Gas absorption in pulmonary airways at low Peclet number

A mathematical model is presented that investigates the mass transport of a diffusible and soluble gas contaminant through a liquid-lined tube when the Peclet number is small. The transport is determined by four dimensionless parameters: lambda, the tube aspect ratio; d, the relative difference in end concentrations; gamma, the radial transport coefficient; and Pe, the Peclet number. The problem is formulated for arbitrary gamma, but in the case of ozone and nitrous oxides the value of gamma is small. An asymptotic analysis for Pe much less than 1 and gamma much less than 1 is presented which yields the concentration field and transport characteristics we seek. It also provides a low Peclet number analysis for the conjugate problem of mass and heat transfer that is not currently available in the literature. The application to transport in the small airways of the lung is discussed, particularly the radial absorption differences in inspiratory and expiratory flow. Depending on the relative sizes of gamma and Pe, fractional uptake decreases with increasing Pe during inspiration but can increase during expiration.     

Residence time distributions of gas flowing through rotating drum bioreactors

Residence time distribution studies of gas through a rotating drum bioreactor for solid-state fermentation were performed using carbon monoxide as a tracer gas. The exit concentration as a function of time differed considerably from profiles expected for plug flow, plug flow with axial dispersion, and continuous stirred tank reactor (CSTR) models. The data were then fitted by least-squares analysis to mathematical models describing a central plug flow region surrounded by either one dead region (a three-parameter model) or two dead regions (a five-parameter model). Model parameters were the dispersion coefficient in the central plug flow region, the volumes of the dead regions, and the exchange rates between the different regions. The superficial velocity of the gas through the reactor has a large effect on parameter values. Increased superficial velocity tends to decrease dead region volumes, interregion transfer rates, and axial dispersion. The significant deviation from CSTR, plug flow, and plug flow with axial dispersion of the residence time distribution of gas within small-scale reactors can lead to underestimation of the calculation of mass and heat transfer coefficients and hence has implications for reactor design and scale-up.     

In vivo kinetics with rapid perturbation experiments in Saccharomyces cerevisiae using a second-generation BioScope

We present a robust second-generation BioScope: a system for continuous perturbation experiments. Firstly, the BioScope design parameters (i.e., pressure drop, overall oxygen (O2) and carbon dioxide (CO2) mass transfer, mean residence time distribution and plug flow characteristics) were evaluated. The average overall mass transfer coefficients were estimated to be 1.8E-5 m s(-1) for O2 and 0.34E-5 m s(-1) for CO2. It was determined that the O2/CO2 permeable membrane accounted for 75% and 95% of the overall resistance for O2 and CO2, respectively. The Peclet number (Pe) of the system was found to be >500 for liquid flow rates between 1 and 4 ml min(-1), ensuring plug flow characteristics. Secondly, steady-state intracellular metabolite concentrations obtained using direct rapid sampling from the fermentor were compared with those obtained by rapid sampling via the pre-perturbation sample port of the BioScope. With both methods the same metabolite levels were obtained. Thirdly, glucose perturbation experiments were carried out directly in the fermentor as well as in the BioScope, whereby steady-state Saccharomyces cerevisiae cells from a glucose/ethanol limited chemostat were perturbed by increasing the extracellular glucose concentration from 0.11 to 2.8 mM. Intracellular and extracellular metabolite levels were measured within a time window of 180 s. It was observed that the dynamic metabolite concentration profiles obtained from both perturbations were nearly the same, with the exception of the C4 metabolites of the TCA cycle, which might be due to differences in culture age.     

