Mass transport in a microchannel bioreactor with a porous wall

A two-dimensional flow model has been developed to simulate mass transport in a microchannel bioreactor with a porous wall. A two-domain approach, based on the finite volume method, was implemented. For the fluid part, the governing equation used was the Navier-Stokes equation; for the porous medium region, the generalized Darcy-Brinkman-Forchheimer extended model was used. For the porous-fluid interface, a stress jump condition was enforced with a continuity of normal stress, and the mass interfacial conditions were continuities of mass and mass flux. Two parameters were defined to characterize the mass transports in the fluid and porous regions. The porous Damkohler number is the ratio of consumption to diffusion of the substrates in the porous medium. The fluid Damkohler number is the ratio of the substrate consumption in the porous medium to the substrate convection in the fluid region. The concentration results were found to be well correlated by the use of a reaction-convection distance parameter, which incorporated the effects of axial distance, substrate consumption, and convection. The reactor efficiency reduced with reaction-convection distance parameter because of reduced reaction (or flux), and smaller local effectiveness factor due to the lower concentration in Michaelis-Menten type reactions. The reactor was more effective, and hence, more efficient with the smaller porous Damkohler number. The generalized results could find applications for the design of bioreactors with a porous wall.     

Conjugate Effects of Heat and Mass Transfer on MHD Free Convection Flow over an Inclined Plate Embedded in a Porous Medium

The aim of this study is to present an exact analysis of combined effects of radiation and chemical reaction on the magnetohydrodynamic (MHD) free convection flow of an electrically conducting incompressible viscous fluid over an inclined plate embedded in a porous medium. The impulsively started plate with variable temperature and mass diffusion is considered. The dimensionless momentum equation coupled with the energy and mass diffusion equations are analytically solved using the Laplace transform method. Expressions for velocity, temperature and concentration fields are obtained. They satisfy all imposed initial and boundary conditions and can be reduced, as special cases, to some known solutions from the literature. Expressions for skin friction, Nusselt number and Sherwood number are also obtained. Finally, the effects of pertinent parameters on velocity, temperature and concentration profiles are graphically displayed whereas the variations in skin friction, Nusselt number and Sherwood number are shown through tables.     

Study of performance of a tubular membrane reactor for an enzyme catalyzed reaction

A tubular membrane reactor offers many advantages over a solid wall reactor to carry out an enzyme catalyzed reaction. With proper membrane selectivity, the product, may be separated from the reacting stream and the enzyme recycled for continuous reuse. In most cases, enzyme reuse contributes to the economic feasibility of a continuous enzyme catalyzed process. Furthermore, the efficiency and performance of a membrane reactor is greater than that of a solid wall reactor. Continuous hydrolysis of starch by the enzyme β-amylase, carried out in a commercially available tubular membrane unit, is studied at different starch and enzyme concentrations for a given system pressure and inlet flow rate. Results show that the performance of the membrane reactor is in all cases greater than that of the solid wall reactor. A steady state in performance of permeation rate is, however, not reached by the membrane reactor, which shows a continuous decline within the periods examined in this study. This decline is caused in part by the aging of the starch solution, but mostly by the formation of a concentrated, or gel, layer at the membrane surface. This appears to be the main limiting factor for this process since the decline in reaction and permeation rate results in a severe decrease in the amount of maltose in the permeate.     

Predicting the performance of immobilized enzyme reactors using reversible Michaelis–Menten kinetics

A general mathematical model is developed in the present work for predicting the steady state performance of immobilized enzyme reactor performing reversible Michaelis - Menten kinetics. The model takes into account the effect of external diffusional limitations, the axial dispersion and the equilibrium constant on reactor performance quantified as relative substrate conversion and yield. The performance of reactor is characterized using the dimensionless parameters of Damkohler number, Stanton number, Peclet number, the equilibrium constant and the dimensionless input substrate concentration. The reactor performance is described for the two extreme cases of plug flow reactor (PFR) and continuous stirred tank reactor (CSTR) in addition to the intermediate case of dispersed plug flow reactor (DPFR). The performance of reactor is compared for the two cases of zero order and reversible first order kinetics.     

