The effective diffusion coefficient and the distribution constant for small molecules in calcium-alginate gel beads

The effective diffusion coefficient, D(e), and the distribution constant, K(i), for selected mono- and disaccharides and organic acids were determined in homogeneous calcium-alginate gel with and without entrapped bacteria. Results were obtained from transient concentration changes in well-stirred solutions of limited volume, in which the gel beads were suspended. The effective diffusioncoefficients and the distribution constants were estimated by fitting mathematical model predictions to the experimental data using a nonlinear model fitting program (MODFIT). Both single solute diffusion and multiple solute diffusion were performed. A small positive effect was obtained onthe values of D(e) for the system of multiple solute diffusion; however, the values of K(i) were not significantly influenced. For the nine solutes tested, D(e) for 2% Ca-alginate gel beads was found to be approximately 85% of the diffusivity measured in water. The effects on D(e) and K(i), for lactose and lactic acid were determined for variations of alginate concentration, pH, temperature, and biomass content in the beads. D(e) decreased linearly for both lactose and lactic acid with increasing cell concentration in the Ca-alginate gel. K(i), was constant for both lactose and lactic acid with increasing cell concentration. D(e) was significantly lower at pH 4.5 than at pH 5.5 and 6.5 for both lactose and lactic acid. Furthermore, D(e) seemed to decrease with increased alginate concentration in the range of 1% to 4%. The diffusion rate increased with increasing temperature, and the activation energy for the diffusion process for both lactose and lactic acid was constant in the temperature range tested. (c) 1995 John Wiley & Sons Inc.     

Effective Bead Preparation of Coimmobilized Methanogenic and Methanotrophic Bacteria for Tetrachloroethene Degradation

Three types of coimmobilized methanogenic and methanotrophic bacterial beads – Ca-alginate, Ba-alginate, and Ca-alginate chitosan – were used for tetrachloroethene (PCE) degradation. For the purpose of effective preparation of coimmobilized bacterial beads, the diameter and broken-loading of beads were measured. The activity tests to find the optimal bacteria concentration in the bead were performed. It was found that Ba-alginate beads had superiority in bacterial growth and the degree of strength of beads from the diameter and broken-loading tests. Also, it was shown that it is most effective to add 200 mL of methanogens into 500 mL of 2% alginate solution and 20 mL of methanotrophs into 500 mL to 2% alginate solution. When methanogens and methanotrophs were applied with the Ba-alginate bead in the actual dechlorination of PCE, the biological PCE dechlorination rate was 92%, and there was highly effective degradation of PCE based on the coimmobilized bead. Additionally, relation to the diameter (X) and broken-loading (Y) of the Ba-alginate bead was derived following equation, Y = 438.02 exp(–1.4815 X).     

A novel technique for measuring solute diffusivities in entrapment matrices used in immobilization

A novel technique has been developed for measuring effective solute diffusivities in entrapment matrices used for cell immobilization. In this technique radiotracers were used to measure effective diffusivities and equilibrium partition coefficients of the solute between the liquid and solid matrix. Ca-alginate was used in this study, because it is one of the most commonly employed matrices for the immobilization of microbial, plant and mammalian cells. The experimental apparatus consisted of a single spherical Ca-alginate bead which was attached to a rotating rod and immersed in water containing C(14)-glucose. The rotational speed of the spherical bead was controlled and resulted in excellent mixing, and negligible external film mass transfer resistance, which allowed the measurement of true effective solute diffusivity within the solid matrix. The rates of C(14)-glucose diffusion within the Ca-alginate sphere were measured using a scintillation spectrometer. A mathematical model of unsteady-state diffusion in a sphere was used with appropriate boundary conditions, and the effective diffusivity of glucose was found from the best fit of the experimental data using a computer regression analysis method. Using 2% (w/v) Ca-alginate beads in this new radiotracer technique the effective diffusivity and partition coefficient of glucose were found to be 6.62 x 10(-10) m(2)/s and 0.98, respectively. The accuracy, advantages, and simplicity of this new method for diffusivity measurements are also compared to other existing methods.     

