Diffusivity of Cu2+ in calcium alginate gel beads

The diffusivity of Cu(2+) in calcium alginate beads calculated by the shrinking core model (SCM) was reevaluated in this work. The results obtained in this work were significantly different than those by the original authors. There were excellent agreements between the results obtained by the SCM in this work and those by the more rigorous linear absorption model (LAM) by the original authors. (c) 1994 John Wiley & Sons, Inc.     

Determination of effective diffusion coefficients and distribution constants in polysaccharide gels with non-steady-state measurements

A non-steady-state method has been used for determining the effective diffusion coefficient, D(e), and a distribution constant, K(i), of small molecules in alginate gel beads. A mathematical model based on Pick's law and includingexternal film diffusion resistance describe the diffusion process. Criticalexperimental parameters for the estimation of D(e) and K(i), for both one- and two-parameter methods were the initial solute concentration in the bulk liquid, the void fraction inthe reactor, and the experimental starting point. In our analysis, the two-parameter method is preferable. Incorporation of an estimate of the film resistance into the overall model increased the estimated values of D(e) significantly and improved the stability of the term over a range of reactor agitation rates. (c) 1995 John Wiley & Sons Inc.     

Determination of effective diffusion coefficient of substrate in gel particles with immobilized biocatalyst

A method of determining of the effective diffusion coefficient of substrate in a particle, where the diffusion and consumption of substrate by biocatalytic reaction are present simultaneously, was designed and experimentally verified. The method is based on measuring the overall rate of heterogeneous biocatalytic reaction in particles of varying diameter. The effective diffusion coefficient, D_e, was determined by fitting the measured reaction rates with the solution of the reaction-diffusion equation. The method is tailored for cases where the enzyme reaction is governed by the Michaelis-Menten kinetics. The value of K_m required for the solution of the mathematical model was adopted from the measurement of the kinetics of free cells, whereas the rate parameter, k₂, was optimized together with D_e. As an experimental model, the sucrose hydrolysis catalyzed by Ca-alginate-entrapped yeast cells was examined. The particle diameter varied in the range of 1.2–3.9 mm and the initial reaction rates were measured in a batch-stirred reactor at a sucrose concentration of 100 m . The D_e of sucrose at 30°C was found to be 2.9 · 10⁻¹⁰ m²s⁻¹.     

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.     

Diffusion of Cu2+ in calcium alginate gel beads: further analyses

The diffusivity of Cu(2+), as determined by previous authors from analysis of experimental data in terms of the shrinking core (SCM) and linear absorption (LAM) models, is examined in light of the ability of the models to curve fit all the data. It is concluded from this further analysis that previous conclusions depicting the LAM to have an advantage over the SCM for predictive value are not justified. It is also shown that equally good curve fits can be obtained with a recent absorption/desorption model of diffusion which considers directly, through distribution theory, the effect of heterogeneity of material properties on the rate of diffusion. (c) 1995 John Wiley & Sons, Inc.     

Diffusivity of Cu2+ in calcium alginate gel beads: recalculation

Calculations of the diffusivity of Cu(2+) in calcium alginate gel beads using the shrinking core model were checked by us. Corrected results are reported here. Diffusivity was still found to increase with increasing alginate concentration, but at a lower rate than reported in the cited paper. The diffusivity increased by a factor of 2 over the range of alginate concentrations studied rather than 10. The original data is included with sample calculations. (c) 1994 John Wiley & Sons, Inc.     

