A dynamic cell cycling model for growth of baker's yeast and its application in profit optimization

A cell cycling model for unequal budding yeast Saccharomyces cerevisiae is proposed and verified by steady state data from experiments available in the literature. This model can be used to determine the relative fraction of the cells in any cycling phase or with any genealogical age during fermentation. As the quality of yeast is strongly influenced by the cycling process, the model could therefore be used to control the quality of the harvested yeast cells. The input of the cell cycling model is the specific growth rate , which is obtained from a metabolic model for S. cerevisiae proposed earlier. With this extended model system not only the quality control, but also the whole economical profit optimization can be carried out. Simulations were done to optimize the profit of a commercial scale baker's yeast production process by manipulating substrate feeding rate and substrate concentration under different aeration rates, fermentation periods and other conditions applied in industry.List of Symbols B h budding phase - C _d1, C _d2, C _p1' parameters in cycling phase equations - C _p2, C _b1, C _b2, d _s m Sauter-diameter - E kg/m³ ethanol concentration - E1, E2 state variables in the metabolic model - E _G mean relative gas hold-up - f parameter vector of the regulation model - F system matrix of the regulation model - F or F(t) m³/h substrate feeding rate - Fr Froude number - FBC, FDC, FPC % fraction of daughter cells, unbudded daughter cells and unbudded parent cells - g m/s² acceleration of gravity - K _B1–3, K _EG parameters in metabolic model - K ₃, K _Ad , L ₃ K ₃ E, K_O, K_S limitation constants for ethanol, oxygen and substrate - k _La h^–1 volumetric mas transfer coefficient - m _ATP mol(gh)^–1 maintenance coefficient - nb, nd, np number of cycling age intervals in budding cycling phase, unbudded daughter cycling phase and unbudded parent cycling phase - Nt number of total cells - OF mg/dm³ concentration of dissolved oxygen - P kg total yeast product in dry weight - P/O effectiveness of oxidative phosphorylation - q _O20 mol(gh)^–1 minimum specific oxygen uptake ability - q _O2 mol(gh)^–1 specific oxygen uptake rate - q _O2max mol(gh)^–1 maximum q _O2 given by metabolic regulation - q _s mol(gh)^–1 specific glucose uptake rate - q _Smax mol(gh)^–1 maximum q _S - R(·) switch function - r _Ac mol(gh)^–1 specific acetyl-CoA-consumption rate - r _Acmax saturation rate of r _Ac - r _E1 mol(gh)^–1 specific ethanol production rate - r _E2 mol(gh)^–1 specific ethanol uptake rate - r _SO mol(gh)^–1 minimum value of r _Smax - r _s mol(gh)^–1 specific rate of glycolysis - r _Smax mol(gh)^–1 maximum specific rate of gluconeogenesis given by metabolic regulation - S kg/m³ total reduced sugar concentration - S _R kg/m³ substrate concentration in feed - T h cell number doubling time - T _f h fermentation period - Ud h unbudded daughter phase - Up h unbudded parent phase - V _F m³ volume of liquid phase in fermentor - V _G m³/h aeration rate - w _sg m/s superficial gas velocity - X kg/m³ dried cell concentration - Y _ATP g(molATP)^–1 yield coefficient of ATP - z state vector in regulation model - the factor of fermentative activity decrease caused by budding cells - or(t) h^–1 specific growth rate - h discrete unit of cycling age     

Ulva rigida (Ulvales,Chlorophyta) tank culture as biofilters for dissolved inorganic nitrogen from fishpond effluents

Ulva rigida was cultivated in 7501 tanks at different densities with direct and continuous inflow (at 2, 4, 8 and 12 volumes d^–1) of the effluents from a commercial marine fishpond (40 metric tonnes, Tm, of Sparus aurata, water exchange rate of 16 m³ Tm^–1) in order to assess the maximum and optimum dissolved inorganic nitrogen (DIN) uptake rate and the annual stability of the Ulva tank biofiltering system. Maximum yields (40 g DW m^–2 d^–1) were obtained at a density of 2.5 g FW 1^–1 and at a DIN inflow rate of 1.7 g DIN m^–2 d^–1. Maximum DIN uptake rates were obtained during summer (2.2 g DIN M^–2 d^–1), and minimum in winter (1.1 g DIN m^–2 d^–1) with a yearly average DIN uptake rate of 1.77 g DIN m^–2 d^–1 At yearly average DIN removal efficiency (2.0 g DIN m^–2 d^–1, if winter period is excluded), 153 m² of Ulva tank surface would be needed to recover 100% of the DIN produced by 1 Tm of fish.Abbreviations DIN= dissolved inorganic nitrogen (NH _inf4 ^sup+ + NO _inf3 ^sup– + NO _inf2 ^sup– ); - FW= fresh weight; - DW= dry weight; - PFD= photon flux density; - V= DIN uptake rate     