Diffusion characteristics of substrates in Ca-alginate gel beads

The diffusion characteristics of several substrates of varying molecular sizes into and from Ca-alginate gel beads in well-stirred solutions were investigated. The values of the diffusion coefficient (D) of substrates such as glucose, L-tryptophan, and alpha-lactoalbumin [with molecular weight (MW) less than 2 x 10(4)] into and from the gel beads agreed with those in the water system. Their substrates could diffuse freely into and from the gel beads without disturbance by the pores in the gel beads. The diffusion of their substrates into and from the gel beads was also not disturbed by increasing the Ca-alginate concentration in the beads and the CaCl(2) concentration used in the gel preparation. In the case of higher molecular weight substances such as albumin (MW = 6.9 x 10(4)), gamma-globulin (MW = 1.54 x 10(5)) and fibrinogen (MW = 3.41 x 10(5)), the diffusion behaviors of the substrates into and from the gel beads were very different. No diffusion of their substrates into the gel beads from solutions was observed, and only albumin was partly absorbed on the surface of the gel beads. The values of D of their substrates from the gel beads into their solutions were smaller than their values in the water system, but all their substrates could diffuse from the gel beads. The diffusion of high molecular weight substrates was limited more strongly by the increase of Ca-alginate concentration in the gel beads than by the increase of the CaCl(2) concentration used in the gel preparation. Using these results, the capacity of Ca-alginate gel as a matrix of immobilization was discussed.     

Diffusivity of oxygen into carriers entrapping whole cells

The effective diffusivity of oxygen, D(e), in Ca-alginate and PVA-SbQ gels was measured using a two-chamber vessel with a membrane between the two chambers. The effect of cell density, C(c), on D(e) in Ca-alginate gels was studied. The effective diffusivity of oxygen decreased with increasing cell density, to C(c) = 170 kg dry cells/m(3) gel. The dependency of D(e) on cell density was discussed in terms of a random-pore model. The model correlated well with experimental data, i.e., kD(e)/D(0) = 0.86(1 - 1.47 x 10(-3) C(c))(2). Here, k is the partition coefficient, and D(0) is diffusivity in water.     

Diffusion of (de)acylated antibiotic A40926 in alginate and carrageenan beads with or without cells and/or soybean meal

Effective diffusion coefficients (D(e)) of antibiotic A40926 and its deacylated derivative were determined in Ca-alginate (2% wt/wt) and kappa-carrageenan (2.6% wt/wt) gel beads with or without immobilized Actinoplanes teichomyceticus cells and/or soybean meal (SBM). The method used was based on transient concentration changes in a well-stirred antibiotic solution in which gel beads, initially free of solute, were suspended. Unsteady-state diffusion in a sphere was applied and D(e) determined from the best fit of experimental data. A40926 showed markedly different diffusion characteristics than its deacylated derivative. Diffusivity of deacyl-A40926 in alginate or carrageenan gel beads was six to seven times that of A40926. Large differences in partition coefficients (Kp) were also found. In case of beads without additions, A40926, in contrast to deacyl-A40926, strongly partitioned to the liquid phase. Introduction of SBM and/or mycelium in the gel beads decreased the effective diffusivity of deacyl-A40926, but increased its partitioning to the solid phase. Our findings indicate that a relatively moderate structural change of a lipoglycopeptide molecule could lead to a major change in its diffusion/partition characteristics.     

Determination of diffusion coefficients and diffusion characteristics for chlorferon and diethylthiophosphate in Ca-alginate gel beads

Diffusion characteristics of chlorferon and diethylthiophosphate (DETP) in Ca-alginate gel beads were studied to assist in designing and operating bioreactor systems. Diffusion coefficients for chlorferon and DETP in Ca-alginate gel beads determined at conditions suitable for biodegradation studies were 2.70 x 10(-11) m(2)/s and 4.28 x 10(-11) m(2)/s, respectively. Diffusivities of chlorferon and DETP were influenced by several factors, including viscosity of the bulk solution, agitation speed, and the concentrations of diffusing substrate and immobilized cells. Diffusion coefficients increased with increasing agitation speed, probably due to poor mixing at low speed and some attrition of beads at high speeds. Diffusion coefficients also increased with decreasing substrate concentration. Increased cell concentration in the gel beads caused lower diffusivity. Theoretical models to predict diffusivities as a function of cell weight fraction overestimated the effective diffusivities for both chlorferon and DETP, but linear relations between effective diffusivity and cell weight fraction were derived from experimental data. Calcium-alginate gel beads with radii of 1.65-1.70 mm used in this study were not subject to diffusional limitations: external mass transfer resistances were negligible based on Biot number calculations and effectiveness factors indicated that internal mass transfer resistance was negligible. Therefore, the degradation rates of chlorferon and DETP inside Ca-alginate gel beads were reaction-limited.     