Biotechnology for the production of nutraceuticals enriched in conjugated linoleic acid: I. Uniresponse kinetics of the hydrolysis of corn oil by a Pseudomonas sp. lipase immobilized in a hollow fiber reactor

The kinetics of the hydrolysis of corn oil in the presence of a lipase from Pseudomonas sp. immobilized within the walls of a hollow fiber reactor can be modeled in terms of a three‐parameter rate expression. This rate expression consists of the product of a two‐parameter rate expression for the hydrolysis reaction itself (which is of the general Michaelis–Menten form) and a first‐order rate expression for deactivation of the enzyme. Optimum operating conditions correspond to 30°C and buffer pH values of 7.0 during both immobilization of the enzyme and the hydrolysis reaction. Under these conditions, the total fatty acid concentration in the effluent oil stream for a fluid residence time of 4 h is approximately 1.6 M. This concentration corresponds to hydrolysis of approximately 50% of the glyceride bonds present in the feedstock corn oil. The fatty acid of primary interest in the effluent stream is linoleic acid. © 1999 John Wiley & Sons, Inc. Biotechnol Bioeng 64: 568–579, 1999.     

Generalized dispersion in a synovial fluid of human joints

An unsteady convective diffusion in a synovial fluid of human joints modeled as a power-law fluid is studied using the generalized dispersion model of Gill and Sankara-subramanian [12]. The contributions of convection and diffusion, and pure convection on the dispersion of nutrient are investigated in detail. It is shown that the effect of decrease in non-Newtonian parameter is to decrease the dispersion coefficient. The mean concentration distribution appears to increase as the non-Newtonian parameter decreases upto a certain value of the axial distance. Beyond this point, however, the reverse pattern is observed.     

Double-diffusion convective biomimetic flow of nanofluid in a complex divergent porous wavy medium under magnetic effects

We explore the physical influence of magnetic field on double-diffusive convection in complex biomimetic (peristaltic) propulsion of nanofluid through a two-dimensional divergent channel. Additionally, porosity effects along with rheological properties of the fluid are also retained in the analysis. The mathematical model is developed by equations of continuity, momentum, energy, and mass concentration. First, scaling analysis is introduced to simplify the rheological equations in the wave frame of reference and then get the final form of equations after applying the low Reynolds number and lubrication approach. The obtained equations are solved analytically by using integration method. Physical interpretation of velocity, pressure gradient, pumping phenomena, trapping phenomena, heat, and mass transfer mechanisms are discussed in detail under magnetic and porous environment. The magnitude of velocity profile is reduced by increasing Grashof parameter. The bolus circulations disappeared from trapping phenomena for larger strength of magnetic and porosity medium. The magnitude of temperature profile and mass concentration are increasing by enhancing the Brownian motion parameter. This study can be productive in manufacturing non-uniform and divergent shapes of micro-lab-chip devices for thermal engineering, industrial, and medical technologies.

     

Analysis of hemodynamic fluid phase mass transport in a separated flow region

The mass transfer behavior in the recirculation region downstream of an axisymmetric sudden expansion was examined. The Reynolds number, 500, and Schmidt number, 3200, were selected to model the mass transfer of molecules, such as ADP, in the arterial system. In a first step the transient mass transport applying zero diffusive flux at the wall was analyzed using experiments and two computational codes. The two codes were FLUENT, a commercially available finite volume method, and FTSP, a finite element code developed at Graz University of Technology. The comparison of the transient wall concentration values determined by the three methods was excellent and provides a measure of confidence for computational mass transfer calculations in convection dominated, separated flows. In a second step the effect of the flow separation on the stationary mass transport applying a permeability boundary condition at the water-permeable wall was analyzed using the finite element code FTSP. The results show an increase of luminal ADP surface concentration in the upstream and in the downstream tube of the sudden expansion geometry in the range of six and twelve percent of the bulk flow concentration. The effect of flow separation in the downstream tube on the wall concentration is a decrease of about ten percent of the difference between wall concentration and bulk concentration occurring at nearly fully developed flow at the downstream region at a distance of 66 downstream tube diameters from the expansion. The decrease of ADP flux into the wall is in the range of three percent of the flux at the downstream region.     