Emission of microorganisms from biofilters

Experiments are reported on the discharge of microbial germs by biofilter systems used for the treatment of waste gases containing volatile organic compounds. The systems investigated concern six full-scale filter installations located in the Netherlands in several branches of industry, as well as a laboratory-scale installation used for modelling the discharge process. It is concluded that the number of microbial germs (mainly bacteria and to a much smaller extent moulds) in the outlet gas of the different full scale biofilters varies between 10³ and 10⁴ m^–3, a number which is only slightly higher than the number encountered in open air and of the same order of magnitude encountered in indoor air. It is furthermore concluded that the concentration of microorganisms of a highly contaminated inlet gas is considerably reduced by the filtration process. On the basis of the experiments performed in the laboratory-scale filter bed, it is shown that the effect of the gas velocity on the discharge process results from two distinctive mechanisms: capture and emission. A theoretical model is presented describing the rate processes of both mechanisms. The model presented and the experimentally determined data agree rather well.List of Symbols a _s m^–1 specific area of the packing material - C m^–3 microbial gas phase concentration - C _e , C _i m^–3 microbial concentration in the exit and inlet gas resp. - CFU colony-forming-units - d _c , d _m m diameter of collecting and captured particle resp. - D m diameter of the filter bed - E single particle target efficiency - H m bed height - k _c s^–1 first order capture rate constant per unit of bedvolume - k _e m^–3 emission rate constant per unit of bedvolume - n number of observations - r _c , r _e m^–3 s^–1 capture and emission rate per unit of bed-volume - Re = Reynolds number - S _t = Stokes number - u m s^–1 superficial gas velocity - u _m m s^–1 superficial gas velocity at which C _e = C _i Greek Symbols void fraction of the filter bed - kg m^–3 density of the gas phase - _m kg m^–3 density of captured particle - Pa s dynamic gas phase viscosity - = filter bed efficiency     

Optimal control strategy for the enhanced production of cellulase enzyme using the new mutant Trichoderma reesei E-12

Cellulase enzyme production was enhanced using the mutant strain Trichoderma reesei, E-12, which was shown to be partially resistant to catabolite repression. An optimal profile for pH, which was found to be the critical environmental parameter, was determined using a rigorous mathematical optimization procedure. Semi-empirical models were used to minimize complications in the computation. A 30% increase in enzyme activity and productivity was obtained using the optimal pH strategy as compared to the pH cycling strategy.List of Symbols a ₁ , a ₂ , a ₃ d^–1, d^–2, d^–3 coefficients of the polynomial in the generalized logistic growth model - a ₄, a ₅, a ₆ d^–1, d^–2, d^–3 coefficients of the polynomial in the generalized logistic product model - b ₁ d^–1 enzyme synthesis rate constant - b ₂ d ^–1 enzyme decay rate constant - b ₃ power coefficient in the polynomial model for enzyme synthesis - H Hamiltonian function - J Objective function of the maximization procedure - K ₁ kg/m³ limiting cell mass concentration in biomass logistic model - K _s kg/m³ saturation constant - K ^s kg/m³ saturation death rate constant - q power coefficient in polynomial model - s kg/m³ substrate concentration - t d fermentation time - T d total fermentation time (=7 d) - x ₁₀ kg/m³ initial biomass concentration - x ₁ kg/m³ biomass concentration at time t - x ₂ F.P.A enzyme activity at time t - x ₃ d state variable replacing time term on the right hand side of biomass equation - x _f kg/m³ final biomass concentration - z ₁, z ₂, z ₃ adjoint variable corresponding to state variable x ₁, x ₂, x ₃ - d^–1 specific death rate - d^–1 specific growth rate     

Fermentation ofCandida utilis for uricase production

Summary Conditions for the production of microbial uricase byCandida utilis were studied. For the selected strain, hypoxanthine proved to be the most effective inducer of uricase formation. The highest values of biomass as well as uricase activity in the mechanically agitated fermentor were obtained under the following conditions: 50 h, rotation impeller speed 7 s^–1, air flow rate 1.25×10^–5 m³s^–1, concentration of inducer 0.1%.List of symbols b width of baffle, m - c length of baffle, m - D diameter of cylindrical fermentor, m - d diameter of impeller, m - d ₁ diameter of impeller disc, m - Fr _m impeller Froud number - g gravitional acceleration, ms^–2 - H height of batch surface above bottom, m - H ₂ height of impeller disc above bottom, m - h height of impeller blade, m - Kp _g flow rate number - L length of impeller blade, m - N rotational speed of impeller, s^–1 - Re _m impeller Reynolds number - T time, h - V volume of batch, m³ - V _g air (gas) flow rate, m³s^–1 - x mass fraction of the dry matter of cells - x ₀ initial value of the mass fraction of the dry matter of cells - _r volume fraction of the dry matter of cells - <eta<₁ viscosity of pure liquid, Pa s - viscosity of batch (suspension of microbial suspension), Pa s - density of batch, kg m^–3     