Production of proteoglycans by immobilized chondrocytes: Effect of divalent cations

Summary Rabbit articular chondrocytes immobilized in alginate beads maintained normal morphology and metabolic activity (glucose consumption) for more than two weeks whether calcium, barium, or strontium were used for the gel forming. Only Ca- and Ba-alginate immobilized chondrocytes produced proteoglycans in the external medium. Only Ca-alginate beads produced proteoglycans at a constant rate.     

Transport limitation of chlorine disinfection of Pseudomonas aeruginosa entrapped in alginate beads

An artificial biofilm system consisting of Pseudomonas aeruginosa entrapped in alginate and agarose beads was used to demonstrate transport limitation of the rate of disinfection of entrapped bacteria by chlorine. Alginate gel beads with or without entrapped bacteria consumed chlorine. The specific rate of chlorine consumption increased with increasing cell loading in the gel beads and decreased with increasing bead radius. The value of an observable modulus comparing the rates of reaction and diffusion ranged from less than 0.1 to 8 depending on the bead radius and cell density. The observable modulus was largest for large (3-mm-diameter) beads with high cell loading (1.8 x 10(9) cfu/cm(3)) and smallest for small beads (0.5 mm diameter) with no cells added. A chlorine microelectrode was used to measure chlorine concentration profiles in agarose beads (3.0 mm diameter). Chlorine fully penetrated cell-free agarose beads rapidly; the concentration of chlorine at the bead center reached 50% of the bulk concentration within approximately 10 min after immersion in chlorine solution. When alginate and bacteria were incorporated into an agarose bead, pronounced chlorine concentration gradients persisted within the gel bead. Chlorine did gradually penetrate the bead, but at a greatly retarded rate; the time to reach 50% of the bulk concentration at the bead center was approximately 46 h. The overall rate of disinfection of entrapped bacteria was strongly dependent on cell density and bead radius. Small beads with low initial cell loading (0.5 mm diameter, 1.1 x 10(7) cfu/cm(3)) experienced rapid killing; viable cells could not be detected (<1.6 x 10(5) cfu/cm(3)) after 15 min of treatment in 2.5 mg/L chlorine. In contrast, the number of viable cells in larger beads with a higher initial cell density (3.0 mm diameter, 2.2 x 10(9) cfu/cm(3)) decreased only about 20% after 6 h of treatment in the same solution. Spatially nonuniform killing of bacteria within the beads was demonstrated by measuring the transient release of viable cells during dissolution of the beads. Bacteria were killed preferentially near the bead surface. Experimental results were consistent with transport limitation of the penetration of chlorine into the artificial biofilm arising from a reaction-diffusion interaction. The methods reported here provide tools for diagnosing the mechanism of biofilm resistance to reactive antimicrobial agents in such applications as the treatment of drinking and cooling waters. (c) 1996 John Wiley & Sons, Inc.     

Diffusion in kappa-carrageenan gel beads

Using a well-mixed and temperature-led vessel, the diffusion characteristics of various solutes into spherical kappa-carrageenan gel beads were experimentally investigated. The diffusion coefficient of glucose was markedly affected by the glucose concentration and the operating temperature. In all cases the diffusivity obtained was noticeably smaller than that of glucose in pure water. The experimental data also indicated an inverse relationship between the diffusivity and the polymer concentration used in the gel preparation. As well, the glucose diffusivity was affected by the presence of other solutes in the glucose solution. Electrolytes such as ammonium sulfate, KCl, and CaCl(2) were observed to enhance the diffusion coefficient. On the other hand, the addition of arginine or bovine serum albumin had an adverse effect on the diffusivity. No diffusion of albumin into the gel beads was observed, and such a solute created a significant mass transfer resistance during the diffusion process.     

