Flow mixing enhancement from balloon pulsations in an intravenous oxygenator

Computational investigations of flow mixing and oxygen transfer characteristics in an intravenous membrane oxygenator (IMO) are performed by direct numerical simulations of the conservation of mass, momentum, and species equations. Three-dimensional computational models are developed to investigate flow-mixing and oxygen-transfer characteristics for stationary and pulsating balloons, using the spectral element method. For a stationary balloon, the effect of the fiber placement within the fiber bundle and the number of fiber rings is investigated. In a pulsating balloon, the flow mixing characteristics are determined and the oxygen transfer rate is evaluated. For a stationary balloon, numerical simulations show two well-defined flow patterns that depend on the region of the IMO device. Successive increases of the Reynolds number raise the longitudinal velocity without creating secondary flow. This characteristic is not affected by staggered or non-staggered fiber placement within the fiber bundle. For a pulsating balloon, the flow mixing is enhanced by generating a three-dimensional time-dependent flow characterized by oscillatory radial, pulsatile longitudinal, and both oscillatory and random tangential velocities. This three-dimensional flow increases the flow mixing due to an active time-dependent secondary flow, particularly around the fibers. Analytical models show the fiber bundle placement effect on the pressure gradient and flow pattern. The oxygen transport from the fiber surface to the mean flow is due to a dominant radial diffusion mechanism, for the stationary balloon. The oxygen transfer rate reaches an asymptotic behavior at relatively low Reynolds numbers. For a pulsating balloon, the time-dependent oxygen-concentration field resembles the oscillatory and wavy nature of the time-dependent flow. Sherwood number evaluations demonstrate that balloon pulsations enhance the oxygen transfer rate, even for smaller flow rates.     

Application of a Novel Oscillatory Flow Micro-bioreactor to the Production of γ-decalactone in a Two Immiscible Liquid Phase Medium

A novel micro-bioreactor based on the oscillatory flow technology was applied to the scale-down of the biotechnological production of γ-decalactone. A decrease up to 50% of the time required to obtain the maximum concentration of the compound was observed, when compared with other scaled-down platforms (stirred tank bioreactor or shake flask). A three-fold increase in γ-decalactone productivity was obtained by increasing oscillatory mixing intensity from Re_o ~482 to Re_o ~1447. This was presumably related to the effective contribution of the reactor geometry to enhanced mass transfer rates between the two immiscible liquid phases involved in the process by increasing the interfacial area. Revisions requested 11 October 2005; Revisions received 4 January 2006     

Mathematical modeling of non-ideal mixing continuous flow reactors for anaerobic digestion of cattle manure

Most conventional digesters used for animal wastewater treatment include continuously stirred-tank reactors. While imperfect mixing patterns are more common than ideal ones in real reactors, anaerobic digestion models often assume complete mixing conditions. Therefore, their applicability appears to be limited. In this study, a mathematical model for anaerobic digestion of cattle manure was developed to describe the dynamic behavior of non-ideal mixing continuous flow reactors. The microbial kinetic model includes an enzymatic hydrolysis step and four microbial growth steps, together with the effects of substrate inhibition, pH and thermodynamic considerations. The biokinetic expressions were linked to a simple two-region liquid mixing model, which considered the reactor volume in two separate sections, the flow-through and the retention regions. Deviations from an ideal completely mixed regime were represented by changing the relative volume of the flow-through region (a) and the ratio of the internal exchange flow rate to the feed flow rate (b). The effects of the hydraulic retention time, the composition of feed, the initial conditions of the reactor and the degree of mixing on process performance can be evaluated by the dynamic model. The simulation results under different conditions showed that deviations from the ideal mixing regime decreased the methane yield and resulted in a reduced performance of the anaerobic reactors. The evaluation of the impact of the characteristic mixing parameters (a) and (b) on the anaerobic digestion of cattle manure showed that both liquid mixing parameters had significant effects on reactor performance.     