Protein diffusion in alginate beads monitored by confocal microscopy. The application of wavelets for data reconstruction and analysis

A microscopic technique has been developed to obtain the protein profiles inside calcium alginate gel. To do this, the diffusion of BSA, previously marked with FITC, inside calcium alginate beads was observed using confocal laser microscopy, thus obtaining the spatio-temporal evolution of the protein concentration. The technique, however, presents certain limitations and zones where it is impossible to obtain experimental data. Wavelets analysis, commonly used in signal processing and statistics, was employed to reconstruct and subsequently analyse the experimental results. Once the diffusion model was defined, the substrate profiles obtained were used to calculate a diffusivity value for BSA in alginate gel. Received 09 February 1999/ Accepted in revised form 14 May 1999     

A gel diffusion assay for visualization and quantification of chitinase activity

Higher plants, bacteria, fungi, insects, and crustaceans all produce chitinases. Chitinase genes in many organisms are currently under investigation. Chitinase activity is usually assayed with radiolabeled or fluorogenic substrates. We developed a simple, inexpensive, nonradioactive gel-diffusion assay for chitinase that can be used to screen large numbers of samples. In this assay, chitinase diffuses from a small circular well cut in an agarose or agar gel containing the substrate glycol chitin, a soluble, modified form of chitin. Chitinase catalyzes the cleavage of glycol chitin as it diffuses through the gel, leaving a dark, unstained circular zone around the well, because the fluorescent dye calcofluor binds only to undigested chitin. Sample activities can be determined from linear regression of logstandard enzyme concentration versus the zone diameter of internal standards on each Petri dish used for a diffusion assay.     

Determination of the effective diffusion coefficient of oxygen in gel materials in relation to gel concentration

Summary The effective diffusion coefficient of oxygen, ID_e, was determined in different gel support materials (calcium alginate, -carrageenan, gellan gum, agar and agarose) which are generally used for immobilization of cells. The method used was based upon fitting Crank's model on the experimental data. The model describes the solute diffusion from a well-stirred solution into gel beads which are initially free of solute. The effect of the gel concentration on ID_e of oxygen in the gel was investigated. The results showed a decreasing ID_e for both agar and agarose at increasing gel concentration. In case of calcium alginate and gellan gum, a maximum in ID_e at the intermediate gel concentration was observed. It is hypothesized that this phenomenon is due to a changing gelpore structure at increasing gel concentrations. The ID_e of oxygen in calcium alginate, -carrageenan and gellan gum varied from 1.5^*10^–9 to 2.1^*10^–9 m²s^–1 in the gel concentration range of 0.5 to 5% (w/v).     

Measurement of the diffusion coefficient of ethanol in agarose gel beads: A reproducibility study

Summary The diffusion coefficient of ethanol in a 4 w/w% agarose gel at 25°C was measured, using the methods of unsteady-state diffusion into, and out of, gel beads dispersed in a solution of finite volume. The results (8.0 – 9.5×10^–6 cm²/s) agreed well with available theory. The results of method out were more reproducible than method in, but the standard deviation was in no case lower than 3.3%.     

Transport and consumption rate of O2 in alginate gel beads entrapping hepatocytes

Experiments carried out with hepatocytes entrapped in alginate gel particles with a cell density of about 10⁷ cells ml^–1 showed an oxygen consumption rate of about 2.2×10^–16 mol cell^–1 s^–1. Under these conditions, no inner anoxic core is present in 1.8 mm diameter beads. From these data, the maximum bead size consistent with non-critical O₂ concentration at the bead center has been evaluated for different cell densities and O₂ concentrations in the medium.     

Effect of a small molecule on diffusion and swelling properties of selected polysaccharide gel beads

The effect of a small molecule (e.g., sodium fluorescein, SF) on the swelling properties of and diffusion from calcium polysaccharide (alginate or pectin) gel beads was investigated. The gel beads were prepared by ionotropic gelation, soaked in different concentrations of SF solution, and then dried. The swelling behavior and release of SF from the dried beads were investigated. After soaking in SF, the beads swelled to sizes that depended on the initial concentration of SF. However, the size of the dried beads was independent of the SF concentration. The swelling of the beads occurred quite rapidly and reached a maximum within 2 h. Although most beads swelled to a size which was less than their original size of wet beads, some of them swelled much more than their original wet size. Higher concentration of SF and lower concentration of sodium alginate provided a greater increase in weight. The release profile of SF from dried gel beads in water consists of a burst or a very rapid release phase during the first 60 min followed by a much slower release phase. The similarity of the relative weight increase and release profiles of SF, suggests that swelling might contribute to release of SF, particularly during the burst phase.     