Organic reduction of tapioca wastewaters using modified RBC

A modified Rotating Biological Contactor (RBC) was used for the treatability studies of synthetic tapioca wastewaters. The RBC used was a four stage laboratory model and the discs were modified by attaching porous nechlon sheets to enhance biofilm area. Synthetic tapioca wastewaters were prepared with influent concentrations from 927 to 3600 mg/l of COD. Three hydraulic loads were used in the range of 0.03 to 0.09 m³·m^–2·d^–1 and the organic loads used were in the range of 28 to 306 g COD· m^–2·d^–1. The percentage COD removal were in the range from 97.4 to 68. RBC was operated at a rotating speed of 18 rpm which was found to be the optimal rotating speed. Biokinetic coefficients based on Kornegay and Hudson models were obtained using linear analysis. Also, a mathematical model was proposed using regression analysis.List of Symbols A m² total surface area of discs - d m active depth of microbial film onany rotating disc - K _s mg ·l^–1 saturation constant - P mg·m^–2·^–1 area capacity - Q l·d^–1 hydraulic flow rate - q m³·m^–2·d^–1 hydraulic loading rate - S ₀ mg·l^–1 influent substrate concentration - S _e mg·l^–1 effluent substrate concentration - w rpm rotational speed - V m³ volume of the reactor - X _f mg·l^–1 active biomass per unit volume ofattached growth - X _s mg·l^–1 active biomass per unit volume ofsuspended growth - X mg·l^–1 active biomass per unit volume - Y _s yield coefficient for attachedgrowth - Y _A yield coefficient for suspendedgrowth - Y yield coefficient, mass of biomass/mass of substrate removed Greek Symbols hr mean hydraulic detention time - (_max)_A d^–1 maximum specific growth rate forattached growth - (_max)_s d^–1 maximum specific growth rate forsuspended growth - _max d^–1 maximum specific growth rate - d^–1 specific growth rate - _v mg·l^–1·hr^–1 maximum volumetric substrateutilization rate coefficient     

Determination of the inherent kinetics of immobilized glucose oxidase using a diffusion cell

The enzyme glucose oxidase (GO) was covalently immobilized onto a poly(vinyl alcohol) hydrogel, cross-linked with glutardialdehyde and a polyazonium salt. To compare the kinetic parameters of immobilized GO with the known kinetic parameters of soluble GO, the diffusion cell method was used.Between two compartments, containing solutions with different glucose concentrations, a GO-containing hydrogel membrane was placed. Simultaneous diffusion through and enzymatic reaction in the membrane occurred. In this way diffusional effects of the membrane could be eliminated from the effective kinetic parameters to yield the inherent kinetic parameters.It appeared that the enzymatic reaction is independent of the oxygen concentration at oxygen concentrations 0.22 mol m^–3 (Michaelis constant for oxygen < 0.22 mol m^–3). Further, the Michaelis constant for glucose does not change dramatically after immobilizing the enzyme. The maximal reaction rate is depending on the enzyme concentration. As the enzyme concentration in the membrane is not exactly known (mainly due to leakage of enzyme out of the membrane during membrane preparation), only an estimation of the turnover number can be made.The diffusion cell method is easy to carry out. Still, some recommendations can be made on the performance.List of Symbols _g , _0x partition coefficient of glucose and oxygen, respectively - thickness of the wetted membrane (m) - A _m surface area of membrane (m^–2) - C constant (mol² m^–3) - c _g , c _0x concentration of glucose and oxygen, respectively (mol m^–3) - c _g,0 c _g, glucose concentration at the filter-paper/membrane interface next to compartment A and B, respectively (mol m^–3) - c _{g, A} c _{g, B} glucose concentration in compartment A and B, respectively (mol m^–3) - c _GO glucose oxidase concentration (mol m^–3) - D _eff effective diffusion coefficient (m² s^–1) - D _m , D _sl diffusion coefficient in, respectively, the membrane and the solution layer (m² s^–1) - d _dl , d _df , d _sl thickness of, respectively, the diffusion layer, the filter-paper and the solution layer (m) - h _B initial slope of concentration versus time curve of compartment B (mol m^–3 s^–1) - J flux (mol m^–2 s^–1) - J ₀ flux in the membrane at membrane/filter-paper interface next to compartment A and B, respectively (mol m^–2 s^–1) - J _A , J _B flux leaving compartment A and entering compartment B, respectively (mol m^–2 s^–1) - J _m flux through the membrane (mol m^–2 s^–1) - k total mass transfer coefficient (m s^–1) - k ₁ , k ₂ rate constant of a particular reaction step (m³ mol^–1 s^–1) - k_–1, k_–2 rate constant of a particular reaction step (s^–1) - k _cat (intrinsic) catalytic constant of turnover number (s^–1) - k _cat ^* inherent catalytic constant, determined by inserting D _m (s^–1) - k _cat ^** inherent catalytic constant, determined by inserting D _eff (s^–1) - k _m (g) (intrinsic) Michaelis constant for glucose (mol m^–3) - k _m (o) (intrinsic) Michaelis constant for oxygen (mol m^–3) - k _m ^* (g) inherent Michaelis constant for glucose (mol m^–3) - k _m ^* (o) inherent Michaelis constant for oxygen (mol m^–3) - m _GO number of moles of GO present (mol) - P _m permeability of glucose in the mebrane (m s^–1) - P _eff effective permeability (m s^–1) - V volume (m³) - v ₀ initial reaction velocity (mol m^–3 s^–1) - V _max ^** inherent maximal reaction velocity, determined by inserting D_eff (mol m^–3 s^–1) - x distance (m)     