Kluyveromyces lactis cells entrapped in Ca-alginate beads for the continuous production of a heterologous glucoamylase

Viable cells of Kluyveromyces lactis, transformed with the glucoamylase gene from Arxula adeninivorans, were entrapped in beads of Ca-alginate and employed on a lab scale in a continuous stirred and a fluidised bed reactor (FBR), both fed with a rich medium (YEP) containing lactose as carbon source. Experiments with freely suspended cells in batch and chemostat had demonstrated that glucoamylase production was favoured in the presence of lactose and YEP medium. Employing controlled-sized beads having a 2.13 mm diameter, specific glucoamylase productivity was higher in the stirred reactor (CSTR) than in the FBR; in the latter a higher volumetric productivity was achieved, due to the lower void degree. The performance of the immobilised cell systems, in terms of specific glucoamylase productivity, was strongly affected by mass transfer limitations occurring throughout the gel due to the high molecular weight of the product. In the perspective to improve and scale-up the immobilised cell system proposed, a mathematical model, which takes into account substrate transfer limitations throughout the gel, has been developed. The effective lactose diffusivity was related to the bead reactive efficiency by means of the Thiele modulus. The regression of the model parameters on the experimental data of substrate consumption obtained both in the CSTR and in the FBR allowed to estimate lactose diffusivity and the kinetic parameters of the immobilised yeast.     

Diffusion of lactose in kappa-carrageenan/locust bean gum gel beads with or without entrapped growing lactic acid bacteria

Effective diffusion coefficients (De) of lactose in kappa-carrageenan (2.75% wt/wt)/locust bean gum (0.25% wt/wt) (LBG) gel beads (1.5-2.0-mm diameter)with or without entrapped lactic acid bacteria (LAB) were determined at 40 degrees C. The effects of lactose concentration, bacteria strain (Streptococcus salivarius subsp. thermophilus and Lactobacillus casei subsp. casei) and cell content at various steps of the fermentation process (after immobilization, pre-incubation of the beads and successive fermentations) were measured on De as a first step for process modelling. Results were obtained from transiend concentration changes n well-stirred lactose solutions in which the beads were suspended. A mathematical model of unsteady-state diffusion in a sphere was used, and De was obtained from the best fit of the experimental data. Diffusivity of lactose in cell-tree beads was significantly lower than in pure water mainly because of the obstruction effect of the polymer chains and the hydration region. Furthermore, effective diffusivity and equilibrium partition factor were independent of lactose concentration in the range from 12.5 to 50 g/L. No significant difference was found for De (effective diffusivity) and Kp (partition) coefficients between beads entrapping S. thermophilus (approximately 5 x 10(9) CFU/mL) and cell-free beads. On the other hand higher cell counts obtained with L. casei (close to 1.8 x 10(11) CFU/mL) increased mass transfer resistance resulting in lower effective diffusivities and Kp. Finally, the effects of the type of bacteria and their distribution in the beads on the diffusivity were also discussed.     

Survival of Bifidobacterium longum Immobilized in Calcium Alginate Beads in Simulated Gastric Juices and Bile Salt Solution

Bifidobacterium longum KCTC 3128 and HLC 3742 were independently immobilized (entrapped) in calcium alginate beads containing 2, 3, and 4% sodium alginate. When the bifidobacteria entrapped in calcium alginate beads were exposed to simulated gastric juices and a bile salt solution, the death rate of the cells in the beads decreased proportionally with an increase in both the alginate gel concentration and bead size. The initial cell numbers in the beads affected the numbers of survivors after exposure to these solutions; however, the death rates of the viable cells were not affected. Accordingly, a mathematical model was formulated which expressed the influences of several parameters (gel concentration, bead size, and initial cell numbers) on the survival of entrapped bifidobacteria after sequential exposure to simulated gastric juices followed by a bile salt solution. The model proposed in this paper may be useful for estimating the survival of bifidobacteria in beads and establishing optimal entrapment conditions.     