Mixing and phase hold-ups variations due to gas production in anaerobic fluidized-bed digesters: influence on reactor performance

The influence of mixing and phase hold-ups on gas-producing fluidized-bed reactors was investigated and compared with an ideal flow reactor performance (CSTR). The liquid flow in the anaerobic fluidized bed reactor could be described by the classical axially dispersed plug flow model according to measurements of residence time distribution. Gas effervescence in the fluidized bed was responsible for bed contraction and for important gas hold-up, which reduced the contact time between the liquid and the bioparticles. These results were used to support the modeling of large-scale fluidized-bed reactors. The biological kinetics were determined on a 180-L reactor treating wine distillery wastewater where the overall total organic carbon uptake velocity could be described by a Monod model. The outlet concentration and the concentration profile in the reactor appeared to be greatly influenced by hydrodynamic limitations. The biogas effervescence modifies the mixing characteristics and the phase hold-ups. Bed contraction and gas hold-up data are reported and correlated with liquid and gas velocities. It is shown that the reactor performance can be affected by 10% to 15%, depending on the mode of operation and recycle ratio used. At high organic loading rates, reactor performance is particularly sensitive to gas effervescence effects. Copyright 1998 John Wiley & Sons, Inc.     

In vitro DNA-based predator-prey system with oscillatory kinetics

A coupled system of two isothermal in vitro DNA/RNA amplification reactions using different primers is modeled kinetically with realistic rate parameters and shown to exhibit oscillatory behavior in a flow reactor. One of the two isothermal amplification reactions acts as a predator of the other, the prey. The mechanism of the oscillatory behavior is analyzed in terms of a hierarchy of kinetic models. The work provides an insight into the choice of parameters for experiments. The latter are important in providing detailed insight into the complex processes of ecological interactions and their evolution.     

Characterization of stirrers for screening studies of enzymatic biomass hydrolyses on a milliliter scale

The evaluation of mixing quality is an important factor for improving the geometry of stirred-tank reactors and impellers used in bioprocess engineering applications, such as the enzymatic hydrolysis of plant materials. Homogeneity depends on different factors, including the stirrer type and the reactor type (e.g., ratio of diameter/height, ratio of impeller tip diameter/reactor diameter) with or without baffles. This study compares two impellers for enzymatic hydrolysis of suspensions of biomass particles on a milliliter scale. Both impellers were derived from industrially relevant geometries, such as blade and grid stirrers, although the geometry of the second stirrer was slightly modified to an asymmetric shape. The stirrers were investigated with different stirrer–reactor configurations. This was done experimentally and with the aid of computational fluid dynamics. The flow field, mixing numbers, power characteristics and initial conversion rates of sugars were considered to compare the two stirrers. The simulated mixing numbers and power characteristics in baffled and unbaffled milliliter-scale reactors were found to be in good agreement with the measured mixing times and power consumption. The mixing numbers required to reach homogeneity were much higher for the symmetric impeller and remained at least twice as high as the mixing numbers required when using the asymmetric impeller. The highest initial sugar releases from milled corn stover suspensions were achieved with the asymmetric impeller shape. Regardless of the differences in the flow fields or mixing times, diverging enzymatic sugar releases could be confirmed for Newtonian media only.     

Oscillatory flow and gas transport through a symmetrical bifurcation

Axial gas transport due to the interaction between radial mixing and radially nonuniform axial velocities is responsible for gas transport in thick airways during High-frequency oscillatory ventilation (HFO). Because the airways can be characterized by a bifurcating tube network, the secondary flow in the curved portion of a bifurcating tube contributes to cross-stream mixing. In this study the oscillatory flow and concentration fields through a single symmetrical airway bifurcating tube model were numerically analyzed by solving three-dimensional Navier-Stokes and mass concentration equations with the SIMPLER algorithm. The simulation conditions were for a Womersley number, alpha = 9.1 and Reynolds numbers in the parent tube between 200 and 1000, corresponding to Dn2/alpha 4 in the curved portion between 2 and 80, where Dn is Dean number. For comparison with the results from the bifurcating tube, we calculated the velocity and concentration fields for fully developed oscillatory flow through a curved tube with a curvature rate of 1/10, which is identical to the curved portion of the bifurcating tube. For Dn2/alpha 4 < or = 10 in the curved portion of the bifurcating tube, the flow divider and area changes dominate the axial gas transport, because the effective diffusivity is greater than in either a straight or curved tube, in spite of low secondary velocities. However, for Dn2/alpha 4 > or = 20, the gas transport characteristics in a bifurcation are similar to a curved tube because of the significant effect of secondary flow.     

Melatonin activates the peroxidase-oxidase reaction and promotes oscillations.