The influence of complex biological feedstock on the fluidization and bed stability in expanded bed adsorption

The stability of expanded bed adsorption systems (EBA) was studied in biomass containing culture broth by residence time distribution (RTD) experiments, using pulse inputs of fluorescent molecules as tracers. Different commercial adsorbents (Streamline DEAE, SP, Phenyl, Chelating, and AC) were tested at various biomass concentrations (2.5–12 %, wet weight) of whole (Saccharomyces cerevisiae) yeast, yeast cell homogenate, and Escherichia coli homogenate. Analyzing the RTD according to the PDE model (PDE: axially dispersed plug‐flow exchanging mass with stagnant zones) allowed the calculation of three parameters: the number of transfer units for mass exchange between mobile and stagnant fraction (N), the Peclet number for overall axial dispersion (P), and the mobile fraction of the liquid in axially dispersed plug flow (φ). When fluidization was performed in particle‐free buffer the normalized response signal (after perfect input pulse) was symmetric (N:0; P: 50–100; φ: 1), thus, demonstrating the formation of a homogeneous fluidized (expanded) bed. Upon application of suspended biomass the RTD was skewed, depending on the adsorbent used and the type and level of biomass present in the sample. This situation leads to three different characteristic pictures: the well‐fluidized system (N: ≥ 7–10; P: ≥ 40; φ: 0.80–0.90), the system exhibiting bottom channeling (N: < 1–2; P: ≥ 40; φ: 0.5–0.7) and, the system where extensive agglomeration develops (N: 4–7; P: 20–40; φ: < 0.5). These results demonstrate that changes in the hydrodynamics of EBA already take place in the presence of moderate concentrations of biomass. Furthermore, those changes can be quantitatively described mainly in terms of the fraction of stagnant zones in the system, which are formed due to the interaction of biomass and adsorbent. The technique described here can be used to evaluate a certain combination of adsorbent and biomass with regard to its suitability for expanded bed adsorption from whole broth. © 1999 John Wiley & Sons, Inc. Biotechol Bioeng 64: 484–496, 1999.     

Characterizing mixing in a rotating drum bioreactor for solid-state fermentation

A method, based on the use of wheat bran particles dyed with Rhodamine-WT as tracer particles, was developed to characterize mixing in a 200 l rotating drum bioreactor used for solid state fermentation. The extraction process contributes a 15% relative error in determining Rhodamine concentrations. Extraction efficiency is not affected by autoclaving of the bran and there is no inter-particle transfer of dye during the mixing of bran within the drum. For an unbaffled drum rotated at 5 rpm the axial dispersion coefficient is 9.15 cm² min^–1.     

A modified model for predicting the performance of a compact artificial kidney.

A modified urea transfer model is presented in this work for predicting the urea removal in a compact artificial kidney. The modified model represents a departure from the previous one in two aspects. A simpler plug flow equation instead of a general dispersion one is employed for describing the urea transport in the blood flow. This is justified by the rather large Peclet number for the present system. Furthermore, the internal and external urea diffusion resistances in the microencapsulated urease particle are incorporated into the urea balance equations in this work. Results of numerical simulation indicate that the urea diffusion resistances play a dominating role in the determination of urea removal from the artificial kidney. Effects of other physical parameters, such as the urea concentration in microencapsule, the membrane thickness and the partition coefficient between the membrane and the urease solution, on the performance of the artificial kidney are found to be of less significance.     

Oxygen transfer and axial dispersion in an aeration tower containing static mixers

Oxygen transfer from gas to liquid under steady-state cocurrent flow conditions was modeled using the dispersion model, and the oxygen transfer coefficients were estimated from available data for a column with Koch motionless mixers. The dispersion in the column was estimated for several different gas and liquid flow rates using steady-state tracer experiments. The estimated oxygen transfer coefficients were compared with those estimated using complete mixing and plug flow models. The results indicate that the dispersion model is the most appropriate model for estimating the mass transfer coefficient from the available data.     