Three-dimensional numerical approach to investigate the substrate transport and conversion in an immobilized enzyme reactor

This numerical study evaluates the momentum and mass transfer in an immobilized enzyme reactor. The simulation is based on the solution of the three-dimensional Navier-Stokes equation and a scalar transport equation with a sink term for the transport and the conversion of substrate to product. The reactor consists of a container filled with 20 spherical enzyme carriers. Each of these carriers is covered with an active enzyme layer where the conversion takes place. To account for the biochemical activity, the sink term in the scalar transport equation is represented by a standard Michaelis-Menten approach. The simulation gives detailed information of the local substrate and product concentrations with respect to external and internal transport limitations. A major focus is set on the influence of the substrate transport velocity on the catalytic process. For reactor performance analysis the overall and the local transport processes are described by a complete set of dimensionless variables. The interaction between substrate concentration, velocity, and efficiency of the process can be studied with the help of these variables. The effect of different substrate inflow concentrations on the process can be seen in relation to velocity variations. The flow field characterization of the system makes it possible to understand fluid mechanical properties and its importance to transport processes. The distribution of fluid motion through the void volume has different properties in different parts of the reactor. This phenomenon has strong effects on the arrangement of significantly different mass transport areas as well as on process effectiveness. With the given data it is also possible to detect zones of high, low, and latent enzymatic activity and to determine whether the conversion is limited due to mass transfer or reaction resistances.     

Computational analysis of coupled blood-wall arterial LDL transport

The transport of macromolecules, such as low density lipoproteins (LDLs), across the artery wall and their accumulation in the wall is a key step in atherogenesis. Our objective was to model fluid flow within both the lumen and wall of a constricted, axisymmetric tube simulating a stenosed artery, and to then use this flow pattern to study LDL mass transport from the blood to the artery wall. Coupled analysis of lumenal blood flow and transmural fluid flow was achieved through the solution of Brinkman's model, which is an extension of the Navier-Stokes equations for porous media. This coupled approach offers advantages over traditional analyses of this problem, which have used possibly unrealistic boundary conditions at the blood-wall interface; instead, we prescribe a more natural pressure boundary condition at the adventitial vasa vasorum, and allow variations in wall permeability due to the occurrence of plaque. Numerical complications due to the convection dominated mass transport process (low LDL diffusivity) are handled by the streamline upwind/Petrov-Galerkin (SUPG) finite element method. This new fluid-plus-porous-wall method was implemented for conditions typical of LDL transport in a stenosed artery with a 75 percent area reduction (Peclet number=2 x 10(8)). The results show an elevated LDL concentration at the downstream side of the stenosis. For the higher Darcian wall permeability thought to occur in regions containing atheromatous lesions, this leads to an increased transendothelial LDL flux downstream of the stenosis. Increased transmural filtration in such regions, when coupled with a concentration-dependent endothelial permeability to LDL, could be an important contributor to LDL infiltration into the arterial wall. Experimental work is needed to confirm these results.     

Analysis of the transient response of a CSTR containing immobilized enzyme particles: Part II. Minimum existence criterion and determination of substrate effective diffusivity and main reaction rate constant

A minimum existence criterion in the transient response of the bulk substrate concentration in a CSTR containing immobilized enzyme (IMEs) in porous solid supports has been obtained from simulation results using several kinetic expressions for the main reaction and the enzyme deactivation reaction. A simple method for the determination of the substrate effective diffusivity and the reaction rate constant is also presented, and applied to the decomposition of hydrogen peroxide, that reacts in a CSTR that contains silica–alumina porous catalyst particles, in which horseradish peroxidase enzyme had been previously immobilized.     

