33 resultados para Reaction diffusion equations


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The industrial production of antibiotics with filamentous fungi is usually carried out in conventional aerated and agitated tank fermentors. Highly viscous non-Newtonian broths are produced and a compromise must be found between convenient shear stress and adequate oxygen transfer. In this work, cephalosporin C production by bioparticles of immobilized cells of Cephalosporium acremonium ATCC 48272 was studied in a repeated batch tower bioreactor as an alternative to the conventional process. Also, gas-liquid oxygen transfer volumetric coefficients, k(L)a, were determined at various air flow-rates and alumina contents in the bioparticle. The bioparticles were composed of calcium alginate (2.0% w/w), alumina (<44 micra), cells, and water. A model describing the cell growth, cephalosporin C production, oxygen, glucose, and sucrose consumption was proposed. To describe the radial variation of oxygen concentration within the pellet, the reaction-diffusion model forecasting a dead core bioparticle was adopted. The k(L)a measurements with gel beads prepared with 0.0, 1.0, 1.5, and 2.0% alumina showed that a higher k(L)a value is attained with 1.5 and 2.0%. An expression relating this coefficient to particle density, liquid density, and air velocity was obtained and further utilized in the simulation of the proposed model. Batch, followed by repeated batch experiments, were accomplished by draining the spent medium, washing with saline solution, and pouring fresh medium into the bioreactor. Results showed that glucose is consumed very quickly, within 24 h, followed by sucrose consumption and cephalosporin C production. Higher productivities were attained during the second batch, as cell concentration was already high, resulting in rapid glucose consumption and an early derepression of cephalosporin C synthesizing enzymes. The model incorporated this improvement predicting higher cephalosporin C productivity. (C) 2004 Wiley Periodicals, Inc.

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Bioprocesses using filamentous fungi immobilized in inert supports present many advantages when compared to conventional free cell processes. However, assessment of the real advantages of the unconventional process demands a rigorous study of the limitations to diffusional mass transfer of the reagents, especially concerning oxygen. In this work, a comparative study was carried out on the cephalosporin C production process in defined medium containing glucose and sucrose as main carbon and energy sources, by free and immobilized cells of Cephalosporium acremonium ATCC 48272 in calcium alginate gel beads containing alumina. The effective diffusivity of oxygen through the gel beads and the effectiveness factors related to the respiration rate of the microorganism were determined experimentally. By applying Monod kinetics, the respiration kinetics parameters were experimentally determined in independent experiments in a complete production medium. The effectiveness factor experimental values presented good agreement with the theoretical values of the approximated zero-order effectiveness factor, considering the dead core model. Furthermore, experimental results obtained with immobilized cells in a 1.7-L tower bioreactor were compared with those obtained in 5-L conventional fermenter with free cells. It could be concluded that it is possible to attain rather high production rates working with relatively large diameter gel beads (ca. 2.5 mm) and sucrose consumption-based productivity was remarkably higher with immobilized cells, i.e., 0.33 gCPC/kg sucrose/h against 0.24 gCPC/kg sucrose/h in the aerated stirred tank bioreactor process. (C) 1999 John Wiley & Sons, Inc.

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We present a model to describe inclusive meson production in e+e- reactions based on a quark cascade approach whose formulation is put in terms of diffusion equations for three quark flavors (u, d, s). These equations are solved by using a formalism previously developed for the problem of the electromagnetic cascade generated in the atmosphere by cosmicray interactions. The obtained solutions are given in terms of a combination of power-law functions whose profiles are adequate to describe the characteristics observed in the inclusive spectrum of mesons.

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Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

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Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

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Usually we observe that Bio-physical systems or Bio-chemical systems are many a time based on nanoscale phenomenon in different host environments, which involve many particles can often not be solved explicitly. Instead a physicist, biologist or a chemist has to rely either on approximate or numerical methods. For a certain type of systems, called integrable in nature, there exist particular mathematical structures and symmetries which facilitate the exact and explicit description. Most integrable systems, we come across are low-dimensional, for instance, a one-dimensional chain of coupled atoms in DNA molecular system with a particular direction or exist as a vector in the environment. This theoretical research paper aims at bringing one of the pioneering ‘Reaction-Diffusion’ aspects of the DNA-plasma material system based on an integrable lattice model approach utilizing quantized functional algebras, to disseminate the new developments, initiate novel computational and design paradigms.

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Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

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The mass transfer during osmotic dehydration of apple slices immersed in 40, 50 and 60% (w/w) aqueous sucrose solutions was investigated to evaluate the influence of solution concentration on diffusivities. In the mathematical model, the diffusion coefficients were functions of the local water and sucrose concentration. The mass transfer equations were, simultaneously, solved for water and sucrose using an implicit numerical method. Material coordinates following the shrinkage of the solid were used. The predicted concentration profiles were integrated and compared to experimental data, showing a reasonable agreement with the measured data. on average, the effective diffusion coefficients for water and sucrose decreased as the osmotic solution concentration increased; that is the behavior of the binary coefficients in water-sucrose solutions. However, the diffusivities expressed as a function of the local concentration in the slices varied between the treatments. Water diffusion coefficients showed a remarkable variation throughout the slice and unusual behavior, which was associated to the cellular structure changes observed in tissue immersed in osmotic solutions. Cell structure changes occurred in different ways: moderate plasmolysis at 40%, accentuated plasmolysis at 50% and generalized damage of the cells at 60%. Intact vacuoles were observed after a long time of exposure (30 h) to 40 and 50% solutions. Effects of the concentration on tissue changes make it difficult to generalize the behavior of diffusion coefficients.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