Measurement of local mass transfer coefficient in biofilms

Local mass transfer rates for an electrochemically formed microsink in an aerobic biofilm was measured by a mobile microelectrode using limiting current technique. Mass transfer coefficients varied both horizontally and vertically in the biofilm. The results implied the existence of an irregular biofilm structure consisting of microbial cell clusters surrounded by tortuous water channels. An unexpected increase of the local mass transfer coefficient just above the biofilm surface suggested the existence, of local flow instability in this region. As expected, the influence of bulk flow velocity on the local mass transfer rate decreased with increasing depth into the biofilm. Mass transfer coefficients fluctuated significantly inside microbial cell clusters, suggesting the existence of internal channels through which liquid could flow. A new conceptual model of biofilm microbial cluster structure is proposed to account for such biofilm microstructure irregularities. (c) 1995 John Wiley & Sons, Inc.     

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.     

Oxygen mass transfer into aerated CMC solutions in a bubble column

Differing findings on the volumetric mass transfer coefficients k(L)a in CMC solutions in bubble column bioreactors have been reported in the literature. Therefore, oxygen mass transfer was studied again in CMC solutions in a 14-cm-i.d. x 270-cm-height bubble column using different spargers. The k(L)a values were determined along with the dispersion coefficients by fitting the prediction of the axial dispersed plug model with the experimental oxygen concentration profiles in the liquid phase. Surprisingly, the obtained liquid phase dispersion coefficients for CMC solution are higher than one would expect from correlations. The k(L)a data depend largely on the flow regime. In general, they are lower than those reported in the literature. The data for developing slug and established slug flow are dependent on the gas velocity and the effective viscosity of the solution and can br correlated by a simple correlation. This correlation describes k(L)a values measured on fermentation broth of Penicillium chrysogenum with striking agreement.     

Gas–liquid mass transfer in an up-flow cocurrent packed-bed biofilm reactor

Gas–liquid mass transfer was investigated in an up-flow cocurrent packed-bed biofilm reactor. In aerobic processes gas–liquid mass transfer can be considered as a key operational parameter as well as in reactor scale-up. The present paper investigates the influence of the liquid phase mixing in the determination of the volumetric gas–liquid mass transfer coefficient (k_La) coefficient. Residence time distribution (RTD) experiments were performed in the reactor to determine the flow pattern of the liquid phase and to model mathematically the liquid phase mixing. The mathematical model derived from RTD experiments was used to evaluate the influence of the liquid mixing on the experimental estimation of the (k_La) in this reactor type. The methods used to estimate the k_La coefficient were: (i) dynamic gassing-out, (ii) sulphite method, and (iii) in-process estimation through biological conversion obtained in the reactor. The use of standard chemical engineering correlations to determine the k_La in this type of bioreactors is assessed. Experimental and modelling results show how relevant can be to take into consideration the liquid phase mixing in the calculations of the most-used methods for the estimation of k_La coefficient. k_La coefficient was found to be strongly heterogeneous along the reactor vertical axis. The value of the k_La coefficient for the packed-bed section ranged 0.01–0.12 s⁻¹. A preliminary correlation was established for up-flow cocurrent packed-bed biofilm reactors as a function of gas superficial velocity.     

Mass transfer resistance of sterile plugs in shaking bioreactors

One of the mass transfer resistances for the gas exchange of shaking flasks is the sterile plug. The gas exchange through the sterile plug is described by an extended model of Henzler and Schedel [Bioprocess Eng. 7 (1991) 123]. Based on this model, a new method was developed to obtain the mass transfer resistance of various sterile closures. It consists of measuring the water evaporation rate of the shaking flask and is therefore very easily applied. Sterile plugs made of cotton, wrapped paper, urethane foam and fibreglass and caps made out of aluminium and silicone have been examined. Instead of the oxygen transfer coefficient (k(O(2))), which is commonly found in the literature, the carbon dioxide diffusion coefficient (D(CO(2))) is used to describe the mass transfer resistance of the sterile plug. The investigation revealed that this resistance is mainly dependent on the neck geometry and to a lesser extent on the plug material and density. The gas exchange of aluminium-caps was not reproducible.     

