Simulated-microcarrier motion and its effect on radial medium transfer inside a horizontally rotating cylindrical bioreactor (HRCB) for animal cell culture

The motion and distribution of microcarriers inside a horizontally rotating cylindrical bioreactor were simulated using spherical ion exchange resin particles. Particle motion deviated much from that expected under ideal conditions. The possible mass transfer enhancing effects of particle translation and cluster rotation are discussed.     

A kinetic, chromatographic method for studying protein hydrodynamic behavior

A chromatographic method based on "split-peak" behavior was described for the determination of the coefficient of mass transfer of proteins on small reversed-phase columns. The coefficient of mass transfer was found to be a linear function of the protein translational diffusion coefficient and inversely proportional to the square of the support particle diameter, as predicted by chromatographic theory. As an example of the practical application of this method for the measurement of protein diffusion coefficients, the denaturation of bovine serum albumin with decreasing solution pH was followed by measuring the change in the coefficient of mass transfer. A major advantage of this method was that the results were not affected by the interaction of the protein with the stationary phase.     

Theoretical investigation of axial and local particle size distribution on expanded bed adsorption process

The general rate model was developed and solved to describe protein adsorption in an expanded bed. The model takes into account axial variation of bed porosity, particle size distribution (PSD), external and intraparticle mass transfer, and dispersion in liquid and solid phase. The analysis of the influence of the model parameters on dynamic capacity (DC) was investigated. The simulation results showed that major impact on dynamic capacity is exerted by intraparticle mass transfer (particle diameter and pore diffusivity). The external mass transfer resistance and dispersion parameters have secondary effect on DC. The replacement of axial PSD by the mean particle diameter results in error in calculation of DC, which increases remarkably with the increase of mean particle diameter. The PSD can promote a very slow approaching of plateau concentration by breakthrough curves. It was shown also that axial bed porosity variation could be replaced by average porosity with negligible error for DC calculations.     

Rigorous model for spherical cell-support aggregate

The activity of immobilized cell-support particle aggregates is influenced by physical and biochemical elements, mass transfer, and physiology. Accordingly, the mathematical model discussed in this study is capable of predicting the steady state and transient concentration profiles of the cell mass and substrate, plus the effects of the substrate and product inhibition in an immobilized cell-support aggregate. The overall mathematical model is comprised of material balance equations for the cell mass, major carbon source, dissolved oxygen, and non-biomass products in a bulk suspension along with a single particle model. A smaller bead size and higher substrate concentration at the surface of the particle, resulted in a higher supply of the substrate into the aggregate and consequently a higher biocatalyst activity.     

Effect of particle-particle shearing on the bioleaching of sulfide minerals

The biological leaching of sulfide minerals, used for the production of gold, copper, zinc, cobalt, and other metals, is very often carried out in slurry bioreactors, where the shearing between sulfide particles is intensive. In order to be able to improve the efficiency of the bioleaching, it is of significant importance to know the effect of particle shearing on the rate of leaching. The recently proposed concept of ore immobilization allowed us to study the effect of particle shearing on the rate of sulfide (pyrite) leaching by Thiobacillus ferrooxidans. Using this concept, we designed two very similar bioreactors, the main difference between which was the presence and absence of particle-particle shearing. It was shown that when the oxygen mass transfer was not the rate-limiting step, the rate of bioleaching in the frictionless bioreactor was 2.5 times higher than that in a bioreactor with particle friction (shearing). The concentration of free suspended cells in the frictionless bioreactor was by orders of magnitude lower than that in the frictional bioreactor, which showed that particle friction strongly reduces the microbial attachment to sulfide surface, which, in turn, reduces the rate of bioleaching. Surprisingly, it was found that formation of a layer of insoluble iron salts on the surface of sulfide particles is much slower under shearless conditions than in the presence of particle-particle shearing. This was explained by the effect of particle friction on liquid-solid mass transfer rate. The results of this study show that reduction of the particle friction during bioleaching of sulfide minerals can bring important advantages not only by increasing significantly the bioleaching rate, but also by increasing the rate of gas-liquid oxygen mass transfer, reducing the formation of iron precipitates and reducing the energy consumption. One of the efficient methods for reduction of particle friction is ore immobilization in a porous matrix.     