Survival of Bifidobacterium longum immobilized in calcium alginate beads in simulated gastric juices and bile salt solution

Bifidobacterium longum KCTC 3128 and HLC 3742 were independently immobilized (entrapped) in calcium alginate beads containing 2, 3, and 4% sodium alginate. When the bifidobacteria entrapped in calcium alginate beads were exposed to simulated gastric juices and a bile salt solution, the death rate of the cells in the beads decreased proportionally with an increase in both the alginate gel concentration and bead size. The initial cell numbers in the beads affected the numbers of survivors after exposure to these solutions; however, the death rates of the viable cells were not affected. Accordingly, a mathematical model was formulated which expressed the influences of several parameters (gel concentration, bead size, and initial cell numbers) on the survival of entrapped bifidobacteria after sequential exposure to simulated gastric juices followed by a bile salt solution. The model proposed in this paper may be useful for estimating the survival of bifidobacteria in beads and establishing optimal entrapment conditions.     

Real and pseudo oxygen gradients in Ca-alginate beads monitored during polarographic Po2-measurements using Pt-needle microelectrodes

Polarographic microcoaxial needle electrodes were used to measure internal profiles of dissolved oxygen tension (Po(2)) within single Ca-alginate beads of different diameter containing entrapped cells of Saccharomyces cerevisiae. For the investigations, single beads coming from variable growing conditions and distinct cultivation stages were fixed in a special holding device. In dependence on microbial growth steep oxygen gradients were observed. The Oxygen penetration depth at steady state lay between 50 and 100 mum. After 8 h of cultivation time, the anaerobic space within the beads (phi 2 mm; cultivation in a packed bed reactor) is beginning at approximately 130 mum, whereas the anaerobic space within the beads (phi 2 mm) coming from the shaker flask culture is located approximately 440 mum below the bead surface. Surprisingly, steep gradients were also observed, when recording profiles from cell-free Ca-alginate beads of different diameter and alginate concentrations. The steep oxygen gradients apparently had to be interpreted as pseudo-Po(2)-gradients. These results were borne by several effects, such as formation of artifacts and diffusion barriers in front of the electrode tip or oxygen "availability" at the tip and consumption of oxygen by the electrode itself. These phenomena could be documented by microscopic observation and photography. Thus, to obtain real Po(2)-profiles it is important to be exactly informed about the physical, chemical, and biological properties of the material to be investigated. Furthermore, it is necessary to apply a special stepwise puncture technique with distinct step-in/step-out movements of the electrode: e.g., unidirectional or contradirectional puncture techniques. (c) 1994 John Wiley & Sons, Inc.     

An investigation of bioreactor performance for the production of recombinant protein in immobilized and suspended Escherichia coli

The performance of packed bed (PBR) and modified bubble tank (MBTR) reactors was compared with respect to recombinant protein (β-galactosidase) production by suspended and immobilized E. coli. The MBTR was superior to the PBR due to easy operation and higher protein production. Gas-liquid mass transfer was not affected by the presence of gel beads, and there were no internal or external oxygen diffusion limitations in either reactor. High substrate concentration, small bead size, low cell densities, and similar values of effective diffusion coefficient of oxygen in water and in alginate may have decreased the internal mass transfer limitations.     

Determination of glucose and ethanol effective diffusion coefficients in Ca-alginate gel.

Glucose and ethanol diffusion coefficients in 2% Ca-alginate gel were measured using the experimental technique based on solute diffusion into or out of gel beads in a well-stirred solution. The aim of the study was to make the measurements under typical conditions found in alcoholic fermentations, such as the concentrations of glucose (100 g l-1) and ethanol (50 g l-1), the simultaneous counter-diffusion of glucose and ethanol, and the presence of cells in the gel beads at a level of 10(9) cells g-1 of beads. Previously, an evaluation of the error associated with the methodology used indicated how the experimental procedure would minimize the error. The individual measurement of glucose and ethanol coefficients in 2% Ca-alginate with no cells gave values of 5.1 and 9.6 x 10(-6) cm2 s-1, respectively, which are lower than those in water. When the effect of counter-diffusion was investigated, both coefficients decreased: glucose by 14% and ethanol by 28%. When cells were incorporated into the beads, only the ethanol coefficient decreased significantly, while the glucose coefficient apparently increased its value to 6.9 10(-6) cm2 s-1.     