Process engineering aspects of the bioleaching of copper ores

The bioleaching of minerals is a complex process that is affected by a number of biological, mineralogical, electrochemical and engineering factors. This work presents and discusses the most significant process engineering aspects involved in the bacterial leaching of copper ores, i.e. bacterial population, type of mineral and particle size, nutrients and inhibitors, oxygen and carbon dioxide, temperature and pH, leaching kinetics and operation mode.It is concluded that more work is needed in this area in order to gain a deeper insight in the many factors that govern this process. This would allow to significantly improve its overall productivity.List of Symbols C _L kg/m³ dissolved oxygen concentration - C ^* kg/m³ equilibrium oxygen concentration - d, e, f, g % percentage of C, H, O and N in the cell - D m impeller diameter - K consistency index - K _S, K₁, K_c constants - k _La h^–1 volumetric oxygen transfer coefficient - M _b mol/kg biomass apparent molecular weight - N s^–1 rotation frequency - n behavior index - P kg/m³ ungassed agitation power, product concentration - P _g kW/m³ gassed agitation power - p % pulp density - Q m³/h air flow rate - S kg/m³ limiting substrate concentration - W kg/(m³ · h) mass transfer rate per unit volume - X cells/cm³ biomass concentration - Y _o g cells/g Fe oxygen cell yield - Y _x g cells/g Fe substrate cell yield - h^–1 specific growth rate - _m h^–1 maximum specific growth rate     

Diffusion of sucrose in xanthan gum solutions

Molecular diffusion of solutes, like sucrose in the xanthan gum fermentation, is important in order to understand the complex behavior of mass transfer mechanisms during the process. This work was focused to determine the diffusion coefficient of sucrose, a carbon source for xanthan production, using similar sucrose and xanthan concentrations to those occurring in a typical fermentation. The diaphragm cell method was used in experimental determinations. The data showed that diffusion coefficient of sucrose significantly decreases when xanthan gum concentration increases. Theoretical and semiempirical models were used to predict sucrose diffusivity in xanthan solutions. Molecular properties and rheological behavior of the system were considered in the modeling. The models tested fitted well the behavior of experimental data and that reported for oxygen in the same system.List of Symbols A constant in eq. (5) - C _pg cm^–3 polymer concentration - D cm² s^–1 diffusivity - D _ABcm² s^–1 diffusivity of A through liquid solvent - D _APcm² s^–1 diffusivity of A in polymer solution - D _AWcm² s^–1 diffusivity of A in water - D _Pcm² s^–1 diffusivity of polymer in liquid solvent - E _D gradient of the activation energy for diffusion - H _P hydratation factor of the polymer in water (g of bound water/g of polymer) - K dyn sⁿ cm^–2 consistency index - K ₁ constant in eq. (5) - K _P overall binding coefficient [g of bound solute/cm³ of solution]/[g of free solute/cm³ of polymer free solution] - n flow behavior index - M _Bg g mol^–1 molucular weight of liquid solvent - M _Pg g mol^–1 molecular weight of the polymer - M _Sg g mol^–1 Molecular weight of polymer solution (= M _BX_B+M_PX_P) - R cm³ atm g mol^–1 K^–1 ideal gas law constant - T K absolute temperature - V _Bcm³ g mol^–1 molar volume of liquid solvent - V _Pcm³ g mol^–1 molar volume of polymer - V _Scm³ g mol^–1 molar volume of polymer solution - X _B solvent molar fraction - X _P polymer molar fraction - polymer blockage shape factor - _P volume fraction of polymer in polymer solution - g cm^–1 s^–1 viscosity - _ag cm^–1 s^–1 apparent viscosity of the polymer solution - _icm³ g^–1 intrinsic viscosity - ₀ g cm^–1 s^–1 solvent viscosity - _Pg cm^–1 s^–1 polymer solution viscosity - _R relative viscosity (= / ₀) - ₌₀ g cm^–1 s^–1 viscosity of polymer solution obtained at zero shear rate - ₀ g cm^–3 water density     

Development of reactor model for glucose isomerization catalyzed by whole-cell immobilized glucose isomerase

Based on the kinetic constants determined and the mathematical model of the reactor system developed, the performance of axial flow packed bed continuous enzyme reactor system was studied experimentally and also simulated with the aid of a computer for ultimate objective of optimization of the glucose isomerase reactor system.A reactor model was established analogous to heterogeneous catalytic reactor model taking into account the effect of fluid mass transfer and reversible kinetics. The investigated catalyst system consists of immobilized Streptomyces bambergiensis cells containing the enzyme glucose isomerase, which catalyzes the isomerization of glucose to fructose.List of Symbols A ₀, A ₁, A ₂ parameters in axial dispersion reactor model - c _go, c_g, c_gemol m^–3 glucose concentration at time t=0, at any time and at equilibrium conditions - c _gsmol m^–3 glucose concentration at particle surface - C dimensionless glucose concentration - d _pm particle diameter - d _rm diameter of reactor tube - Da Damkohler number - D _eff m² s^–1 effective glucose diffusion coefficient in Ca-alginate gel beads - k _fm s^–1 film transfer coefficient - K _e equilibrium constant - K _mg, K_mfmol m^–3 Michaelis-Menten constant for glucose and fructose, respectively - K _mmol m^–3 modified Michaelis-Menten constant - K dimensionless parameter - K ^* dimensionless parameter - L m length of reactor tube - Pe Peclet number - Pe _p particle Peclet number - Q m³ s^–1 volumetric flow rate - (-r _g) mol m^–3 s^–1 reaction rate - Re _p Reynolds particle number - Sc Schmidt number - Sh Sherwood number - t s time - v ₀ m s^–1 linear superficial fluid velocity - V _mg, V_mfmol g^–1 s^–1 maximal reaction rate for glucose and fructose, respectively - V _mmol m^–3 s^–1 modified maximal reaction rate for glucose - V _mg ^x mol m^–2 s^–1 maximal reaction rate for glucose - X _g, X_ge glucose conversion and glucose conversion at equilibrium conditions - X normalized conversion - Y dimensionless glucose concentration - void fraction of fixed bed - effectiveness factor of biocatalyst - Pa s kinematic viscosity of substrate - ₁ s first absolute weighted moment - ₂ s² second central weighted moment - _gkg m^–3 substrate density - _pkg m^–3 particle density - ² dimensionless variance of RTD curve - s residence time     