New Insights into the Pelletization Mechanism by Extrusion/Spheronization

Pellet manufacturing by extrusion/spheronization is quite common in the pharmaceutical field because the obtained product is characterized by a high sphericity as well as a narrow particle size distribution. The established mechanisms only consider deformation of the initially fractured particles but do not account for mass transfer between the particles as a factor in achieving spherical particles. This study dealt with the visualization of mass transfer during spheronization. Therefore, two common pelletization aids, microcrystalline cellulose and kappa-carrageenan, were used alone as well as in combination with lactose as a filler. This study proves that mass transfer between particles must be considered in addition to plastic deformation in order to capture the spheronization mechanism. Moreover, it is evident that there are regional distinctions in the amount of mass transfer at the particle surface. Therefore, the commonly espoused pelletization mechanisms need to be extended to account for material transfer between pellet particles, which has not been considered before.     

The influence of particle size distribution and operating conditions on the adsorption performance in fluidized beds

The influence of matrix properties and operating conditions on the performance in fluidized-bed adsorption has been studied using Streamline diethyl-aminoethyl (DEAE), an ion exchange matrix based on quartz-weighted agarose, and bovine serum albumin (BSA) as a model protein. Three different particle size fractions (120-160 mum, 120-300 mum, and 250-300 mum) were investigated. Dispersion in the liquid phase was reduced when particles with a wide size distribution were fluidized compared to narrow particle size distributions. When the mean particle diameter was reduced, the breakthrough capacities during frontal adsorption were enlarged due to a shorter diffusion path length within the matrix. At small particle diameters the effect of film mass transfer became more relevant to the adsorption performance in comparison to larger particles. Therefore matrices designed for fluidized-bed adsorption should have small particle diameter and increased mean particle density to ensure small diffusion path length in the particle and a high interstitial velocity to improve film mass transfer. Studies on the influence of sedimented matrix height on axial mixing showed an increased Bodenstein number with increasing bed length. Higher breakthrough capacities were also found for longer adsorbent beds due to reduced dispersion and improved fluid and particle side mass transfer. With increasing bed height the influence of flow rate on breakthrough capacity was reduced. For a settled bed height of 50 cm breakthrough capacities of 80% of the equilibrium capacity for flow rates varying from 3 to 9 cm/min could be achieved. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 55: 54-64, 1997.     

Local overall volumetric gas-liquid mass transfer coefficients in gas-liquid-solid reversed flow jet loop bioreactor with a non-Newtonian fluid

The local overall volumetric gas-liquid mass transfer coefficients at the specified point in a gas-liquid-solid three-phase reversed flow jet loop bioreactor (JLB) with a non-Newtonian fluid was experimentally investigated by a transient gassing-in method. The effects of liquid jet flow rate, gas jet flow rate, particle density, particle diameter, solids loading, nozzle diameter and CMC concentration on the local overall volumetric gas-liquid mass transfer coefficient (K(L)a) profiles were discussed. It was observed that local overall K(L)a profiles in the three-phase reversed flow JLB with non-Newtonian fluid increased with the increase of gas jet flow rate, liquid jet flow rate, particle density and particle diameter, but decreased with the increase of the nozzle diameter and CMC concentration. The presence of solids at a low concentration increased the local overall K(L)a profiles, and the optimum of solids loading for a maximum profile of the local overall K(L)a was found to be 0.18x10(-3)m(3) corresponding to a solids volume fraction, varepsilon(S)=2.8%.     

Performance of a shaking vessel with current pole

To improve solid particle suspensions in liquids in a shaking vessel, a pole was installed at the axis of the shaking vessel, which was referred to as the "current pole". The performance of a shaking vessel with current pole at its central axis was examined experimentally with respect to particle dispersion, power consumption, mixing time and solid-liquid mass transfer coefficient. The current pole improved the particle suspension without an increase in power consumption and reduced the critical circulating frequency for complete suspension. The current pole was very effective in eliminating the stagnation point on the vessel bottom and to decrease the mixing time. The mass transfer coefficient with a current pole had the same value as that without a current pole above the critical circulating frequency for complete suspension. As the diameter of the current pole increased, the mixing time decreased. A pole diameter of 5% of the vessel diameter was effective for suspension.     