A new method to determine active enzyme distribution, effective diffusivity, rate constant for main reaction and rate constant for deactivation

A new method is presented to determine (1) the rate constant for the main reaction, (2) the rate constant for deactivation, (3) the effective diffusivity, and (4) the active enzyme distribution within a porous solid support by utilizing data of bulk substrate concentration versus time in a continuous stirred basket reactor. The method relies on an assumption of parallel deactivation mechanism with strong pore diffusional resistance with respect to substrate species. The data of hydrogen peroxide-immobilized catalase published in the literature are used to demonstrate the theory. A parameter determination procedure is also presented.     

A CSTR-hollow fiber system for continuous hydrolysis of proteins. Performance and kinetics

The effect of four operating variables (enzyme concentration, substrate concentration, flow rate, and reaction volume) on the performance of CSTR-hollow fiber membrane reactor was studied for the continuous hydrolysis of a soy protein isolate using Pronase. Based on a residence time distribution study, the reactor system was modeled as an ideal CSTR in combination with the Michaelis-Menten equation of enzyme kinetics. This kinetic model correlated conversion with a space-time parameter modified to include all four independent variables. An empirical model based on curvilinear regression analysis was also developed. Both models predicted conversion fairly well, although the kinetic model slightly underpredicts at high conversion.     

Modelling and optimisation of enzymatic separating micro-reactor

A mathematical model of an enzymatic separating microreactor with the electro-osmotic control of reaction component transport rates is analysed. The micro-reactor is considered in a form of a thin channel filled with a gel containing an immobilised enzyme and an adsorbent where the enzyme reaction, the molecular diffusion, the electro-osmotic flux and the adsorption take place. The substrate inhibited enzyme reaction splitting a non-ionic substrate to two non-ionic products is considered. The reactor operates in a periodic regime, when the channel entry is exposed to the periodic substrate concentration pulses. A chromatographic separation of reaction components, therefore, proceeds in the channel. Effects of principal operational parameters of the reactor system—the reaction channel length, the electric current density, the substrate inlet concentration, the rate of adsorption, and the enzyme activity—on resolution of the products at reactor outlet are analysed. The existence of optimum parameter values (maximising the resolution of reaction products) is shown and a multiparametric optimisation of the reactor performance is accomplished.     

Degradation of ribonucleic acid by immobilized ribonuclease.

An immobilized enzyme (pancreatic ribonuclease bound to porous titania) was investigated for the degradation of purified yeast ribonucleic acid as a substrate. The immobilized enzyme is active and stable in the pH range 4--8. Dependence of enzymatic activity on ionic strength, pH, temperature, fluid flow rate, and substrate concentration were investigated. A cumulative fluid residence time of 6 sec is sufficient for 50% substrate conversion at 25 degrees C and pH 7.0. The critical flow rate (i.e., the fluid flow rate necessary to remove film diffusion resistance) approximately doubles with each 10 degree C rise in reaction temperature. The critical flow rates obtained in this study are about 40 times greater than those obtained for a similar study on immobilized glucose oxidase. Arrhenius plots gave activation energies of -9.6 and -7.1 kcal/g mol at pH 4.6 and 7.0, respectively. The work reported herein is a bench-scale investigation of an immobilized enzyme with primary emphasis on the mass transfer and kinetic characteristics of the system. The rapid reaction rates obtainable at relatively low temperatures offer a potential alternative method of purifying yeast single cell protein (SCP) with miminum loss of desired protein. The key questions are how such a system would react in a yeast homogenate, what conditions in such a system must be controlled, and what type of immobilized reactor should be utilized, if such further work continued to show promise.     

Enzymatic hydrolysis of waste office paper using viscosity as operating parameter

Enzymatic hydrolysis of waste office (WO) paper with feeding WO paper in a reactor was investigated using apparent viscosity as operating parameter. Since the apparent viscosity was correlated with the concentration of pulping WO paper, the amount of hydrolyzed WO paper was assumed by measuring the decrease in the apparent viscosity. Then the amount of hydrolysis WO paper and the amount of enzyme corresponding to the desired ratio were fed into the reactor. When the WO paper and 1% (to the amount of WO paper) enzyme were fed to the hydrolytic reaction, 87 g/L of reducing sugar (RS) with a hydrolytic yield of 42.2% was obtained for a 24-h hydrolysis. However, when nonpulping WO paper and 5% (to the amount of WO paper) enzyme were fed to the hydrolytic reaction, 120 g/L of RS with a hydrolytic yield of 40% was obtained for a 24-h hydrolysis. Therefore, the RS concentration from this hydrolysis process feeding WO paper using apparent viscosity as operating parameter may be of sufficient concentration to serve as a carbon source in microorganism culture or chemical feedstock.     

