry reactor as mentioned in Levenspiel.20... 

Table 3.1 shows the kinetic parameters for cell growth, rate models with or without inhibition and mass transfer coefficient calculation at various acetate concentrations in the culture media. The Monod constant value, KM, in the liquid phase depends on some parameters such as temperature, initial concentration of the carbon source, presence of trace metals, vitamin B solution, light intensity and agitation speeds. The initial acetate concentrations in the liquid phase reflected the value of the Monod constants, Kp and Kp. The average value for maximum specific growth rate (/xm) was 0.01 h. The value... 

Many semibatch reactions involve more than one phase and are thus classified as heterogeneous. Examples are aerobic fermentations, where oxygen is supplied continuously to a liquid substrate, and chemical vapor deposition reactors, where gaseous reactants are supplied continuously to a solid substrate. Typically, the overall reaction rate wiU be limited by the rate of interphase mass transfer. Such systems are treated using the methods of Chapters 10 and 11. Occasionally, the reaction will be kinetically limited so that the transferred component saturates the reaction phase. The system can then be treated as a batch reaction, with the concentration of the transferred component being dictated by its solubility. The early stages of a batch fermentation will behave in this fashion, but will shift to a mass transfer limitation as the cell mass and thus the oxygen demand increase. 

VOF or level-set models are used for stratified flows where the phases are separated and one objective is to calculate the location of the interface. In these models, the momentum equations are solved for the separated phases and only at the interface are additional models used. Additional variables, such as the volume fraction of each phase, are used to identify the phases. The simplest model uses a weight average of the viscosity and density in the computational cells that are shared between the phases. Very fine resolution is, however, required for systems when surface tension is important, since an accurate estimation of the curvature of the interface is required to calculate the normal force arising from the surface tension. Usually, VOF models simulate the surface position accurately, but the space resolution is not sufficient to simulate mass transfer in liquids. 

Laboratory reactors for studying gas-liquid processes can be classified as (1) reactors for which the hydrodynamics is well known or can easily be determined, i.e. reactors for which the interfacial area, a, and mass-transfer coefficients, ki and kc, are known (e.g. the laminar jet reactor, wetted wall-column, and rotating drum, see Fig. 5.4-21), and (2) those with a well-defined interfacial area and ill-determined hydrodynamics (e.g. the stirred-cell reactor, see Fig. 5.4-22). Reactors of these two types can be successfully used for studying intrinsic kinetics of gas-liquid processes. They can also be used for studying liquid-liquid and liquid-solid processes. 

Although the Lewis cell was introduced over 50 years ago, and has several drawbacks, it is still used widely to study liquid-liquid interfacial kinetics, due to its simplicity and the adaptable nature of the experimental setup. For example, it was used recently to study the hydrolysis kinetics of -butyl acetate in the presence of a phase transfer catalyst [21]. Modeling of the system involved solving mass balance equations for coupled mass transfer and reactions for all of the species involved. Further recent applications of modified Lewis cells have focused on stripping-extraction kinetics [22-24], uncatalyzed hydrolysis [25,26], and partitioning kinetics [27]. 

L Stowe, J Shaewitz. Hydrodynamics and mass transfer characteristics of a liquid/ liquid stirred cell. Chem Eng Commun 11 17, 1981. 

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