Intraparticle mass-transfer resistance and apparent time stability of immobilized yeast alcohol dehydrogenase

The stability and, consequently, the lifetime of immobilized enzymes (IME) are important factors in practical applications of IME, especially so far as design and operation of the enzyme reactors are concerned. In this paper a model is presented which describes the effect of intraparticle diffusion on time stability behaviour of IME, and which has been verified experimentally by the two-substrate enzymic reaction. As a model reaction the ethanol oxidation catalysed by immobilized yeast alcohol dehydrogenase was chosen. The reaction was performed in the batch-recycle reactor at 303 K and pH-value 8.9, under the conditions of high ethanol concentration and low coenzyme (NAD⁺) concentration, so that NAD⁺ was the limiting substrate. The values of the apparent and intrinsic deactivation constant as well as the apparent relative lifetime of the enzyme were calculated.The results show that the diffusional resistance influences the time stability of the IME catalyst and that IME appears to be more stabilized under the larger diffusion resistance.List of Symbols C _A, C_B, C_E mol · m^–3 concentration of coenzyme NAD⁺, ethanol and enzyme, respectively - C _p mol · m³ concentration of reaction product NADH - d _p mm particle diameter - D _eff m² · s^–1 effective volume diffusivity of NAD⁺ within porous matrix - k _d s^–1 intrinsic deactivation constant - K _A, K_A, K_B mol · m^–3 kinetic constant defined by Eq. (1) - K _A ^x mol · m^–3 kinetic constant defined by Eq. (5) - r _A mol · m^–3 · s^–1 intrinsic reaction rate - R m particle radius - R _v mol · m^–3 · s^–1 observed reaction rate per unit volume of immobilized enzyme - t _E s enzyme deactivation time - t _r s reaction time - V mol · m^–3 · s^–1 maximum reaction rate in Eq. (1) - V ^x mol · m^–3 · s^–1 parameter defined by Eq. (4) - V _f m³ total volume of fluid in reactor - w _s kg mass of immobilized enzyme bed - factor defined by Eqs. (19) and (20) - kg · m^–3 density of immobilized enzyme bed - unstableness factor - effectiveness factor - Thiele modulus - relative half-lifetime of immobilized enzyme Index o values obtained with fresh immobilized enzyme     

Model for the production of L-tryptophan from L-serine and indole by immobilized cells in a three-phase liquid-impelled loop reactor

Production of L-tryptophan from L-serine and indole catalyzed by Escherichia coli, immobilized in k-carrageenan gel beads, is technically feasible in the liquidimpelled loop reactor (LLR), using an organic solvent, e.g. n-dodecane.With L-serine in large excess intrinsic reaction kinetics is approximately first order with respect to indole, with a reaction constant of 8.5×10^–5 m³ kg _dw ^–1 s^–1.The overall process kinetics is jointly controlled by intrinsic kinetics and by intraparticle mass transfer resistance, which can be quantified using an effectiveness factor.Mass transfer of indole from the organic to the aqueous phase and from the aqueous to the gel phase are relatively fast and thus have negligible influence in the overall process kinetics, under the operational conditions tested. However, they may become important if the process is intensified by increasing the cell concentration in the gel and/or the gel hold-up in the reactor.A simple model which includes indole mass balances over the aqueous and organic phases, mass transfer and reaction kinetics, with parameters experimentally determined in independent experiments, was successful in simulating L-tryptophan production in the LLR.List of Symbols a, b, c coefficients of the equilibrium curve for indole between organic and aqueous phases - A, B, C, D, E, F auxiliary variables used in liquid-liquid mass transfer studies - a _x specific interfacial area referred to the volume of the aqueous phase (m^–1) - A _x interfacial area (m²) - a _Y specific interfacial area referred to the volume of the organic phase (m^–1) - A _Y interfacial area (m²) - C _b substrate concentration in the bulk of the aqueous phase (kg m^–3) - C _e substrate concentration in exit stream (kg m^–3) - C _E biocatalyst concentration referred to the aqueous phase (kg m^–3) - C _{E s} biocatalyst concentration referred to the volume of gel (kg m^–3) - C _s substrate concentration at the gel surface (kgm^–3) - d, e, f coefficients of the equilibrium curve for indole between aqueous and organic phases - dp particle diameter (m) - K ₂ kinetic constant (s^–1) - K ₁ kinetic constant K₂/K_M (kg^–1 m³ s^–1) - K _M Michaälis-Menten constant (kgm^–3) - K _X mass transfer coefficient referred to the aqueous phase (ms^–1) - K _Xa_X volumetric mass transfer coefficient based on the volume of the aqueous phase (s^–1) - k _Y mass transfer coefficient referred to the organic phase (ms^–1) - K _Ya_Y volumetric mass transfer coefficient based on the volume of the organic phase (s^–1) - N _X mass flux of indole from organic to aqueous Phase (kg m^–2s^–1) - N _Y mass flux of indole from aqueous to organic phase (kg m^–2s^–1) - Q _e volumetric flow rate in exit stream (m³s^–1) - Q _f volumetric flow rate in feed stream (m³s^–1) - _obs observed reaction rate (kg s^–1 m^–3) - intrinsic reaction rate (kg s^–1 m^–3) - Re Reynolds number - Sc Schmidt number - Sh Sherwood number - t time (s) - u superficial velocity (m s^–1) - V _max maximum reaction rate (kg s^–1m^–3) - V _S volume of the support (m³) - V _X volume of aqueous phase (m³) - V _Y volume of the organic phase (m³) - X indole concentration in the aqueous phase (kgm^–3) - Y indole concentration in the organic phase (kg m^–3 Greek Letters overall effectiveness factor - _e external effectiveness factor - _i internal effectiveness factor - Thiele module A fellowship awarded to one of us (D.M.R.)by INICT is gratefuly acknowledged.     

