Precipitation of protein by ultracentrifuge with angle rotor

Precipitation of a protein by ultracentrifuge with an angle rotor was simulated by a model for sedimentation process. Assuming that the concentration of solute in an inclined ultracentrifugal tube is given by averaging the concentration in the imaginary horizontal tube, the governing equation describing the concentration in the rectangular-shaped tube with a uniform field of ultracentrifugal force for an inclined tube in an angle rotor was derived. The exact solution to this governing equation was obtained under the condition that the diffusion is absent or present. The dimensionless concentration which is reduced by the initial concentration can be expressed as the function of a dimensionless ultracentrifugal times ² t in case that the diffusion is absent, and as the function of dimensionless parameters andt ^*in case that the diffusion is present. From our first approximated model it is found that the precipitation of a protein by ultracentrifuge with an angle rotor proceeds more rapidly than that with a swing rotor whether diffusion is absent or present.List of Symbols c kg/m³ concentration of solute - c ⁰ kg/m³ initial concentration of solute - c ^A kg/m³ concentration of solute for angle rotor - c ^s kg/m³ concentration of solute for swing rotor - D cm²/s diffusion coefficient - d cm diameter of ultracentrifugal tube - k ₁ dimensionless constant - k ² dimensionless constant - r cm radial coordinate - r ₁ cm minimum radius of ultracentrifugal tube - r ₂ cm maximum radius of ultracentrifugal tube - r _m cm mean radius of ultracentrifugal tube - r _s cm radius from which sedimentation starts - s s sedimentation constant - t s time - z cm vertical coordinate - dimensionless parameter - ^m dimensionless parameter - deg inclination of ultracentrifugal tube - s^–1 angular velocity of rotation     

One-dimensional model of the acid hydrolysis of cellulosic substrates in a solid-liquid cyclone reactor

The use of rotating flow in an annulus is investigated as a means of enhancing the yield of glucose and xylose in the acid hydrolysis of cellulosic slurries. A one-dimensional model of such a cyclone reactor is developed for flow cases, co-current and counter-current flow. For the case of 250°C, 1% w/w acid, the one-dimensional model indicates an increase in the maximum glucose yield from 48.1% in a plug flow reactor to 69.3% in a co-current cyclone reactor, and up to 81.0% in a countercurrent cyclone reactor. The corresponding xylose yields are 91.6% for co-current operation and 97.7% for countercurrent operation. In the co-current case the maximum glucose and xylose yields do not occur at the same location in the reactor; however, in the countercurrent case they do. Although product yields are dramatically improved over those obtained in a plug flow reactor, the product concentrations are lower than would typically be obtained in a plug flow reactor.List of Symbols A cm² cross sectional area perpendicular to radial flow - A _c cm² cross sectional area of slurry inlet - A _c cm² cross sectional area of steam inlet - A _w cm² cross sectional area of water inlet - C _c concentration of cellulose as potential glucose (grams of potential glucose/cm³ of total stream) - C _c ^* grams cellulose/cm³ of solids concentration of cellulose as potential glucose - C _ginitial ^* grams glulose/cm³ of solids concentration of cellulose entering reactor - C _g grams glucose/cm³ of total stream concentration of glucose - C _g ^* grams glucose/cm³ of liquid stream concentration of glucose - C _cinitial ^* grams cellulose/cm³ of liquid concentration of glucose entering reactor - C _xn concentration of xylan as potential xylose (grams of potential xylose/cm³ of total stream) - C _xs grams xyclose/cm³ of total stream concentration of nylose - d _f dilution factor - dr cm radial increment - g cm/s² gravitational acceleration - g ^* centrifugal acceleration proportionality constant - h cm height of cyclone reactor - j cm/s flux - K constant in general equation for vortex flow, Eq. (4.9) - k ₁ 1/s kinetic rate constant of cellulose hydrolysis - k _a 1/s kinetic rate constant of xylan hydrolysis - k ₂ 1/s kinetic rate constant of glucose decomposition - k _2a 1/s kinetic rate constant of xylose decomposition - m vortex exponent - M _steam g/s mass rate of steam addition at outer radius - M _water g/s mass rate of cold water addition at outer radius - n cm³/s empirically determined settling parameter - Q cm³/s net volumetric flow in outward radial direction - Q _tot cm³/s total volumetric flow through reactor - q _c cm³/s volumetric flow of slurry feed - q _s cm³/s volumetric flow of stream feed - q _water cm³/s volumetric flow of cold water feed - r cm radial position - r _c 1/s rate of cellulose hydrolysis - r _g 1/s rate of glucose decomposition - r _i cm inner radius - r _o cm outer radius - r _xn 1/s rate of xylan hydrolysis - r _xs 1/s rate of xylose decomposition - s _mom cm g/s² inlet steam momentum - T _bulk s bulk residence time in reactor - T °C reactor temperature - v _c cm³/g specific volume of slurry feed - v _s cm³/g specific volume of steam - v _w cm³/g specific volume of water - V _f cm/s velocity of liquid as a function of radius - V _i cm/s inlet velocity - V _s cm/s velocity of solids as a function of radius - V _steam cm/s inlet steam velocity to cyclone - V cm/s terminal settling velocity - V _q cm/s tangential velocity - w _mom cm g/s² water inlet momentum - Y grams product out/grams reactant in yield of product - solids volumetric fraction - _f solids volumetric fraction in slurry feed - _i initial solids volumetric fraction of slurry - Pi     