We have studied the peroxidase-oxidase reaction with NADH and O2 as substrates and melatonin as a cofactor in a semibatch reactor. We show for the first time that melatonin is an activator of the reaction catalyzed by enzymes from both plant and animal sources. Furthermore, melatonin promotes oscillatory dynamics in the pH range from 5 to 6. The frequency of the oscillations depends on the pH such that an increase in pH was accompanied by a decrease in frequency. Conversely, an increase in the flow rate of NADH or an increase in the average concentration of NADH resulted in an increase in oscillation frequency. Complex dynamics were not observed with melatonin as a cofactor. These results are discussed in relation to observations of oscillatory dynamics and the function of melatonin and peroxidase in activated neutrophils.     

Quantitative measurements of mixing intensity in shake-flasks and stirred tank reactors. Use of the Mixmeter, a mixing process analyzer

A new mixing probe has been developed which measures the motions of the fluid during mixing as pressure fluctuations and converts the measurements into a mixing signal (MS). The MS is the root mean square (RMS) pressure fluctuation in the 1-64Hz range as determined by a sensitive pressure sensor and a digital signal processor specifically designed for the purpose. The MS is a measure of the actual mixing flow of the fluid rather than a measurement of the input motions or energies into the reactor system (e.g. RPM, torque or power). In other studies, the MS has been measured as a function of mixing speed in numerous sized reactors from 10 to 1000l, and provides consistent and reproducible measurements. The MS increases monotonically as a function of mixing speed, with a change of slope corresponding to the transition from laminar to turbulent mixing regimes. Maps of MS as a function of location in the reactor are useful in understanding stirred tank reactor design and performance. Quantitative measurements of mixing are especially useful during process development as a tool to increase the success of scale-up during the transition from process development to manufacturing. Measurements at a fixed location in a given reactor are useful in understanding changes in mixing that occur during the course of a given process, and are useful in manufacturing situations where validated documentation of lot-to-lot consistency of mixing is required (e.g. pharmaceutical manufacturing). In addition, the probe has been used to measure mixing in vessels with vibrational mixers with similar results. The probe has been successfully used in feedback loops to control either mixing speed or vibrational mixing amplitude in order to maintain constant mixing of the fluid during processing. With this system it is possible to maintain constant mixing over a wide range of fluid volumes in a given reactor, and, for instance, to compensate for changes in viscosity throughout the course of the process. Adaptations of this system for the measurement of mixing in shake-flasks is described in this paper.     

Fluid flow pattern in upflow reactors for anaerobic treatment of beet sugar factory wastewater

Residence-time-distribution experiments for the fluid in a 30-m(3) pilot plant and a 200-m(3) prototype upflow reactor were performed by means of continuous injection of an LiCl solution as a tracer in the influent of the reactor and measurement of the response of this stimulus on several location in the reactor and in the effluent. In a similar way as described in an article published earlier, models have been developed by use of the measured data of the fluid flow pattern which consisted of region of ideal mixing, plug flow, dead space, and short circuiting. It appeared that the fluid flow patterns in the two reactors were to a large extent analogous. For the pilot plant, three-mixer models appeared to be appropriate while for the prototype reactor two-mixer models have been found. This differences was a result of the difference in the heights of the sludge beds in the reactors: 2-3 m in the pilot plant and only 0.4 m in the prototype reactor, a result of too small an amount of sludge. Another differences was that, due to large amount of mud in the prototype reactor, a region of dead space occurred in the models for the fluid flow pattern in this reactor. The dimension of the prototype reactor have been chosen according to several recommendations obtained from work with the pilot plant (e.g., scale-up should be done by increasing the cross section of the reactor; one influent point should be applied per 5 m(2) bottom surface). The results presented here clearly show the value of these recommendations.     

Numerical simulation of a fully baffled biological reactor: the differential circumferential averaging mixing plane approach

A modified mixing plane approach for steady state simulation of flow field in fully baffled biological reactor is presented and discussed. Without requiring any experimental input, this approach of dividing the vessel into suitable number of connected and disconnected zones; solving steady state equation separately in each zone and then transferring information between them, provides a computationally less intensive alternative for simulating the flow in the whole vessel. Impeller used is the standard Rushton Turbine positioned at mid-height of the reactor and simulations are carried out using standard k-epsilon turbulence model implemented in CFD code FLUENT. Meshing is done using tetrahedral elements such that mesh size gradually increases from the center to the periphery. Most of the previous simulation works present only a few aspects of the flow field with scant importance to the energy balance in the tank and near tip turbulence. In this work, complete model prediction for velocity field and turbulence parameters (near tip and in the bulk region) are validated by comparison with experimental data. As compared to previous simulation works, the results predicted by this "Differential circumferential averaging mixing plane approach" show a better qualitative and quantitative agreement with the published experimental data. A distribution of energy dissipation in various zones of vessel is presented. Also a qualitative picture of flow field and stagnant zones inside the reactor is presented and discussed. Comparison of flow characteristics for different number of baffles shows that for the present dimension of the vessel, five baffles gives maximum enhanced mixing.     