Mathematical modeling of production of microbial lipids

In the microbial lipid production system using the yeast Rhodotorula gracilis, CFR-1, kinetics of lipid accumulation and substrate utilisation at initial substrate concentrations in the range of 20–100 kg/m³ were investigated using shake flask experiments. A mathematical representation based on logistic model for biomass and Luedeking-Piret model for lipid accumulation gave reasonably good agreement between the theoretical and experimental values for substrate concentration less than 60 kg/m³. The kinetic expressions and parameters obtained through shake flask studies were directly applied to experiments in the laboratory fermentors also and the models were found to hold good for the prediction of the change of biomass, product as well as substrate with time. The attainment of a saturation in the intracellular lipid accumulation with time, however, was not predicted by the model which was shown to be an inherent feature of the Luedeking-Piret model.List of Symbols S ₀, P ₀ kg/m³ Initial concentrations of sugar and lipid respectively - S, S(t) kg/m³ Concentrations of sugar and lipid respeclively at any timet - p,p(t) L kg/m³ Maximum concentration of lipid produced - E % Maximum sugar utilised - dP/dt kg/(m³ · h) Rate of lipid production - -dS/dt kg/(m³ · h) Rate of sugar utilisation - _max h^–1 Maximum specific growth rate - X _max kg/m³ Maximum biomass reached in a run - P _max kg/m³ Maximum product concentration - m, n Constants used in Luedeking-Piret model in eq. (7) - , Constants used to predict residual sugar - k _e maintainance coefficient - Y _x g/g Biomass yield based on sugar consumed - Y _p g/g Lipid yield based on sugar consumed - (dP/d t)_stat kg/(m³ · h) Rate of lipid production at stationary phase - (dS/dt)_stat kg/(m³ · h) Rate of sugar utilisation at stationary phase     