Estimation of oxygen penetration depth in immobilized cells

Summary A simple method is proposed for calculating oxygen pentration depth in immobilized cells by assuming zero order kinetics in the presence of several external oxygen transport resistances. Calculations indicate that typical penetration depths of oxygen for immobilized microbial cells are in the range of 50–200 and those for immobilized or encapsulated animal and plant tissue culture are about 500–1000 . Based on calculations, oxygen transport in microencapsulation and microcarriers for tissue cultures are not transport-limited, but a slight limitation is expected for those in a hollow fiber reactor.Nomenclature a_s specific area of a support (cm) - Bi Biot number - dimensionless - C_b oxygen concentration in the bulk liquid (mM) - C _b C _b ^* -C_cr (mM) - C _b ^* bulk oxygen concentration in equilibrium with air (mM) - C_cr critical oxygen concentration (mM) - C_s oxygen concentration in the solid phase (mM) - d_p diameter or thickness of a support (cm) - D_eff effective diffusivity of oxygen in the solid phase (cm²/s) - k_m membrane permeability of oxygen (cm/s) - k _m ^* D_eff/_m - k_La_L liquid phase mass transfer rate coefficient (1/s) - k_sa_s solid phase mass transfer rate coefficient (1/s) - (OUR)_v volumetric oxygen uptake rate (mmol O₂/l) - p geometry parameter, p=0 for slab, p=1 for cylinder, p=2 for sphere - P_d oxygen penetration depth (cm) - P _d oxygen penetration depth in the absence of external diffusion limitation (cm) - Q volumetric oxygen uptake rate, (mmol O₂/l·h) - specific oxygen uptake rate (mmol O₂gm biomass (dry)·h) - r length coordinate (cm) - r_c oxygen penetration depth for sphere (cm) - r _c r_c in the absence of external diffusion limitation (cm) - r _c ^* oxygen penetration depth for cylinder (cm) - r _c ^* r _c ^* in the absence of external diffusion limitation (cm) - r_com combined mass transfer rate resistance (s) - r_d location where C_s becomes zero or C_cr (cm) - r_i radius of cylinder or sphere, half thickness of slab (cm) - U_sg superficial gas velocity (cm/s) - X cell concentration (g/l) Greek letters Thiele modulus, dimensionless - _L, _s liquid and solid phase volume fraction, respectively, dimensionless - effectiveness factor On sabbatical leave from KAIST, Seoul, Korea     

Effect of aggregate size in cell cultures of Tagetes patula on thiophene production and cell growth