Unsteady Magnetohydrodynamic Free Convection Flow of a Second Grade Fluid in a Porous Medium with Ramped Wall Temperature

Magnetic field influence on unsteady free convection flow of a second grade fluid near an infinite vertical flat plate with ramped wall temperature embedded in a porous medium is studied. It has been observed that magnitude of velocity as well as skin friction in case of ramped temperature is quite less than the isothermal temperature. Some special cases namely: (i) second grade fluid in the absence of magnetic field and porous medium and (ii) Newtonian fluid in the presence of magnetic field and porous medium, performing the same motion are obtained. Finally, the influence of various parameters is graphically shown.     

Copper reduction in a pilot-scale membrane-free bioelectrochemical reactor

A pilot-scale, membrane-free, bioelectrochemical system (BES) reactor (16L in volume) installed by five cathodes with different distance to anode was tested for the removal of copper. CuSO4 solution was used as catholyte and anaerobic microorganisms grew as anodic biocatalyst. In the reactor, Cu(II) was reduced and recovered as solid-state copper deposits on cathodes accompanied with power production. When 600 and 2000 mg of Cu2+ were added into the cathode chamber, removal efficiency of 92% over 480 h and 48% over 672 h period with electric quantities of 2724 C and 8703 C, and cathodic efficiencies of 61.92% and 45.60% were achieved, respectively. The reduction reaction rate depended on the initial average Cu2+ concentration. The internal resistance decreased and voltage output increased as the distance of each cathode to anode decreased. The mass of metal Cu crystals and Cu(I) compounds deposited on each cathode was dependent on current intensity.     

Hydromagnetic Flow and Heat Transfer over a Porous Oscillating Stretching Surface in a Viscoelastic Fluid with Porous Medium

An analysis is carried out to study the heat transfer in unsteady two-dimensional boundary layer flow of a magnetohydrodynamics (MHD) second grade fluid over a porous oscillating stretching surface embedded in porous medium. The flow is induced due to infinite elastic sheet which is stretched periodically. With the help of dimensionless variables, the governing flow equations are reduced to a system of non-linear partial differential equations. This system has been solved numerically using the finite difference scheme, in which a coordinate transformation is used to transform the semi-infinite physical space to a bounded computational domain. The influence of the involved parameters on the flow, the temperature distribution, the skin-friction coefficient and the local Nusselt number is shown and discussed in detail. The study reveals that an oscillatory sheet embedded in a fluid-saturated porous medium generates oscillatory motion in the fluid. The amplitude and phase of oscillations depends on the rheology of the fluid as well as on the other parameters coming through imposed boundary conditions, inclusion of body force term and permeability of the porous medium. It is found that amplitude of flow velocity increases with increasing viscoelastic and mass suction/injection parameters. However, it decreases with increasing the strength of the applied magnetic field. Moreover, the temperature of fluid is a decreasing function of viscoelastic parameter, mass suction/injection parameter and Prandtl number.     

Performance of the anaerobic baffled reactor under steady-state and shock loading conditions

The anaerobic baffled reactor (ABR) contains a granulated, mixed anaerobic culture segregated into compartments. Operation of four reactors under a range of hydraulic retention times showed that this novel reactor design offers highly efficient performance in the conversion of carbon in the feed stream to methane and carbon dioxide. The design parameter varied was the number of compartments. COD removal at 20 h retention time was routinely over 95% in all reactors, with low washout of biomass. Very high specific reaction rates were achievable (although with a loss of efficiency) at low biomass concentrations and high loading rates. In order to optimize volumetric reaction rates, a tradeoff has to be made between high biomass concentration, granule size, and the resulting mass transfer limitations. Formate is shown to be an important intermediate in the process under conditions of high loading.