Animal coat color and radiative heat gain: A re-evaluation

Summary Thermal resistance and heat gain from simulated solar radiation were measured over a range of wind velocities in black and white pigeon plumages. Plumage thermal resistance averaged 39% (feathers depressed) or 16% (feathers erected) of that of an equivalent depth of still air. Feather erection increased plumage depth four-fold and increased plumage thermal resistance about 56%. At low wind speeds, black plumages acquired much greater radiative heat loads than did white plumages. However, associated with the greater penetration of radiation into light than dark plumages, the radiative heating of white plumages is affected less by convective cooling than is that of black plumages. Thus, the heat loads of black and white plumages converge as wind speed is increased. This effect is most prominent in erected plumages, where at wind speeds greater than 3 ms^–1 black plumages acquire lower radiative heat loads than do white plumages. These results suggest that animals with dark-colored coats may acquire lower heat loads under ecologically realistic conditions than those forms with light-colored coats. Thus, the dark coat colors of a number of desert species and the white coat color of polar forms may be thermally advantageous.These results are used to test a new general model that accounts for effects of radiation penetration into a fur or feather coat upon an animal's heat budget. Even using simplifying assumptions, this model's predictions closely match measured values for plumages with feathers depressed (the typical state). Predictions using simplifying assumptions are less accurate for erected plumages. However, the model closely predicts empirical data for erected white plumages if one assumption is obviated by additional measurements. Data are not sufficient to judge whether this is also the case for erected black plumages.List of Symbols A body surface area (m²) - a _L long-wave absorptivity of coat - a _s short-wave absorptivity of coat - d characteristic dimension (m) - E evaporative water loss (kg m^–2 s^–1) - h coat thermal conductance (W m^–2 °C^–1) - k convection constant (s^1/2 m^–1) - l coat thickness (m) - L _i long-wave irradiance at coat surface (W m^–2) - M metabolic heat production (W m^–2) - m body mass (kg) - P plumage mass (kg) - p probability per unit coat depth that a penetrating ray will strike a coat element (m^–1) - q(Z) radiation absorbed at level z (W m^–2) - R _abs radiation absorbed by animal (W m^–2) - r _e external resistance to convective and radiative heat transfer (s m^–1) - r _Ha boundary layer resistance to convective heat transfer (s m^–1) - r _Hb whole-body thermal resistance (s m^–1) - r _Hc coat (plumage) thermal resistance (s m^–1) - r _Ht tissue thermal resistance (s m^–1) - r _s apparent resistance to radiative heat transfer (s m^–1) - r(Z) thermal resistance from level z to coat surface (s m^–1) - S _i short-wave irradiance at coat surface (W m^–2) - S ^– radiant flux going toward skin surface (W m^–2) - S ⁺ radiant flux going away from skin surface (W m^–2) - T _a air temperature (°C) - T _b core body temperature (°C) - T _e equivalent black-body temperature (°C) - T _e air temperature plus temperature increment due to longwave radiation (°C) - u wind velocity (m s^–1) - V heat load on animal from short-wave radiation (W m^–2) - z depth within coat (m) - short-wave absorptivity of individual hairs or feather elements - emissivity - {ie211-1} - latent heat of vaporization of water (J kg^–1) - short-wave reflectivity of individual hairs or feather elements - {ie211-2} short-wave reflectivity of coat - {ie212-1} short-wave reflectivity of skin - c _p volumetric specific heat of air (J m^–3 °C^–1) - Stefan-Boltzmann constant (W m^–2 °K^–4) - short-wave transmissivity of individual hairs or feather elements - {ie212-2} short-wave transmissivity of coat     

Modelling continuous culture of Rhodospirillum rubrum in photobioreactor under light limited conditions

Rhodospirillum rubrum was grown continuously and photoheterotrophically under light limitation using a cylindrical photobioreactor in which the steady state biomass concentration was varied between 0.4 to 4 kg m^–3 at a constant radiant incident flux of 100 W m^–2. Kinetic and stoichiometric models for the growth are proposed. The biomass productivities, acetate consumption rate and the CO₂ production rate can be quantitatively predicted to a high level of accuracy by the proposed model calculations. Nomenclature: C _X, biomass concentration (kg m^–3) D, dilution rate (h^–1) Ea, mean mass absorption coefficient (m² kg^–1) I , total available radiant light energy (W m^–2) K, half saturation constant for light (W m^–2) R _W, boundary radius defining the working illuminated volume (m) r _X, local biomass volumetric rate (kg m^–3 h^–1) <r _X>, mean volumetric growth rate (kg m^–3 h^–1) V _W, illuminated working volume in the PBR (m^–3). Greek letters: , working illuminated fraction (–) _M, maximum quantum yield (–) bar, mean energetic yield (kg J^–1).     

Phytoplankton primary production in a shallow,well- mixed,hypertrophic South African lake

This paper reports on a two-year analysis of the wind climateand its effect on phytoplankton primary production in ashallow (mean depth = 1.9 m), hypertrophic South Africancoastal lake, Zeekoevlei. The lake is subject to continuousmixing of the euphotic zone (Z _eu = 0.8 m), andcomplete mixing of the water column to the mean depth on adaily basis. Median annual wind speeds, prevailing fromeither the north or the south, were 6.4 m s^–1. There wasan almost total absence of calms, measured as hourly meanwind speeds of <1 m s^–1. Notwithstanding the highfrequency of mixing, the lake supports a dense population ofphytoplankton, dominated by Cyanophyte and Chlorophytespecies. Mean concentrations of chlorophyll-a were240 g l^–1. The attenuation of photosyntheticallyavailable radiation, PAR, was high, with mean K _dvalues of 6.4 m^–1 and water transparencies of <0.5 m.Levels of primary productivity, determined using the lightand dark bottle oxygen method, were very high, comparable toor exceeding that of the most productive systems yet studied.Maximum volumetric productivity ranged from 525 to 1524 mg Cm^–3 h^–1, and was confined to the upper 0.5 m of thewater column. Daily areal productivity, P _d,varied between 1.2 and 4.3 g C m^–2 d^–1, and that ofthe maximum chlorophyll-a specific photosynthetic rate,P _{B max}, between 1.6 and 7.9 mg C (mgChl-a)^–1 h^–1. Primary production was limited bywater temperature and the attenuation of PAR. The highfrequency of wind-induced mixing resulted in regular mixingof the phytoplankton through the euphotic zone, and reducedthe overall importance of P _max at a single layer inthe depth profile. Similarly, the regularity of mixing wasrecognized as a limitation of the incubation of bottle chainsto determine primary production levels.     