Summary The effect of the size of Tagetes patula (marigolds) cell aggregates on growth and thiophene production in MS-medium was studied. A heterogeneous aggregate suspension was aseptically divided into 7 fractions, each with a defined aggregate diameter range, with subsequent inoculation of the fractions into MS growth medium. Growth occurred in all aggregate fractions and thiophene production increased with increasing aggregate diameter starting at about 3 mm, an effect possibly due to an increasing lack of oxygen in the aggregate centre. Calculations of oxygen concentration profiles in the aggregates showed namely, that the critical aggregate diameter where the oxygen concentration in the aggregate centre becomes very low, is about 3 mm. Aggregates with a diameter exceeding 1.2 cm showed a decreased thiophene production, however, these aggregates were hollow. The thiophenes produced mainly consisted of 5-(4-hydroxy-1-butenyl)1-2,2-bithienyl, which was excreted into the medium.Nomenclature ID _e effective diffusion coefficient (m²s^-1) - c oxygen concentration (mol m^-3) - c _s substrate concentration at surface (mol m^-3) - c _s.exp experimental value of c _s (mol m^-3) - c _eq substrate concentration at equilibrium (mol m^-3) - r _s consumption rate (mol m^-3 s^-1) - d _crit critical aggregate diameter (m) - d _agg aggregate diameter (m) - L length of aggregate (m) - W width of aggregate (m) - t time (s) - r distance from aggregate centre (m) - R radius of aggregate (m) - R(c) oxygen consumption (mol m^-3 s^-1) - V _c convection velocity (m s^-1) - V _m intrinsic maximum consumption rate (mol kg^-1 s^-1) - K _m intrinsic Michaelis Menten constant (mol m^-3) - V _m apparent maximum consumption rate (mol kg^-1 s^-1) - K _m apparent Michaelis Menten constant (mol m^-3) - * multiplication sign     

The relationship between nutrient feed rate and specific growth rate in fed batch cultures

Summary Equations are described which relate nutrient feed rate to specific microbial growth rate in fed batch culture. Fed batch cultures are classified into three types: 1) those allowing constant specific microbial growth rate, 2) those in which the rate of change of flow rate is constant and 3) those in which the nutrient flow rate is constant. The basic properties of these three types are described.Symbols F medium flow rate, L³ T^–1 - F _o medium flow rate at zero time, L³ T^–1 - g rate of change of flow rate with time, L³ T^–2 - K _v volume constant, being the total cell weight at zero time divided by the product of the yield coefficient and growth-limiting substrate concentration in the feed, L³ - s _r growth limiting substrate concentration in the feed, ML^–3 - V volume of liquid in the growth vessel, L³ - V _f volume of medium fed to the growth vessel, L³ - V _o volume of liquid in the growth vessel at zero time, L³ - X total weight of cells, M - x concentration of cells, ML^–3 - X _g total weight of cells grown, M - X _o total weight of cells at zero time, M - Y yield coefficient, weight of cells grown per unit weight of growth-limiting substrate - specific microbial growth rate, T^–1     

Flow dynamics of immobilized enzyme reactors

Summary Enzymic conversion of glucose to fructose was carried out in a packed bed and in a fluidized bed reactor. The flow dynamics of these two flow systems, loaded with two different types of immobilized loaded with two different types of immobilized glucose isomerase particles, were studied. The theoretical RTD curve calculated from the axial dispersed plug flow model equation was matched to the experimental RTD curve by an optimization technique. The effect of fluid velocity on the extent of liquid dispersion was established. Theoretical predictions on the conversion of glucose to fructose were calculated using three mathematical models, namely, a plug flow model, a continuous stirred tank reactor (CSTR) model and an axial dispersed plug flow model. The experimental results showed that the axial dispersed plug flow model was superior in predicting the performance of both the packed bed and fluidized bed reactor.Abbreviations C Dimensionless concentration - D Dispersion coefficient [cm²/sec] - d _p Mean particle diameter [cm] - E Enzyme concentration [mol/gm] - F Fructose concentration [mol/cm³] - F _e Equilibrium fructose concentration [mol/cm³] - G Glucose concentration [mol/cm³] - G _e Equílibrium glucose concentration [mol/cm³] - G _o Initial glucose concentration [mol/cm³] - Reduced glucose concentration [mol/cm³] - K Equilibrium constant - K _mf Forward reaction rate constant [mol/cm³] - K _mr Reserve reaction rate constant [mol/cm³] - K _m Rate constant [mol/cm³] - L Total length of the reactor bed [cm] - l Length [cm] - Q Flow rate [cm³/s] - r Rate of reaction based on volume of substrate - u Superficial liquid velocity [cm/s] - v Interstitial liquid velocity [cm/s] - V Reactor bed volume [cm³] - V _mf Forward reaction rate constant [mol/s·g enzyme] - V _mr Reserve reaction rate constant [mol/s·g enzyme] - z Dimensionless distance along the reactor - Density [g/cm²]     