Albumin recovery with centrifugal adsorption technology (CAT)

Centrifugal adsorption technology (CAT) is a new compact, countercurrent technology for efficient adsorption from large liquid streams by using adsorbent particles in the micrometer range. CAT seems particularly suited for the recovery of macromolecules at low concentrations, because the small particle dimensions lead to fast mass transfer rates. In this work, the potential of CAT for protein recovery is studied by model and experiment. A predictive model for the separation performance of CAT is presented, incorporating mass transfer resistance and axial dispersion transport in the liquid and the adsorbent phases. The model calculations were compared to experimental data for the adsorption of bovine serum albumin (BSA) on a standard commercial anion-exchange resin with particle diameter d(p) = 50 microm in a pilot-scale CAT apparatus. The model calculations accurately predicted the separation efficiency of CAT. The experimental set-up is shown to be mass transfer limited for the conducted experiments, which agrees with the model predictions. The model was also used to estimate the dimensions and performance of a CAT apparatus for the large-scale recovery of human serum albumin (HSA) from fermentation broth at the scale of 40 tons per year. The resulting equipment dimensions proved to be very small indeed, making CAT a potentially very attractive technology.     

Application of genetic algorithm for determination of the effective diffusivity of andrographolide in plant materials

The effective diffusivity of natural medicinal components is an important property for a detailed pharmaceutical extraction study and a proper design of the extraction process and unit. A mass transfer mathematical model for solvent extraction of andrographolide was developed and numerically solved taking into account particle geometries, solvent concentration, mass fraction of two different geometries of plant materials, external mass transfer resistance and solid–liquid equilibrium concentration. Using inverse simulation approach with genetic algorithm, unknown four key parameters in the developed model, effective diffusivity, partition coefficient, average particle size and mass fraction of leaf particles were determined at different extraction temperatures and solvent concentrations. The simulated data through the genetic algorithm-numerical model (GA-NM) and experimental data showed a good agreement (r² > 0.97 and MSE < 0.0016) indicating that the scheme with genetic algorithm can be effectively used for determination of the effective diffusivity of andrographolide in plant materials.     

Relationship between mass transfer coefficient and liquid flow velocity in heterogenous biofilms using microelectrodes and confocal microscopy

The relationship between local mass transfer coefficient and fluid velocity in heterogenous biofilms was investigated by combining microelectrodes and confocal scanning laser microscopy (CSLM). The biofilms were grown for up to 7 days and consisted of cell clusters separated by interstitial channels. Mass transfer coefficient depth profiles were measured at specific locations in the cell clusters and channels at average flow velocities of 2.3 and 4.0 cm/s. Liquid flow velocity profiles were measured in the same locations using a particle tracking technique. The velocity profiles showed that flow in the open channel was laminar. There was no flow at the top surface of the biofilm cell clusters but the mass transfer coefficient was 0.01 cm/s. At the same depth in a biofilm channel, the flow velocity was 0.3 cm/s and the mass transfer coefficient was 0.017 cm/s. The mass transfer coefficient profiles in the channels were not influenced by the surrounding cell clusters. Local flow velocities were correlated with local mass transfer coefficients using a semi-theoretical mass transfer equation. The relationship between the Sherwood number (Sh,) the Reynolds number (Re,) and the Schmidt number (Sc) was found using the experimental data to find the dimensionless empirical constants (n1, n2, and m) in the equation Sh = n(1) + n(2)Re(m) Sc(1/3). The values of the constants ranged from 1.45 to 2.0 for n(1), 0.22 to 0.28 for n(2), and 0.21 to 0.60 for m. These values were similar to literature values for mass transfer in porous media. The Sherwood number for the entire flow cell was 10 when the bulk flow velocity was 2.3 cm/s and 11 when the bulk flow velocity was 4.0 cm/s. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 56: 681-688, 1997.     