Solid-state fermentation in rotating drum bioreactors: operating variables affect performance through their effects on transport phenomena

Aspergillus oryzae ACM 4996 was grown on an artificial gel-based substrate and on steamed wheat bran during solid-state fermentations in 18.7 L rotating drum bioreactors. For gel fermentations fungal growth decreased as rotational speed increased, presumably due to increased shear. For wheat bran fermentations fungal growth improved under agitated compared to static culture conditions, due to superior heat and mass transfer. We conclude that the effects of operational variables on the performance of SSF bioreactors are mediated by their effects on transport phenomena such as mixing, shear, heat transfer, and mass transfer within the substrate bed. In addition, the substrate characteristics affect the need for and the rates of these transport processes. Different transport phenomena may be rate limiting with different substrates. This work improves understanding of the effects of bioreactor operation on SSF performance.     

A semi-analytical model for dissolved oxygen mass transfer coefficient at the sediment–water interface

Relying on the fundamental principles of mass transport in a turbulent flow, we have developed a semi-analytical model for a mass transfer coefficient in a sediment water interface over a smooth bed. The governing equations with boundary conditions reflect a mechanism of shear dispersion in a turbulent flow. The model is formulated in terms of the Sherwood-Reynolds-Schmidt functional dependence. Unlike previous regression-type models, the mass transfer coefficient at the sediment-water interface is parameterized by the friction coefficient. Flow conditions over a smooth bed ranging in Reynolds number from 1800 to 7000 were used to verify the model. The predicted mass transfer coefficients are in very good agreement with the experimental data.     

Axial mixing in rotating drums using magnetic resonance imaging using bran as a model for solid state fermentations

Magnetic resonance imaging (MRI) is an easily automated, reliable technique to investigate axial mixing within rotating drums. Moist bran can be clearly differentiated from dry bran using MRI allowing a non-segregating tracer for axial mixing. For a 20-cm diameter drum, the axial dispersion coefficient in the particle bed was 0.51 cm s^–2. Axial dispersion is scale-dependent.     

Microelectrode measurements of local mass transport rates in heterogeneous biofilms

Microelectrodes were used to measure oxygen profiles and local mass transfer coefficient profiles in biofilm clusters and interstitial voids. Both profiles were measured at the same location in the biofilm. From the oxygen profile, the effective diffusive boundary layer thickness (DBL) was determined. The local mass transfer coefficient profiles provided information about the nature of mass transport near and within the biofilm. All profiles were measured at three different average flow velocities, 0.62, 1.53, and 2.60 cm sec-1, to determine the influence of flow velocity on mass transport. Convective mass transport was active near the biofilm/liquid interface and in the upper layers of the biofilm, independent of biofilm thickness and flow velocity. The DBL varied strongly between locations for the same flow velocities. Oxygen and local mass transfer coefficient profiles collected through a 70 micrometer thick cluster revealed that a cluster of that thickness did not present any significant mass transport resistance. In a 350 micrometer thick biofilm cluster, however, the local mass transfer coefficient decreased gradually to very low values near the substratum. This was hypothetically attributed to the decreasing effective diffusivity in deeper layers of biofilms. Interstitial voids between clusters did not seem to influence the local mass transfer coefficients significantly for flow velocities of 1.53 and 2.60 cm sec-1. At a flow velocity of 0.62 cm sec-1, interstitial voids visibly decreased the local mass transfer coefficient near the bottom.     

An analysis of pollutant gas transport and absorption in pulmonary airways

A mathematical model of ozone absorption, or for any soluble gas that has similar transport properties, is developed for a branching network of liquid-lined cylinders. In particular, we investigate specific flow regimes for finite length tubes where boundary layer phenomena and entrance effects exist in high Reynolds and Peclet (Pe) number airways. The smaller airways which have lower Reynolds and Peclet number flows are modelled by incorporating the detailed analysis found in [10] and modifying it for airways which have alveolated surfaces. We also consider a reacting gas and treat specific regimes where the reaction front is located at the air-liquid interface, within the liquid or at the liquid-tissue interface. Asymptotic methods are used in regions of the tracheobronchial tree where Pe much less than 1 and Pe much greater than 1. In addition, the fact that the radial transport parameter gamma much less than 1 for this toxin, and others such as nitrous oxides, is employed to simplify the analysis. The ozone concentrations, airway absorption and tissue dose are examined as a function of airway generation for several values of the governing parameters. The general result is a maximal dosing in airway generations 17 to 18 that is much larger (up to an order of magnitude) than the predictions of previous theories.     