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We show that diffusion can play an important role in protein-folding kinetics. We explicitly calculate the diffusion coefficient of protein folding in a lattice model. We found that diffusion typically is configuration- or reaction coordinate-dependent. The diffusion coefficient is found to be decreasing with respect to the progression of folding toward the native state, which is caused by the collapse to a compact state constraining the configurational space for exploration. The configuration- or position-dependent diffusion coefficient has a significant contribution to the kinetics in addition to the thermodynamic free-energy barrier. It effectively changes (increases in this case) the kinetic barrier height as well as the position of the corresponding transition state and therefore modifies the folding kinetic rates as well as the kinetic routes. The resulting folding time, by considering both kinetic diffusion and the thermodynamic folding free-energy profile, thus is slower than the estimation from the thermodynamic free-energy barrier with constant diffusion but is consistent with the results from kinetic simulations. The configuration- or coordinate-dependent diffusion is especially important with respect to fast folding, when there is a small or no free-energy barrier and kinetics is controlled by diffusion. Including the configurational dependence will challenge the transition state theory of protein folding. The classical transition state theory will have to be modified to be consistent. The more detailed folding mechanistic studies involving phi value analysis based on the classical transition state theory also will have to be modified quantitatively.

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Direct muon transfer in low-energy collisions of the muonic hydrogen H-mu and helium (He++) is considered in a three-body quantum-mechanical framework of coordinate-space integro-differential Faddeev-Hahn-type equations within two- and six-state close coupling approximations. The final-state Coulomb interaction is treated without any approximation employing appropriate Coulomb waves in the final state. This procedure of treating Coulomb interaction leads to much improved results for low-energy transfer rates. The present results agree reasonably well with previous semiclassical calculations. (C) 2002 Elsevier B.V. B.V. All rights reserved.

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We discuss in this paper equations describing processes involving non-linear and higher-order diffusion. We focus on a particular case (u(t) = 2 lambda (2)(uu(x))(x) + lambda (2)u(xxxx)), which is put into analogy with the KdV equation. A balance of nonlinearity and higher-order diffusion enables the existence of self-similar solutions, describing diffusive shocks. These shocks are continuous solutions with a discontinuous higher-order derivative at the shock front. We argue that they play a role analogous to the soliton solutions in the dispersive case. We also discuss several physical instances where such equations are relevant.

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The eutectoid transformation may be defined as a solid-state diffusion-controlled decomposition process of a high-temperature phase into a two-phase lamellar aggregate behind a migrating boundary on cooling below the eutectoid temperature. In substitutional solid solutions, the eutectoid reaction involves diffusion of the solute atoms either through the matrix or along the boundaries or ledges. The effect of Ag on the non-isothermal kinetics of the reverse eutectoid reaction in the Cu-9 mass%Al, Cu-10 mass%Al, and Cu-11 mass%Al alloys were studied using differential scanning calorimetry (DSC), X-ray diffraction (XRD), and scanning electron microscopy (SEM). The activation energy for this reaction was obtained using the Kissinger and Ozawa methods. The results indicated that Ag additions to Cu-Al alloys interfere on the reverse eutectoid reaction, increasing the activation energy values for the Cu-9 mass%Al and Cu-10 mass%Al alloys and decreasing these values for the Cu-11 mass%Al alloy for additions up to 6 mass%Ag. The changes in the activation energy were attributed to changes in the reaction solute and in Ag solubility due to the increase in Al content.

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The spatial distribution of water and sugars in half-fresh apples dehydrated in sucrose solutions (30% and 50% w/w, 27 degrees C) for 2, 4 and 8 h, was determined. Each half was sliced as from the exposed surface. The density, water and sugar contents were determined for each piece. A mathematical model was fitted to the experimental data of the water and sucrose contents considering the overall flux and tissue shrinkage. A numerical method of finite differences permitted the calculation of the effective diffusion coefficients as a function of concentration, using material coordinates and integrating the two differential equations (for water and sucrose) simultaneously. The coefficients obtained were one or even two orders of magnitude lower than those for pure solutions and presented unusual concentration dependence. The behaviour of the apple tissue was also studied using light microscopy techniques to obtain images of the osmotically treated pieces (20%, 30% and 50% w/w sucrose solutions for 2, 4 and 8 h). (c) 2006 Elsevier Ltd. All rights reserved.

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A flow-injection system is proposed for the spectrophotometric determination of sulphite in white wines. The method involves analyte conversion to SO2, gas diffusion through a Teflon® semi-permeable membrane, collection into an alkaline stream (pH 8), reaction with Malachite green (MG) and monitoring at 620 nm. With a concentric tubular membrane, the system design was simplified. Influence of reagent concentrations, pH of donor and acceptor streams, temperature, timing, surfactant addition and presence of potential interfering species of the wine matrix were investigated. A pronounced (ca. 100%) enhancement in sensitivity was noted by adding cetylpyridinium chloride (CPC). The proposed system is robust and baseline drift is not observed during 4 h operating periods. Only 400 μL of sample and 0.32 mg MG are required per determination. The system handles 30 samples per hour, yielding precise results (r.s.d. < 0.015 for 1.0 - 20.0 mg L-1 SO2) in agreement with those obtained by an alternative procedure.