NMR diffusion as a novel tool for measuring the association constant between cyclodextrin and guest molecules

In this paper we introduce the use of diffusion measurements by nuclear magnetic resonance (NMR) spectroscopy for determining association constants of weak and very weak interactions between cyclodextrin and guest molecules, as long as both the free and complexed guest molecules are soluble to an extent that allows good sensitivity in the NMR experiment. The experimental setup and data analysis is discussed for three different guest molecules: L-phenylalanine, L-leucine and L-valine, representing different strengths of interaction. The underlying assumptions are discussed and the scope of the method (range of K(a) values, requirements to the guest molecule) are discussed. The method's main advantage is its general applicability independent of chromogenic or electrochemical properties of the guest molecule. Whereas calorimetric methods that exhibit a similar generality, are applicable mainly to strong interactions, NMR diffusion measurements are applicable to weaker interactions down to the theoretical limit of 1 M(-1), the upper limit for K(a) values to be determined by it is approximately 200. A further advantage of the method is the low amount of sample needed. The method is in principle applicable to any case of molecular recognition between a host and guest molecule leading to weak interactions.     

Evaluation of effective diffusion coefficient and intrinsic kinetic parameters on azo dye biodegradation using PVA-immobilized cell beads

An immobilized mixed culture (Aeromonas hydrophila, Comamonas testosteroni, and Acinetobacter baumannii) was prepared by entrapment into phosphorylated polyvinyl alcohol (PVA) gel beads. The unsteady-state diffusion mechanism in a gel bead was applied to estimate the effective diffusion coefficients (D(e)) and the partition coefficients (K(p)) of azo dye. In addition, a simple method was developed to determine the intrinsic kinetic parameters of immobilized cells from observed reaction rates and the intrinsic kinetic parameters were then verified by fitting the experimental data into the reaction-diffusion model in a batch reactor running at a well-stirred state. The calculated effectiveness factor (eta(cal)) approached unity at Thiele modulus (Phi) < 0.3 (i.e., d(p) < 0.475 mm). The experimental effectiveness factor (eta(exp)) was in the range of 0.71-0.45 for a corresponding sphere diameter (d(p)) of 1.91 +/- 0.16 to 4.43 +/- 0.07 mm at an initial dye concentration of 200 mg/L. The results show that intraparticle diffusion resistance has a significant effect on the azo dye biodegradation rate.     

Determination of the interparticular effective diffusion coefficient for CO(2) and O(2) in solid state fermentation

A simple experimental diffusion controlled fermentor (DCF), coupled with the use of a mathematical model based on mass balance, is proposed to measure the variation of the gas (CO(2) and O(2)) diffusion coefficients in solid state fermentation. The DCF was packed with an ion-exchange resin impregnated with a nutritive medium and inoculated with Aspergillus niger. The growth conditions in the DCF were very similar to those found in equipment operated with convective oxygen supply. The diffusion coefficient was shown to be very dependent on the biomass concentration within the solid state fermentor, and attained values of less than 5% of the molecular diffusion in air when the biomass in the fermentor reached 27 mg dry/g dry support.     

Production of erythropoietin by BHK cells growing on the microcarriers trapped in alginate gel beads

Baby hamster kidney (BHK) cells engineered to produce recombinant human erythropoietin (EPO) were cultured at high density on microcarriers entrapped by calcium alginate gel particles. In this system, the BHK cells proliferated not only on the microcarriers but also in vacant spaces in the alginate gel particles. These spaces contributed greatly to high-density cultivation of the cells and a high productivity of EPO.Abbreviations BHK Baby Hamster Kidney - EPO Erythropoietin     

包埋法固定化真菌漆酶及其应用研究

采用海藻酸钠包埋法固定真菌漆酶,海藻酸钠和CaCl2的最佳浓度分别为3%和4%,最佳给酶量为30U,最大回收率为48.0%.与游离漆酶相比,固定化漆酶的热稳定性有明显改善,最适反应pH向酸性方向漂移0.5,最适反应温度提高了5℃.使用固定化酶处理低浓度造纸废水,运行8批次后残留酶活为64%.     

