Osmotic dehydration of apples in sugar/salt solutions: Concentration profiles and effective diffusion coefficients

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

Effective diffusion coefficients behavior in osmotic dehydration of apple slices considering shrinking and local concentration dependence

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.

Coordinate and time-dependent diffusion dynamics in protein folding

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Configuration-Dependent Diffusion Dynamics of Downhill and Two-State Protein Folding

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

Particular solution for anomalous diffusion equation with source term

In literature the phenomenon of diffusion has been widely studied, however for nonextensive systems which are governed by a nonlinear stochastic dynamic, there are a few soluble models. The purpose of this study is to present the solution of the nonlinear Fokker-Planck equation for a model of potential with barrier considering a term of absorption. Systems of this nature can be observed in various chemical or biological processes and their solution enriches the studies of existing nonextensive systems.

Configuration-dependent diffusion can shift the kinetic transition state and barrier height of protein folding

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.

Symmetry analysis of an integrable reaction-diffusion equation

In this paper, we investigate the invariance and integrability properties of an integrable two-component reaction-diffusion equation. We perform Painleve analysis for both the reaction-diffusion equation modelled by a coupled nonlinear partial differential equations and its general similarity reduced ordinary differential equation and confirm its integrability. Further, we perform Lie symmetry analysis for this model. Interestingly our investigations reveals a rich variety of particular solutions, which have not been reported in the literature, for this model. (C) 2000 Elsevier B.V. Ltd. All rights reserved.

Mathematical models of generalized diffusion

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.

Anomalous diffusion of pions at RHIC

After pointing out the difference between normal and anomalous diffusion, we consider a hadron resonance cascade (HRC) model simulation for particle emission at RHIC and point out that rescattering in an expanding hadron resonance gas leads to a heavy tail in the source distribution. The results are compared to recent PHENIX measurements of the tail of the particle emitting source in Au+Au collisions at RHIC. In this context, we show how can one distinguish experimentally the anomalous diffusion of hadrons from a second order QCD phase transition.

Blocking Radial Diffusion in a Double-Waved Hamiltonian Model

A non-twist Hamiltonian system perturbed by two waves with particular wave numbers can present Robust Tori, barriers created by the vanishing of the perturbing Hamiltonian at some defined positions. When Robust Tori exist, any trajectory in phase space passing close to them is blocked by emergent invariant curves that prevent the chaotic transport. We analyze the breaking up of the RT as well the transport dependence on the wave numbers and on the wave amplitudes. Moreover, we report the chaotic web formation in the phase space and how this pattern influences the transport.

Diffusion and interface controlled reactions in alpha-(Cu-Al-Ag) alloys

The isothermal kinetics of Ag precipitation was studied in Cu-Al-Ag alloys with concentrations ranging from 2 to 8 wt.%Al and 2 to 12 wt.%Ag, using scanning electron microscopy (SEM), X-ray energy dispersive spectroscopy (EDX) and microhardness measurements. The results indicated a change in the precipitates growing mechanism from diffusion to interface controlled process, probably due to a change in the nature of the interface with the Ag and Al enrichment of the precipitates. (C) 2006 Elsevier B.V. All rights reserved.

NONLINEAR DIFFUSION PROCESS IN A BENARD SYSTEM AT THE CRITICAL-POINT FOR THE ONSET OF CONVECTION

The evolution equation governing surface perturbations of a shallow fluid heated from below at the critical Rayleigh number for the onset of convective motion, and with boundary conditions leading to zero critical wave number, is obtained. A solution for negative or cooling perturbations is explicitly exhibited, which shows that the system presents sharp propagating fronts.

Diffusion coefficients during osmotic dehydration of tomatoes in ternary solutions

The apparent diffusion coefficients for sucrose, NaCl and water during osmotic dehydration of tomatoes in ternary solutions were determined. Long time experiments (up to 60 h) were carried out in order to determine equilibrium concentrations inside tomatoes, whereas short time experiments (up to 4 h) were performed to provide detailed information on kinetics of water loss and solids gain at the beginning of osmotic treatment. The mass transfer rates for water and solutes showed to be dependent of NaCl and sucrose concentrations in osmotic solution and simple regression models as functions of solutes concentration were determined for diffusion coefficients. Salt and sucrose diffusivities showed to be interdependent, with increasing NaCl concentration causing the enhancement of water loss, at the same time that higher sucrose contents hindered the excessive salt penetration. (C) 2003 Elsevier Ltd. All rights reserved.

Diffusion coefficient of K+ in ion exchanged glasses calculated from the refractive index and the Vickers hardness profiles

The top faces of float glass samples were exposed to vapors resulting from the decomposition of KNO3 at 565 degrees C for up to 32 h. X-ray dispersive spectra (EDS) show that K+ ions migrate into the glass. The K+ concentration profile was obtained and its diffusion coefficient was calculated by the Boltzmann-Matano technique. The mean diffusion coefficient was approximately 10 X 10(-11) cm(2) s(-1). It was observed that the refractive index and the Vickers hardness decrease with the depth (after the removal of successive layers), and their profiles were thus obtained. These profiles enabled the calculation of the diffusion coefficient of K+ through the Boltzmann-Matano technique, with mean results ranging between 6 x 10(-11) and 30 x 10(-11) cm(2) s(-1). (c) 2006 Elsevier B.V. All rights reserved.

Concentration profiles and effective diffusion coefficients of sucrose and water in osmo-dehydrated apples

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.