Mixing characteristics and startup of anaerobic downflow stationary fixed film (DSFF) reactors

Tests to determine the mixing characteristics of the anaerobic downflow stationary fixed film (DSFF) reactor during startup showed that mixing characteristics affected performance. Different mixing profiles were obtained by keeping the same flow distribution system and by varying the number of clay channels (1, 4, and 25) in the DSFF reactors (2-32 L). Results with a clean bed reactor indicated a plug flow pattern with a relatively large extent of dispersion. Recirculation dramatically improved the mixing and the residence time distribution (RTD) changed to that of the completely mixed type. Multiple-channel reactors exhibited a dead space of ca. 12% of the total volume, likely a result of a less than optimally designed flow distributor. A startup period of 90 days was necessary to achieve a maximum loading rate of between 10 and 15 kg COD/m(3) day, a volumetric methane production rate of up to 3 m(3) (STP)/m(3) day and a COD reduction efficiency of up to 90%. For the first 50 days of operation, the difference in achievable volumetric loading rate and volumetric methane production rate was only related to the surface-to-volume ratio of the reactors and was not affected by the number of channels present. After 90 days, the bacterial growth on the support material was sufficient to dramatically increase the amount of dead space in the reactors, especially in multiple-channel reactors (up to 55% of their volume). As a result, the performance of these reactors deteriorated and overloading characteristics were observed. Other results showed that biogas production alone was not sufficient to improve reactor mixing and that little or no shortcircuiting or channelling occurred. Furthermore, the nonmethanogenic bacterial activity in the liquid phase was not affected by the degree of mixing but acetoclastic methanogenic and hydrogenophilic methanogenic activity in the liquid phase were reduced as the fluid flow pattern in the reactor improved.     

A horizontal bioreactor for ethanol production by immobilized cells

The one-parameter-tanks-in-series model was found to be an adequate model for the characterization of flow dynamics in a horizontal immobilized cell reactor, when blue dextran was used as tracer. Isobutanol proved to be inadequate, because it diffused inside the beads and thus caused tailing in RTD. The CO₂ evolution rate displayed the most pronounced effect on axial liquid dispersion. At high CO₂ production rates and low dilution rates each stage of the reactor behaved like a well-mixed reactor. At lower CO₂ evolution rates the number of tanks (N) related to the reactor increased up to 10. The medium flow rate affects axial dispersion to a minor degree. An increase of the dilution rate from 0.328 to 1.34 h^?1 resulted in a slight rise of N from 3.5 to 5 at high CO₂ production and from 4 to 7 at medium CO₂ production rates. Variation in the bead hold up showed the same characteristic axial mixing behavior as reflected by changing the medium flow rate. The quantitative correlation between axial mixing and the most significant fermentation parameters (dilution rate, CO₂ evolution rate and bead hold up) allow to develop an overall model, which besides kinetic expressions also contains terms related to the flow dynamics of the reactor. In the third part of this communication such a model will be presented and compared with actual fermentation data.     

Countercurrent multistage fluidized bed reactor for immobilized biocatalysts: III. Hydrodynamic aspects