Mixing time in a down-flow jet loop bioreactor

Mixing time was determined in a down-flow jet loop bioreactor with Newtonian and non-Newtonian fluids. It was observed that the mixing time decreased with an increase in linear liquid velocity, superficial gas velocity, draft tube to column diameter ratio, nozzle diameter and shear thinning of media. The optimum draft tube to column diameter ratio was found to be about 0.44. Correlations were presented for prediction of mixing time.List of Symbols A m² cross sectional area of the column - C kmol/m³ local tracer concentration - A _D m² flow area,A _D =/4 (D _Z ² -D _TO ² ) - D m column diameter - D _E m draft tube diameter - D _TO m outside diameter of the air tube - D _TFL m equivalent flow diameter,D _TFL =(D _Z ² -D _TO ² )^0.5 - D _z m nozzle diameter - g m/s² gravitational acceleration - h % inhomogeneity - H m height of the column - H _B m distance between the lower edge of the draft tube and the impact plate - H _T m distance between the upper edge of the draft tube and the liquid nozzle - K Pa.sⁿ consistency index in power-law model - L _E m length of the draft tube - n flow index in the power-law model - Re _j jet Reynolds number,Re _j =(D _TFL×w₁×_L)/ _eff - t _M s mixing time - t _sg m/s superficial gas velocity based onA - W _l m/s linear liquid velocity based onD _D Greek Letters N/m² shear stress - s shear rate - kg/m³ density of liquid - N/m surface tension of the liquid - Pa.sⁿ viscosity of liquid Indices X concentration at infinite time maximum value of tracer concentration - eff effective - L Liquid - obs observed - pred Predicted     

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     

Determination of effective diffusivity of substrate in biological films and particles

Summary Particle supported biofilms of uniform thickness were generated in an aerobic fluidized-bed reactor with phenol as the carbon source. A method was developed for determining the effective diffusivities of oxygen and phenol using trypan blue, a vital stain as the tracer. The effective diffusivities of oxygen and phenol were found to be 2.72×10^–6 cm²/s and 1.12×10^–6 cm²/s respectively.Nomenclature C_i initial solute concentration in bulk, g/cm³ - C_t solute concentration in bulk at time t, g/cm³ - C bulk solute concentration at equilibrium, g/cm³ - D molecular diffusivity, cm²/s - D effective diffusivity, cm²/s - D_o D_p D_tb molecular diffusivity of oxygen, phenol and trypan blue, cm²/s - D_o, D_p, D_tb effective diffusivity of oxygen, phenol and trypan blue, cm²/s - D_s molecular diffusivity of substrate, cm²/s - D_s effective diffusivity of substrate, cm²/s - K partition coefficient - M_t amount of solute in the particle at time t, g - M amount of solute in the particle at equilibrium, g - r particle radius, cm - r _bp radius of the particle with biofilm, cm - S substrate concentration, g/cm³ - S_b substrate concentration in bulk, g/cm³ - S_i initial substrate concentration, g/cm³ - V₁ solute molar volume, cm³/g mol Greek Symbols bf porosity of the biofilm - tortuosity factor     

Growth and death rates of bovine embryonic kidney cells in turbulent microcarrier bioreactors

Bead-bead collisions have been characterized using the velocity of the smallest turbulent eddies to calculate a turbulent collision severity (defined as the energy of collisions times their frequency), but a shear-based collision mechanism with a different dependence on the system variables is also applicable. This shearbased mechanism and the ratio of smallest eddy size to microcarrier diameter can explain the beneficial effects of both smaller diameter microcarriers and higher viscosity of the medium on the growth rate of bovine embryonic kidney cells. Death rates of these cells have also been measured at several levels of agitation. The decrease in apparent growth rate from increasing agitation is caused both by a higher rate of cell death as well as a lower intrinsic growth rate.List of Symbols B unspecified biological variable - d cm bead diameter - d _i cm impeller diameter - e error in estimate of power number - F _n , F _s (g·cm)/s² normal and shear forces on a cell - Fr Froude number - g 980cm/s² acceleration of gravity - k k^–1 first order death rate constant - m g mass of a bead - n s^–1 impeller rotational rate - n _b number of impeller blades - N _p impeller power number - R _i cm impeller leading edge radius - TCS (g·cm²)/s³ turbulent collision severity - V cm³ reactor volume - v _br cm/s rms relative velocity between beads - v _e cm/s velocity in smallest eddies - X number of cells/cm₃ cell population Greek Symbols volume fraction microcarriers - s^–1 shear rate - cm²/s³ turbulent power dissipation rate - cm size of smallest eddies - g/(cm·s) dynamic viscosity - h^–1 apparent growth rate of cells - ₀ h^–1 intrinsic growth rate of cells in absence of death - v cm²/s kinematic viscosity - _b g/cm³ bead density - _f g/cm³ fluid density - g/(cm·s²) shear stress     