Peristaltic transport as the travelling deformation waves

Geometry approach to the theoretical and experimental investigations of peristaltic waves based on the travelling deformation waves and wave mass transfer theory (Dobrolyubov, 1991) is presented. The theory of travelling deformation waves is employed to determine uniformed expressions for mass transfer capability parameters of peristalsis. Slow (quasi-static) wave motion is considered which permits not to take into account dynamic phenomena.     

Hydrodynamic characteristics and gas-liquid mass transfer in a biofilm airlift suspension reactor

The hydrodynamics and mass transfer, specifically the effects of gas velocity and the presence and type of solids on the gas hold-up and volumetric mass transfer coefficient, were studied on a lab-scale airlift reactor with internal draft tube. Basalt particles and biofilm-coated particles were used as solid phase. Three distinct flow regimes were observed with increasing gas flow rate. The influence of the solid phase on the hydrodynamics was a peculiar characteristic of the regimes. The volumetric mass transfer coefficient was found to decrease with increasing solid loading and particle size. This could be predominantly related to the influence that the solid has on gas hold-up. The ratio between gas hold-up and volumetric mass transfer coefficient was found to be independent of solid loading, size, or density, and it was proven that the presence of solids in airlift reactors lowers the number of gas bubbles without changing their size. To evaluate scale effects, experimental results were compared with theoretical and empirical models proposed for similar systems.     

Hydrolysis of particulate tributyrin in a fluidized lipase reactor.

Pancreatic lipase has been immobilized onto stainless steel beads by adsorption followed by crosslinking, and onto polyacrylamide by covalent bonding. The activities of the two types of immobilized enzyme toward the particulate substrate, tributyrin emulsion droplets, were determined experimentally, and rate constants based on Michaelis-Menten kinetics were calculated. The activity of the stainless steel-lipase was determined for various flow conditions and for various support sizes by the use of a differential fluidized bed recycle reactor. The rate constants calculated indicate that the experimental reaction rate is free from mass transfer influences, since the observed Michaelis constant does not vary with the fluidization velocity or with the support particle size. In addition, the Michaelis constant of the stainless steel-lipase was found to be equal to that of the free enzyme, suggesting that adsorption and subsequent crosslinking does not alter the enzyme-substrate affinity. The emulsion substrate mass transfer rates, calculated from the filtration theory, indicate that each substrate particle which contact the immobilized enzyme is hydrolyzed to a significant extent. The experimentally determined kinetic rate constants may be used directly to predict the size of integral fluidized bed reactors.     

Parametric sensitivity of stoichiometric flux balance models applied to wild-type Escherichia coli metabolism

The esterification of lauric acid with geraniol catalyzed by the commercially immobilized lipase preparation from Mucor miehei, Lipozyme(R), was studied in well-stirred flasks. The enzyme support was characterized in terms of its internal and external surface area, protein location, and protein content. It was found that the enzyme was mainly located on the external surface of the support, therefore, internal diffusional limitations were not important. It was also shown that the protein content of the support depends on the size of the particle, with smaller particles containing higher amounts of protein per unit weight. Under the conditions studied, the reaction was not under external mass transfer limitations, and the initial reaction rate depended on the size of the support particles. This was mainly due to the different protein contents on the support as a function of particle size and not to internal or external mass transfer limitations. Also, it was found that the inhibition exerted by water was predominantly a physical effect due to its accumulation around the enzyme. It was also found that the reaction was substrate inhibited by lauric acid, but not by geraniol. (c) 1995 John Wiley & Sons, Inc.     

Relationship between cholesteryl ester transfer protein and LDL heterogeneity in familial hypercholesterolemia