Removal and recovery of uranium (VI) from aqueous solutions by immobilized Aspergillus niger powder beads

The immobilized Aspergillus niger powder beads were obtained by entrapping nonviable A. niger powder into Ca-alginate gel. The effects of pH, contact time, initial uranium (VI) concentration and biomass dosage on the biosorption of uranium (VI) onto the beads from aqueous solutions were investigated in a batch system. Biosorption equilibrium data were agreeable with Langmuir isotherm model and the maximum biosorption capacity of the beads for uranium (VI) was estimated to be 649.4?mg/g at 30?°C. The biosorption kinetics followed the pseudo-second-order model and intraparticle diffusion equation. The variations in enthalpy (26.45?kJ/mol), entropy (0.167?kJ/mol?K) and Gibbs free energy were calculated from the experimental data. SEM and EDS analysis indicated that the beads have strong adsorption capability for uranium (VI). The adsorbed uranium (VI) on the beads could be released with HNO₃ or HCl. The results showed that the immobilized A. niger powder beads had great potential for removing and recovering uranium (VI) from aqueous solutions.     

Studies on the suitability of alginate-entrapped Chlamydomonas reinhardtii cells for sustaining nitrate consumption processes

Some aspects of the suitability of alginate beads entrapping Chlamydomonas reinhardtii cells for nitrate consumption from nitrate-containing waters were studied and discussed. Among 14 different metal cations tested as gel bead stabilizing agents, only calcium and barium formed beads showing nitrate-consuming activity. Pure calcium alginate cell entrapment resulted in the most suitable method for active cell immobilization compared to alginate-composite-gel beads based on poly-vinylcaprolactam (PVCL) and poly-vinylpyrrolidone (PVP). To perform a continuous nitrate consumption process, calcium alginate-entrapped cells were first grown in a 2.5 l airlift-loop reactor. A cell loading of about 150 microg Chl. g(-1) gel was achieved. Afterwards, five days nitrate consumption processes were performed and three different dilution rates were applied: (i) D < mu; (ii) D = mu; (iii) D > mu, where mu is the specific growth rate (h(-1)). The maximum consumption rates calculated for each dilution rate were: (i) 3.8, (ii) 6.4 and (iii) 7.2 mg nitrate mg(-1) Chl. h(-1). For low dilution rates (D < mu) some nitrite (< 300 microM) was excreted into the culture medium. However, this concentration of nitrite was not high enough to inhibit nitrate consumption.     

Enhancing the Viability of Lactobacillus plantarum Inoculum by Immobilizing the Cells in Calcium-Alginate Beads Incorporating Cryoprotectants

Many literature reports have cited the importance of the rehydration conditions of lyophilized cultures in determining viability. The rate of rehydration and the volume of fluid used have been identified as two important factors. One possible means of controlling these is by immobilizing the cells before lyophilization within a gel matrix in which the subsequent rehydration rate and fluid volume would be controlled by the properties of the gel. In this study Lactobacillus plantarum was immobilized and lyophilized in Ca-alginate beads in which 1 M glycerol or 0.75 M adonitol with skim milk were incorporated as a cryoprotectant. The properties of these Ca-alginate beads were examined before and after lyophilization and rehydration. The beads incorporating glycerol were smaller and stronger than those with adonitol. After lyophilization, size decreased and strength increased but to a greater extent in the beads with glycerol, indicating that the microenvironment within the two bead types was probably different. The protective effect of the bead microenvironment on immobilized L. plantarum was also examined. Lyophilization and rehydration within the alginate beads with either polyol yielded higher survival rates than that attained with free cell cultures during rehydration in optimal or suboptimal conditions. During rehydration under suboptimal conditions, the immobilized cell survival was greatest when 0.75 M adonitol was the incorporated cryoprotectant.