Preparative electrophoresis: on the estimation of maximum temperature

The quantity of proteins processed by an electrophoretic technique is proportional to the cross-sectional area of the gel. For preparative purifications, an increase in the cross-sectional area is desired, but the Joule heating phenomenon restricts such an increase. The governing heat equation is analyzed and simplified with reference to Counteracting Chromatographic Electrophoresis. The application of the method of weighted residuals yields a compact and accurate solution for the maximum temperature rise in the column which is suitable for design calculations. Similar estimations indicate the efficiency of heat dissipation in annular configuration.List of Symbols C _p specific heat capacity, J g^–1 K^–1 - h heat transfer coefficient at the wall, W cm^–2K^–1 - i current density, A cm^–2 - k effective thermal conductivity of the packing, W cm^–1 K^–1 - k _b electrical conductivity of the buffer, mho cm^–1 - k _e effective electrical conductivity of the packing, mho cm^–1 - k _g electrical conductivity of the gel, mho cm^–1 - L length of the packing, cm - N _Pr Prandtl number - N _Re Reynolds number - r radial coordinate, cm - r _i inner radius of annulus, cm - r _o outer radius of annulus, cm - S heat source term, defined by eqn. (6) - T temperature, K - T _c cooling fluid temperature, K - T _i initial temperature, K - T _max highest temperature in the column, K - u superficial buffer velocity, cm s^–1 - V voltage gradient, V cm^–1 - porosity of the packing, dimensionless - buffer density, g cm^–3 - temperature, dimensionless Material presented in this paper has been adapted from the author's dissertation [15] which was accepted (supervisor: Dr. Jean B. Hunter) by the Cornell University Graduate Faculty in partial requirement of a graduate degree. Thoughtful discussions with Professors J. Robert Cooke and Michael L. Shuler regarding the annulus problem and the financial support provided by the Department of Agricultural and Biological Engineering, Cornell University, Ithaca, USA are gratefully appreciated.     

Hydraulic resistance to radial water flow in growing hypocotyl of soybean measured by a new pressure-perfusion technique

Hydraulic resistances to water flow have been determined in the cortex of hypocotyls of growing seedlings of soybean (Glycine max L. Merr. cv. Wayne). Data at the cell level (hydraulic conductivity, Lp; half-time of water exchange, T _1/2; elastic modulus, ; diffusivity for the cell-to-cell pathway, D _c) were obtained by the pressure probe, diffusivities for the tissue (D _t) by sorption experiments and the hydraulic conductivity of the entire cortex (Lp_r) by a new pressure-perfusion technique. For cortical cells in the elongating and mature regions of the hypocotyls T _1/2=0.4–15.1 s, Lp=0.2·10^-5–10.0·10^-5 cm s^-1 bar^-1 and D _c=0.1·10^-6–5.5·10^-6 cm² s^-1. Sorption kinetics yielded a tissue diffusivity D _t=0.2·10^-6–0.8·10^-6 cm² s^-1. The sorption kinetics include both cell-wall and cell-to-cell pathways for water transport. By comparing D _c and D _t, it was concluded that during swelling or shrinking of the tissue and during growth a substantial amount of water moves from cell to cell. The pressure-perfusion technique imposed hydrostatic gradients across the cortex either by manipulating the hydrostatic pressure in the xylem of hypocotyl segments or by forcing water from outside into the xylem. In segments with intact cuticle, the hydraulic conductance of the radial path (Lp_r) was a function of the rate of water flow and also of flow direction. In segments without cuticle, Lp_r was large (Lp_r=2·10^-5–20·10^-5 cm s^-1 bar^-1) and exceeded the corticla cell Lp. The results of the pressure-perfusion experiments are not compatible with a cell-to-cell transport and can only the explained by a preferred apoplasmic water movement. A tentative explanation for the differences found in the different types of experiments is that during hydrostatic perfusion the apoplasmic path dominates because of the high hydraulic conductivity of the cell wall or a preferred water movement by film flow in the intercellular space system. For shrinking and swelling experiments and during growth, the films are small and the cell-to-cell path dominates. This could lead to larger gradients in water potential in the tissue than expected from Lp_r. It is suggested that the reason for the preference of the cell-to-cell path during swelling and growth is that the solute contribution to the driving force in the apoplast is small, and tensions normally present in the wall prevent sufficiently thick water films from forming. The solute contribution is not very effective because the reflection coefficient of the cell-wall material should be very small for small solutes. The results demonstrate that in plant tissues the relative magnitude of cell-wall versus cell-to-cell transport could dependent on the physical nature of the driving forces (hydrostatic, osmotic) involved.Abbreviations and symbols D _c diffusivity of the cell-to-cell pathway - D _t diffusivity of the tissue - radial flow rate per cm² of segment surface - Lp hydraulic conductivity of plasma-membrane - Lp_r radial hydraulic conductance of the cortex - T _1/2 half-time of water exchange between cell and surroundings - volumetric elastic modulus     