Viscous media in tower bioreactors: Hydrodynamic characteristics and mass transfer properties

Studies in tower reactors with viscous liquids on flow regime, effective shear rate, liquid mixing, gas holdup and gas/ liquid mass transfer (k _La) are reviewed. Additional new data are reported for solutions of glycerol, CMC, PAA, and xanthan in bubble columns with diameters of 0.06, 0.14 and 0.30 m diameter. The wide variation of the flow behaviour index (1 to 0.18) allows to evaluate the effective shear rate due to the gas flow. New dimensionless correlations are developed based on the own and literature data, applied to predict k _La in fermentation broths, and compared to other reactor types.List of Symbols a(a) m^–1 specific interfacial area referred to reactor (liquid) volume - Bo Bond number (g D _c ² _L/) - c _L(c _L ^* ) kmol m^–3 (equilibrium) liquid phase oxygen concentration - C coefficient characterising the velocity profile in liquid slugs - C _s m^–1 coefficient in Eq. (2) - d _B(d_vs) m bubble diameter (Sauter mean of d _B) - d ₀ m diameter of the openings in the gas distributor plate - D _c m column diameter - D _L m²s^–1 diffusivity - E _L(E_W) m² s^–1 dispersion coefficient (in water) - E ² square relative error - Fr Froude number (u _G/(g D_c)^0.5) - g m s^–2 gravity acceleration - Ga Gallilei number (g D _c ³ _L ² / _eff ² ) - h m height above the gas distributor the gas holdup is characteristic for - k Pasⁿ fluid consistency index (Eq. 1) - k _L m s^–1 liquid side mass transfer coefficient - k _La(k_La) s^–1 volumetric mass transfer coefficient referred to reactor (liquid) volume - L m dispersion height - n flow behaviour index (Eq. 1) - P W power input - Re liquid slug Reynolds number ( _L(u _G +u _L) D _c/_eff) - Sc Schmidt number ( _eff/( _L D _L )) - Sh Sherwood number (k _La D _c ² /D_L) - t s time - u _B(u_sw) m s^–1 bubble (swarm) rise velocity - u _G(u_L) m s^–1 superficial gas (liquid) velocity - V(V_L) m³ reactor (liquid) volume Greec Symbols W m^–2 K^–1 heat transfer coefficient - y(y _eff) s^–1 (effective) shear rate - _G relative gas holdup - s relaxation time of viscoelastic liquid - _L(_eff) Pa s (effective) liquid viscosity (Eq. 1) - _L kg m^–3 liquid density - N/m surface tension     

Effect of serum concentration on production of monoclonal antibodies and on shear sensitivity of a hybridoma

The effect of serum content of culture medium on the specific production rate of monoclonal antibodies (Mab's) and on shear sensitivity has been studied with hybridoma's, cultured in a continuous stirred tank reactor (CSTR). No decrease in specific Mab-production was found when the serum concentration was reduced from 10 to 2.5%, while steady state cell concentrations were hardly affected as well. In contrast the cell death rate in a bubble column strongly increased when the serum concentration was lowered, which could be ascribed to a reduced physical protective effect by the serum.List of Symbols k _d s^–1 death-rate constant - k _g s^–1 growth-rate constant - D m diameter of bubble column - d m diameter of air bubble - H m height of bubble column - X m³ hypothetical killing volume - X (m³/m³) specific hypothetical killing volume - F m³/s volumetric air-flow rate - C cells/m³ number of viable cells - C₀ cells/m³ number of viable cells at t=0 - t s time     

Separation of proteins by ion-exchange chromatography using gradient elution

Chromatographic separation of proteins by the gradient elution method using DEAE Toyopearl 650^® was carried through. The concentration gradient was effected by changing the ionic strength of NaCl in the carrier buffer solution. Bovine serum albumin and hemoglobin were used as model proteins for separation. The experimental chromatogram was compared with theoretical results of Yamamoto et al. [1, 2]. Adsorption equilibria of the proteins onto the carrier were measured and expressed by a function of the ionic strength. The retention volume and peak width of the resulting chromatogram can be calculated from the equilibrium data using the Yamamoto theory. The calculated results agreed well with the experimental data.The method presented in this paper will be useful to predict the viability of ion-exchange chromatography in protein separation.List of Symbols c kg m^–3 concentration in the liquid phase - c _s kg m^–3 concentration in the solid phase - D _s m² s^–1 intraparticle diffusivity - d _p m particle diameter - E _z m² s^–1 longitudinal diffusivity of the protein - E _{z I} m² s^–1 longitudinal diffusivity of ionic strength - H /(1 – ) - I kmol m^–3 ionic strength - I _O kmol m^–3 initial ionic strength - I _p kmol m^–3 ionic strength at the peak - I _s kmol m^–3 ionic strength in the solid phase - I/V mol (dm³)^–2 slope of the ionic gradient elution - m distribution coefficient - m distribution coefficient at I - m _I distribution coefficient for ionic strength - Q cm³s^–1 flow rate - R m particle radius - R _s degree of separation - r m radial position inside particles - t s time - u m s^–1 linear velocity - V cm³ eluted volume of liquid - V _p cm³ eluted volume of liquid at the peak - V _T cm³ volume of the packed bed - W cm³ peak width - Z m bed height - z m vertical position in the bed - z _p m peak position from the inlet of the bed - (t) delta input at time - void fraction - ₁ s first moment - ₂ s² second central moment - s superficial space time