In Parts I and II of this series we described the modelling, design, and operation of a multistage fluidized bed reactor (MFBR) for immobilized biocatalysts. This article deals with those aspects of the MFBR which are different from single-stage fluidized beds which are operated in batch mode with respect to the solids. The semicontinuous transport of the particles requires perfect mixing of the particles in the reactor compartments, because particles are mainly transported from the bottom of these compartments. A large spread in the physical properties of the biocatalyst particles, especially of both size and density, may cause the particles to segregate into layers with different diameter and/or density. This affects the efficient use of the biocatalyst. The properties of the particles are dependent on the immobilization method. The suitability of different methods for possible future application in the MFBR is therefore compared. Because of segregation, successful use of a biofilm catalyst with a nonuniform thickness of the biofilm is doubtful. Experiments in a small scale reactor (+/- 0.1 m diameter) demonstrated that perfect particle mixing is possible using commercially available biocatalyst particles of uniform density. Co-immobilization of the biocatalyst with glass powder in a gel is a simple and effective method of increasing gel density. High density particles allow high liquid flow rates, and thus an improved external mass transfer can be achieved.The distributor plates, which separate the reactor compartments, must allow unhindered transport of particles. Therefore, the holes in these plates must have a diameter of at least 4.5 times that of the largest particles which are present in the particle mixture used. Furthermore, the plates must be designed such that, when scaling-up the reactor, a uniform liquid distribution over the cross-sectional area of the reactor occurs. Large-scale experiments were not carried out, but published correlations, indicate that particle mixing and a uniform liquid distribution can be accomplished in a large-scale reactor under similar flow conditions.     

Diffusion induced oscillatory insulin secretion

Oscillatory secretion of insulin has been observed in many different experimental preparations. Here we examine a mathematical model for in vitro insulin secretion from pancreatic beta cells in a flow-through reactor. The analysis shows that oscillations result because of an important interplay between flow rate of the reactor and insulin diffusion. In particular, if the ratio of flow rate to volume of the reaction bed is too large, oscillations are eliminated, in contradiction to the conclusions of Maki and Keizer (L. W. Maki and Keizer J. Mathematical analysis of a proposed mechanism for oscillatory insulin secretion in perifused HIT-15 cells. Bull. Math. Biol., 57 (1995), 569–591). Furthermore, with reasonable numbers for the experimental parameters and the diffusion of insulin, the model equations do not exhibit oscillations.     

Backmixing and mass transfer in the design of immobilized-enzyme reactors

The effects of dispersion and mass transfer resistance on the degree of conversion in an immobilized-enzyme reactor have been considered theoretically. It is assumed that the immobilized enzymes obey a Michaelis–Menten relationship and backmixing can be characterized by a dispersion model. For two extreme cases (perfect mixing and piston flow), approximate equations are obtained, which can be readily used to evaluate the effect of mass transfer on degree of conversion. Numerical solutions are obtained for other intermediate cases. Design charts are given which set practical limits of enzyme reactor design.     

A scale-down two-compartment reactor with controlled substrate oscillations: Metabolic response of Saccharomyces cerevisiae

Substrate concentration gradients are likely to appear during large scale fermentations. To study effects of such gradients on microorganisms, an aerated scale-down reactor system was constructed. It consists of a plug flow reactor (PFR) and a stirred tank reactor (STR), between which the medium is circulated. The PFR, which is an aerated static mixer reactor, was characterized with respect to plug flow behaviour and oxygen transfer. A Bodenstein number of 15–220, depending on residence time and aeration rate, and a k_La of 500–1130 h^–1, depending mainly on aeration rate, were obtained. The biological test system used, was aerobic ethanol production by Saccharomyces cerevisiae, due to sugar excess. The ethanol concentration profile and the yield of biomass were compared in two fed-batch fermentations. In the first case, the feeding point of molasses was located at the inlet of the PFR. This simulates location of the feeding point in the segregated part of a heterogeneous reactor, with local high sugar concentrations. In the second mode of operation, as a control with good mixing conditions, the PFR was disconnected from the STR, into which the substrate was fed. Differences were found: Up to 6% less biomass was produced and a larger amount of ethanol was formed in the two-compartment reactor system, due to the uneven sugar concentration distribution. This emphasizes the importance of the location of, and the mixing conditions at, the feeding point in a bioreactor.     

Mixing in liquid-impelled loop reactors

The liquid-impelled loop reactor is a new column-type bioreactor. The design of this device is based on the principle of the air-lift loop reactor. In the external-loop configuration used in this work, descending perfluorochemical drops bring about circulation of the continuous aqueous phase. Mixing of this continuous phase is characterized per section of the rector. Axial-dispersion coefficients for the tube with two-phase flow are determined and correlated with the energy dissipation in the tube. Comparisons with similar systems such as bubble columns and air-lift loop reactors are made. Overall mixing parameters are derived and used for calculation of the number of circulatins needed to achieve a certain degree of mixing. The hydrodynamic model from previous work is tested for the reactor configurations of this work. It can be useful to calculate circulation times.