Small, dense LDL particles have been associated with an increased risk of coronary artery disease, and cholesteryl ester transfer protein (CETP) has been suggested to play a role in LDL particle remodeling. We examined the relationship between LDL heterogeneity and plasma CETP mass in familial hypercholesterolemia (FH). LDL particles were characterized by polyacrylamide gradient gel electrophoresis in a total of 259 FH heterozygotes and 208 nonFH controls. CETP mass was measured by enzyme-linked immunosorbent assay in a subgroup of 240 participants, which included 120 FH patients matched with 120 controls. As compared with controls, FH subjects had an 11% higher CETP mass. Moreover, LDL-peak particle diameter (LDL-PPD) was significantly smaller in FH heterozygotes than in controls (258.1 +/- 4.8 vs. 259.2 +/- 4.1 A; P = 0.01) after adjustment for covariates. There was also an inverse relationship between LDL-PPD and CETP mass (R = -0.15; P = 0.02), and this relationship was abolished by adjustment for the FH/control status, indicating that LDL-PPD changes in FH are mediated, at least in part, by an increase in plasma CETP mass concentrations. These results suggest that increased plasma CETP mass concentrations could lead to significant LDL particle remodeling in FH heterozygotes and could contribute to the pathogenesis of atherosclerosis.     

Generalized transition state method and continuous diffusion in multi-dimensional systems with relation to ion transport in channels of biological membranes

An exact expression for the escape rate of a particle in a multi-dimensional system, with respect to an arbitrary reaction coordinate, is derived from first principles according to the transition state method, using a simple geometrical argument. It is shown how the mutual coupling of all degrees of freedom due to the interaction forces leads to the appearance of an effective mass and the potential of the mean force. The same relevant quantities dominate the effective one-particle Fokker-Planck equation, which is derived by a similar projection procedure from the multi-dimensional transport equation. In the limit of a large, position-dependent friction the respective effective Smoluchowski equation is obtained. It allows for the discussion of a diffusing particle which is subject to a temperature bath only through the coupled motion with the constituent lattice particles, or ligands in the case of a molecular ion channel. This treatment is of particular importance for the analysis of ion transport in membrane pores in which the ionic motion is mediated by internal ligand motion.     

Role of diffusion in nonaqueous enzymology. 1. Theory.

Using a set of standard equations, we have calculated the role of internal and external mass transfer in limiting the rate of enzyme-catalysed reactions in anhydrous organic solvents and supercritical fluids. We have shown that enzyme particles suspended in anhydrous organic solvents will be subject to increasing diffusional limitation as the enzyme activity and particle size increase. Using particle dimensions, as measured by scanning electron microscopy, we have prepared a series of graphs that will enable investigators to determine whether their combination of particle size and activity will result in internal or external diffusional limitations. We have shown that supercritical fluids can be expected to enhance the activity of enzymes in nonaqueous environments as a result of the high diffusivity of the bulk solvent. The plots also clearly indicate that enzyme particles in supercritical fluids require nearly two orders of magnitude less agitation than those suspended in conventional solvents in order to overcome any external mass transfer limitations.     

Oxygen supply to immobilized cells: 5. Theoretical calculations and experimental data for the oxidation of glycerol by immobilized Gluconobacter oxydans cells with oxygen or p-benzoquinone as electron acceptor

Theoretical calculations of reaction kinetics were done for one-step reactions catalyzed by cells immobilized in spherical beads. The reactions catalyzed by free cells were assumed to obey Michaelis-Menten kinetics for a one-substrate reaction. Both external (outside the beads) and internal (inside the beads) mass transfer of the substrate were considered for the immobilized preparations. The theoretical calculations were compared with experimental data for the oxidation of glycerol to dihydroxyacetone by Gluconobacter oxydans cells immobilized in calcium alginate gel. Glycerol was present in excess so that the reaction rate was limited by oxygen. The correlation between experimental data and theoretical calculations was quite good. The calculations showed how the overall effectiveness factor was influenced by, for example, the particle size and the cell density in the beads. In most cases the reaction rate was mainly limited by internal mass transfer of the substrate (oxygen). As shown previously, p-benzoquinone can replace oxygen as the electron acceptor in this reaction. The same equations for reaction kinetics and mass transfer were used with p-benzoquinone as the rate-limiting substrate. Parameters such as diffusivity, maximal reaction rate, and K were, of course, different. In this case also, the correlation between the model and the experimental results was quite good. Much higher production rates were obtained with p-benzoquinone as the electron acceptor compared to when oxygen was used. The reasons for this fact were that p-benzoquinone gave a higher maximal reaction rate for free cells and the solubility of p-benzoquinone was higher than for oxygen. Different methods of increasing the rate of microbial oxidation reactions are discussed.