Disruption of a filamentous fungal organism (N. sitophila) using a bead mill of novel design I. General disruption characteristics

The disruption of a typical filamentous fungus, a native strain of Neurospora sitophila, was studied using a glass bead mill of novel design (the Sulzer Annu Mill 01). Cell concentration (in the range of 2.5–5 g dry weight/L) had little influence on the disruption attained. Disruption increased with increasing rotor speed (1000 –4000 r.p.m.) and number of passes (up to six passes) through the Annu Mill. Disruption was observed to follow traditional first-order kinetics for bead mills possessing predominantly plug flow characteristics. It was concluded that in general the Annu Mill would be applicable for the disruption of filamentous organisms.Nomenclature C_P aqueous-phase soluble protein concentration of disrupted sample (g/mL) - CP,MAX aqueous-phase soluble protein concentration of a completely disrupted sample (g/mL) - C_PO aqueous-phase soluble protein concentration of undisrupted sample (g/mL) - N number of passes though the bead mill (–) - R total fraction of cells disrupted (–) Greek Letters _C internal moisture volume fraction of undisrupted cells (–) - _L aqueous phase volume fraction of disrupted cell suspension (–) - _LO aqueous phase volume fraction of undisrupted cell suspension (–) - _L,MAX aqueous phase volume fraction at complete disruption (R=1) (–) - fluid density (kg/m³) - _C density of the microorganism (kg/m³) - _L density of the suspending aqueous phase (kg/m³) - suspension batch residence time in the Annu Mill 01 (min.) Abbreviations DW dry weight     

A simple dynamic method for on-line and off-line determination of kLa during cultivation of animal cells

Summary A new, fast method is described to determine k_La either off-line, or on-line during animal-cell cultivation. Since it does not need the equilibrium concentration of oxygen in the liquid phase (C*), it is not required to await a new steady state. Furthermore, the results do not depend on the calibration value of the dissolved-oxygen probe. The method yielded accurate values for k_La, both for an oxygen-consuming and a non-consuming system.Nomenclature C _L Dissolved-oxygen concentration [mol·m^-3] - C ^* C _L in equilibrium with the oxygen concentration in the gas phase [mol·m^-3] - C _L, Equilibrium oxygen concentration at stationary conditions [mol·m^-3] - k_La Volumetric oxygen transfer coefficient [s^-1] - r Specific oxygen consumption of biomass [mol·cell^-1·s^-1] - X Cell concentration [cells·m^-3] - t Time [s] - Noise of dissolved-oxygen probe [mol·m^-3] - Absolute error of k_La-measurement [s^-1]     

A mathematical model for solid state fermentation in tray bioreactors

A simple mathematical model for the interaction of mass transport with biochemical reaction in solid state fermentations (SSF) in static tray type bioreactors under isothermal conditions has been developed. The analysis has enabled scientific explanations to a number of practical observations, through the concept of critical substrate bed thickness. The model will be most useful in the prediction of the concentration gradients as also in efficient design of these bioreactors.List of Symbols C g/cm³ Oxygen concentration in the bed - C _g g/cm³ Atmospheric oxygen concentration - C ^* Dimensionless oxygen concentration, C/C _g - D _e cm²/h Effective diffusivity - H cm Bed thickness or height - H _c cm Critical bed thickness or height - H _m cm Maximum height of zone of zero oxygen concentration - p _i mg/(g · h) Productivity (Eq. 13) - R g/(cm³ · h) Biochemical reaction rate - t h Fermentation time - t ^* Dimensionless time, D _e t/H² - X mg/cm³ Biomass concentration - X _max mg/cm³ Maximum biomass concentration - y Dimensionless thickness or height, (y = z/H) - y cm Thickness of zone of zero oxygen concentration (Eq. 12) - Y Yield coefficient - z cm Bed thickness or height along tray axis - Bed void fraction - _max h^–1 Specific growth rate - Thiele modulus      