Dispersion optimization to enhance PHB production in fed-batch cultures of Ralstonia eutropha

Despite its many useful properties, microbial production of poly-beta-hydroxybutyrate (PHB) is not yet commercially competitive with synthetic polymers. One reason is inadequate optimization of the fermentation under industrial conditions. In this study, a physiologically reasonable and experimentally validated kinetic model for PHB synthesis by Ralstonia eutropha was incorporated into a dispersion model to simulate a large fed-batch bioreactor. Solutions of the model indicated that cell growth and PHB synthesis were maximum at Peclet numbers (Pe) between 20 and 30, representing limited finite dispersion. At these Peclet numbers, the optimum feed rates also showed lower consumptions of the substrates than at Pe=0. Since complete dispersion was also difficult to achieve in production-scale bioreactors, these results pointed to the possibility of exploiting controlled dispersion for productivity enhancement.     

Axial dispersion in respiratory bronchioles and alveolar ducts

The mixing of gases in the pulmonary acinus was characterized by analyzing axial gas dispersion during steady flow in models of respiratory bronchioles and alveolar ducts. An analysis (method of moments) developed for addressing dispersion in porous media was used to derive an integral expression for the axial dispersion coefficient (D*). Evaluation of D* required solving the Navier-Stokes equations for the flow field and a convection-diffusion type equation arising from the analysis. D* was strongly dependent on alveolar volume per central duct volume, the aperture size through which the alveoli communicate with the central duct, and the Péclet number (Pe). At smaller Pe (flow rate) D* was substantially smaller than the molecular diffusion coefficient, whereas at larger Pe (flow rate) D* was much greater than the Taylor-Aris result for flow-enhanced dispersion in straight tubes. Also, flow-enhanced dispersion became appreciable at smaller Pe than indicated by the Taylor-Aris result. These behaviors transcend both the lower and upper limits established previously for gas mixing in the pulmonary acinus.     

Influence of the tracer characteristics on hydrodynamic models of packed-bed bioreactors

A bench-scale horizontal-flow anaerobic immobilized sludge (HAIS) reactor filled with porous ceramic spheres (5?mm diameter) was used for evaluating the effects of the tracer characteristics on the residence time distribution (RTD) curves and on the parameters of the hydrodynamic mathematical models. Stimulus-response assays were carried out with bromophenol blue, dextran blue, eosin Y, mordant violet, rhodamine WT and bromocresol green as tracers. The reactor was operated at the hydraulic residence time (HRT) of approximately 2 hours and the flow characteristics were evaluated by fitting the single-parameter models of dispersion and N-continuous stirred tank reactors (CSTR) in series to the experimental data. Tracer characteristics were found to affect deeply the form of RTD curves and the apparent degree of mixing observed in the responses were attributed to the tracer diffusion into the porous media, except for dextran blue. The best adjustment was obtained for the N-CSTR in series model. Thereafter, dextran blue and rhodamine WT were used in hydrodynamic experiments in the HAIS reactor operating with additional residence times. Values of N ranging from 34 to 62 were obtained from the dextran blue experiments for HRT ranging from 2 to 7 hours. The application of the statistical analysis ANOVA one-way method indicated that there was no significant statistical difference in the flow-pattern within the range of hydraulic residence times applied. The mean N value of 9 was obtained from the experiments with rhodamine WT. Such disagreement in the responses was attributed to the diffusion of rhodamine WT into the porous media, interfering in the shape of the experimental curves.