Reaction and diffusion in a gel membrane reactor containing immobilized cells

To investigate the effect of diffusional limitations and heterogeneous cell distribution in a gel-immobilized cell system, a gel membrane reactor has been constructed. The reactor consists essentially of a gel layer with immobilized cells, flanked by two well-mixed chambers. Through one chamber substrate is pumped, and this chamber is the equivalent of the outside of a spherical gel bead. The second closed measuring chamber contains a small quantity of liquid that can equilibrate with the inside surface of the membrane, eventually after a long transient. Analysis of the liquid in this chamber can give direct information on substrate and product concentrations at the gel surface, and is and indication of the situation in the center of a gel bead. The gel membrane reactor appears to be an excellent tool to study diffusion and reaction in a gel-containing immobilized cells. A mathematical model with time- and position-dependent cell concentration and diffusion coefficient is described. Experimental data show the effective diffusion coefficient of glucose in an alginate gel to decrease with yeast cell concentration. Moreover, kinetic parameters could be determined, using the mathematical model. Microscopic analysis confirmed the proliferation of the gel-entrapped microorganisms in the outer layer of the matrix, as predicted by the model. Potentially, this type of reactor has a clear potential to study the physiology of gel-immobilized cells. (c) 1992 John Wiley & Sons, Inc.     

Two dimensional diffusion of small molecules on protein surfaces: an EPR study of the restricted translational diffusion of protein-bound spin labels

Heisenberg spin exchange rates and dipole-dipole spin lattice relaxation rates for deuterated ¹⁴N- and ¹⁵N-spin labels bound selectively to the histidine His15 and to the lysines Lys13, 96, 97 of the lysozyme molecule have been determined with the aid of electron spin resonance spectroscopy. The results can be interpreted in terms of a two dimensional translational diffusion of the nitroxide tips of the spin labels along the protein surface within restricted surface areas. The spin labels are regarded as models for long amino acid side chains and as probes for the dynamics of protein and water in the vicinity of the protein surface. The translational diffusion coefficient DP_II is reduced by a factor of between six and thirty compared to the value of D found for the spin labels in bulk water, its value for T = 295 K is given by (1.3±0.6)·10^–10m²s^–1 D (2.4±0.3) 10^–11 m²s^–1. Offprint requests to: H.-J. Steinhoff     

A method for the determination of diffusion coefficients for small molecules in aqueous solution

A method is described for determining the diffusion coefficients of small solutes in limited volumes (approximately equal to 4-9 ml) of fluid. Diffusion is measured in a three-chamber diffusion cell across a central unstirred compartment. Compartments are separated by nitrocellulose membranes. The instantaneous concentration gradient and the instantaneous flux of solute into the dilute end compartment are derived from changes in the concentration of solute in the two stirred end compartments through time. The diffusion coefficient is calculated from the slope of the least-squares regression line relating the magnitude of the instantaneous solute flux to that of the instantaneous concentration gradient. The apparatus is calibrated with a solute of known diffusivity (KCl). Diffusion coefficients thus determined in water at 25 degrees C for CaCl2 (7.54 X 10(-6) cm2.s-1), Na2-ATP (7.01 X 10(-6) cm2.s-1), 2-deoxyglucose (5.31 X 10(-6) cm2.s-1), and D-Na-lactate (5.62 X 10(-6) cm2.s-1) differed by an average of 3.7% from literature values. The method described results in accurate estimates of diffusion coefficients by a simple and relatively rapid procedure.