Performance characteristics of yeast growth in a modified airlift fermenter

Two types of airlift fermenters, conventional (UT-ALF) and modified (CDT-ALF) were investigated to evaluate their performance with respect to baker's yeast growth. The riser tube of conventional external loop airlift fermenter is replaced by a converging-diverging tube, which is named as modified airlift fermenter having downcomer to riser cross-sectional area ratio A _d /A _r =1.8.The results were compared for the two types of airlift fermenter. A modified growth kinetics model for baker's yeast with oxygen as limiting substrate, has been proposed. The values of K _s and K _d of the growth model were determined from experimental data. The proposed model represented better for CDT-ALF system compared to UT-ALF. Compared to UT-ALF, CDT-ALF always showed higher cell mass concentration and low residual sugar concentration irrespective of the operating conditions. At optimum operating condition (initial glucose concentration 30 g/l, air flow rate 0.5 vvm and fermentation time 8 hrs.) 16.7% higher cell mass was observed in CDT-ALF compared to that in UT-ALF and yield (Y _x/s ) was found to be 0.51 which was theoretically very near to maximum achievable value.Symbols ALF Airlift fermenter - UT Uniform tube - CDT Converging-diverging tube - A _r Cross sectional area of riser - A _d Cross sectional area of downcomer - C _s Glucose cone, at any time, g/l - C _l Dissolved oxygen conc, at any time, g/l - _max Max. sp. growth rate, hr^–1 - Sp. growth rate, hr^–1 - X ₀ Initial cell mass cone. (dry wt.), g/l - X Cell mass conc. at any time t, g/l - C _s0 Initial glucose conc., g/l - C _s Glucose conc. at any time t, g/l - C _l Equilibrium conc. of oxygen, 0.0076 g/l - y _x/s Yield coefficient (dimensionless) - y _x/s gm cell mass produced/gm glucose consumed - Y _O2 gm cell produced/gm oxygen consumed - k _d maintenance coefficient, hr^–1 - K _L a volumetric mass transfer coefficient, hr^–1 - k _s saturation constant for the substrate, g/l - K _O2 saturation constant for the substrate of dissolved oxygen, g/l. This work was supported by a research grant from the Department of Biotechnology Govt. of India.     

Gas-phase influence on the mixing in a fluidized bed bio-reactor

Summary The liquid and solids mixing in fluidized bed bio-reactors containing particles with a density only slightly higher than water (1100 kg/m³) is generally consistent with the results found in previous studies for reactors with particles of higher density. The liquid mixing can be described by an axial dispersion model for a large variety of conditions while the solids follow the streamlines of the liquid. In the presence of a gas phase the degree of mixing of both the liquid and the solid phase increased. This effect became larger with increasing reactor diameter. In the extrapolation of laboratory data of three phase fluidized bed bio-reactors to pilot plant systems this effect should be taken into account. The liquid and solids mixing may have a substantial effect on overall conversion rates and on possible microbial stratification in the reactor.Nomenclature Bo Bodenstein number v L/D (-) - D _r diameter of the fluidized bed reactor (m) - D ₁ Dispersion coefficient of the liquid phase (m²/s) - D _g dispersion coefficient of the solid phase (m²/s) - E(in) normalized dye concentration function entering the ideally mixed tank reactor (-) - E(t) normalized dye concentration function as measured (-) - L length of the axial dispersed reactor (m) - t time after dye injection (s) - t _m time constant for microbial selection (s) - t _s solid mixing time constant (s) - t time interval in which a particle migrates within the bed (s) - v _t superficial gas velocity (m/s) - v _g superficial liquid velocity (m/s) - z migration distance of a particle in the bed (m) - ₁ in situ growth rate of a dominant organism (s^-1) - ₂ in situ growth rate of a recessive organism (s^-1) - average residence time in the axial dispersed reactor (s) - _t average residence time in the ideally mixed tank reactor (s)     

Oxygen transfer in an airlift reactor with multiple net draft tubes

A pilot scale airlift reactor with multiple net draft tubes was developed to improve oxygen transfer in the reactor. The reactor was 0.29 m in diameter and 2 m height. A steadystate sulfite oxidation method was applied to determine an overall volumetric mass transfer coefficient. Oxygen transfer of the proposed airlift reactor can be 60–100% higher than that of bubble columns under the same operating conditions.List of Symbols C ^* mol·dm^–3 saturated concentration of dissolved oxygen - C _L mol·dm^–3 bulk concentration of dissolved oxygen - G mol/min nitrogen flow rate - k _L a hr^–1 the volumetric gas-liquid mass transfer coefficient - Mo ₂ g/mol molecular weight of oxygen - OTR g/min the oxygen transfer rate - U _g cm/s superficial air velocity - V _L dm³ volume of the liquid phase - _in oxygen mole ratio in the inlet gas - _out oxygen mole ratio in the outlet gas     

Model aided design of repeated fed-batch penicillin fermentation

Structured models of antibiotic fermentation that quantify maturation and aging of product forming biomass are fitted to experimental data. Conditions of superiority of repeated fed batch cultivation are characterized on the basis of a performance criterion that includes penicillin productivity and costs of operation. Emphasis is placed on the relevance of such research to the model aided design of optimal cyclic operation.List of Symbols c IU/mg cost factor - D s^–1 dilution rate - J IU · cm^–3 · h^–1 net productivity - k _p IU · mg^–11 · h^–1 specific product formation rate - k _pm IU · mg^–1 · h^–1 maximum specific product formation rate - p IU/cm³ concentration of penicillin - T s final time of fermentation - t s fermentation time - X kg/m³ concentration of biomass dry weight - X ₁kg/m³ concentration of young, immature biomass - X ₂ kg/m³ concentration of mature product forming biomass - X _c kg/m³ biomass concentration of the end of growth phase - X _mkg/m³ maximum biomass concentration Greek Letters s^–1 specific maturation rate - s^–1 specific aging rate - s^–1 specific growth rate - _m s^–1 maximum specific growth rate - _p s^–1 specific growth rate during the product formation phase - s cycle time - % volume fraction of draw-off Abbreviations CC chemostat culture - RFBC repeated fed batch culture - RBC repeated batch culture     

A mechanism for isotonic fluid flow through the tight junctions of Necturus gallbladder epithelium

During isotonic fluid flow, Necturus gallbladder epithelium mediates net fluxes of paracellular probes by a convective process. We show here that the paracellular system is modeled by permeation through three populations of channels: (i) convective parallel-sided ones of width 7.7 nm (ii) small diffusive ones of radius 0.6 nm, and (ii) large diffusive ones of radius exceeding 50 nm. The reflexion coefficient of the convective channels is very low and the calculated osmotic flow rate is close to zero when compared with the observed fluid absorptive rate of 2 x 10^–6 cm/sec. Analysis reveals that the convective channels behave as though closed to back-diffusion of probes; if this is due to solvent drag then very high fluid velocities are required, acting through minute areas. There are no transjunctional gradients that could drive the flow, and so the fluid must be propelled through the channel by components of the junction.We propose a mechanism based upon an active junctional peristalsis which allows discrimination on the basis of molecular size, in which the channels are always occluded at some point and so back-diffusion cannot occur. There is no local gradient of salt distal to the junctions and therefore the osmotic permeability of the membranes is irrelevant. High fluid velocities are not required, and the flow can occur over a substantial fraction of the junction. The mechanism must involve motile and contractile elements associated with the junction for which there is already considerable evidence.Symbols A _i filtration area of channel i;i=b (big), s (small) and c (convectional) - B constant for streamline flow - C _i concentration of probe at i - D diffusion coefficient - D ^o diffusion coefficient in free solution - d width of junction - F _i diffusive drag factor in channel i - g ionic conductivity - G _i convective drag factor in channel i - J _ij probe flux from i to j - J _net net probe flux - J _v volume flow per cm² of epithelium - l linear extent of junction per cm² epithelial plane - L length of junctional channel - L _p hydraulic conductivity - N Avogadro's number - q available filtration area fraction of channel - r _s probe molecular radius - r _c channel radius or half-width - S _i steric factor in channel i - V _w,s partial molar volume of water or salt - v _i fluid velocity in channel i - _w dynamic viscosity of water - specific conductivity - ratio of solute radius to channel radius or half-width - diffusive/pressure-driven flow ratio - reflexion coefficient