Theoretical and experimental approaches towards the determination of solute effective diffusivities in foods

The aim of this review paper is to present experimental methodologies and the mathematical approaches used to determine effective diffusivities of solutes in food materials. The paper commences by describing the diffusion phenomena related to solute mass transfer in foods and effective diffusivities. It then focuses on the mathematical formulation for the calculation of effective diffusivities considering different diffusion models based on Fick's second law of diffusion. Finally, experimental considerations for effective diffusivity determination are elucidated primarily based on the acquirement of a series of solute content versus time curves appropriate to the equation model chosen. Different factors contributing to the determination of the effective diffusivities such as the structure of food material, temperature, diffusion solvent, agitation, sampling, concentration and different techniques used are considered. (c) 2005 Elsevier Inc. All rights reserved.

Influence of mass diffusion in sea ice dynamical models

The mixing of floes of different thickness caused by repeated deformation of the ice cover is modeled as diffusion, and the mass balance equation for sea ice accounting for mass diffusion is developed. The effect of deformational diffusion on the ice thickness balance is shown to reach 1% of the divergence effect, which describes ridging and lead formation. This means that with the same accuracy the mass balance equation can be written in terms of mean velocity rather than mean mass-weighted velocity, which one should correctly use for a multicomponent fluid such as sea ice with components identified by floe thickness. Mixing (diffusion) of sea ice also occurs because of turbulent variations in wind and ocean drags that are unresolved in models. Estimates of the importance of turbulent mass diffusion on the dynamic redistribution of ice thickness are determined using empirical data for the turbulent diffusivity. For long-time-scale prediction (≫5 days), where unresolved atmospheric motion may have a length scale on the order of the Arctic basin and the time scale is larger than the synoptic time scale of atmospheric events, turbulent mass diffusion can exceed 10% of the divergence effect. However, for short-time-scale prediction, for example, 5 days, the unresolved scales are on the order of 100 km, and turbulent diffusion is about 0.1% of the divergence effect. Because inertial effects are small in the dynamics of the sea ice pack, diffusive momentum transfer can be disregarded.

Position-dependent effective mass Dirac equations with PT-symmetric and non-PT-symmetric potentials

We present a new procedure to construct the one-dimensional non-Hermitian imaginary potential with a real energy spectrum in the context of the position-dependent effective mass Dirac equation with the vector-coupling scheme in 1 + 1 dimensions. In the first example, we consider a case for which the mass distribution combines linear and inversely linear forms, the Dirac problem with a PT-symmetric potential is mapped into the exactly solvable Schrodinger-like equation problem with the isotonic oscillator by using the local scaling of the wavefunction. In the second example, we take a mass distribution with smooth step shape, the Dirac problem with a non-PT-symmetric imaginary potential is mapped into the exactly solvable Schrodinger-like equation problem with the Rosen-Morse potential. The real relativistic energy levels and corresponding wavefunctions for the bound states are obtained in terms of the supersymmetric quantum mechanics approach and the function analysis method.

On the solutions of the position-dependent effective mass Schrodinger equation of a nonlinear oscillator related with the isotonic oscillator

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

RELATING THE QCD POMERON TO AN EFFECTIVE GLUON MASS

We construct the Pomeron as an exchange of two nonperturbative gluons, where the nonperturbative gluon propagator is described by an approximate solution of the Schwinger-Dyson equation which contains a dynamically generated gluon mass. We compute the total and elastic differential (dsigma/dt) cross sections for pp scattering, obtaining agreement with the experimental data for a gluon mass m = 370 MeV for LAMBDA(QCD) = 300 MeV. In particular, the Pomeron effectively behaves like a photon-exchange diagram with a coupling determined by the glucon mass.

BROKEN SU(8) AND HADRONIC MASS RELATIONS IN HEAVY-QUARK EFFECTIVE THEORY

Mass relations for hadrons containing a single heavy quark (charm or beauty) are studied from the viewpoint of a quark model with broken SU(8) symmetry, developed by Hendry and Lichtenberg some time ago, in comparison to that of the heavy quark effective theory. The interplay of the two approaches is explored and spectroscopic consequences derived.

Effective tooth-bleaching protocols capable of reducing H2O2 diffusion through enamel and dentine

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

Quantifying The Diffusion And Erosion Of Degradable Hydrogels Using A Microfluidic Technique

Hydrogels are composed of cross-linked networks of hydrophilic polymers that are biocompatible due to their high water content. Mass transfer through hydrogels has been suggested as an effective method of drug delivery, specifically in degradable polymers to minimize lasting effects within the body. Diffusion of small molecules in poly (ethylene glycol) diacrylate (PEG-DA) and dextran methacrylate (dex-MA) hydrogels was characterized in a microfluidic device and by complementary techniques. Microfluidic devices were prepared by crosslinking a formulation of hydrogel and photo-initiator, with and without visible dye, using photolithography to define a central microchannel. Channel sizes within the devices were approximately 600 ¿m to simulate vessels within the body. The microfluidic technique allows for both image and effluent analyses. To visualize the diffusive behavior within the dextran hydrogel, methylene blue and sulforhodamine 101 dyes were used in both elution and uptake experiments. Three analysis techniques for measuring diffusion coefficients were used to quantify the diffusion of solute in the hydrogel, including optical microscopy, characterization of device effluent, and NMR analyses. The optical microscopy technique analyzes images of the dye diffusion captured by a stereomicroscope to generate dye concentration v. position profiles. The data was fit to a diffusion model to determine diffusion coefficients and the dye release profile. In a typical elution experiment, aqueous solution is pumped through the microchannel and dye diffuses out of the hydrogel and into the aqueous phase. During elution, images are taken at regular time intervals and the effluent was collected. Analysis of the device effluent was performed using ultraviolet-visible (UV/Vis) spectroscopy to determine the effluent dye concentration and thus a short-time diffusion coefficient. Nuclear magnetic resonance (NMR) was used to determine a free diffusion coefficient of molecules in hydrogel without the effect of a concentration gradient. Diffusion coefficients for methylene blue and sulforhodamine 101 dyes in dex-MA hydrogel calculated using the three analysis methods all agree well. It was determined that utilizing a combination of the three techniques offers greater insight into molecular diffusion in hydrogels than employing each technique individually. The use of the same microfluidic devices used to measure diffusion is explored in the use of studying the degradation of dex-MA hydrogels. By combining what is known about the degradation rate in regards to the effect of pH and crosslinking and the ability to use a dye solution in contrast to establish the hydrogel boundaries could be a novel approach to studying hydrogel degradation.

The effective Planck mass and the scale of inflation

Observable quantities in cosmology are dimensionless, and therefore independent of the units in which they are measured. This is true of all physical quantities associated with the primordial perturbations that source cosmic microwave background anisotropies such as their amplitude and spectral properties. However, if one were to try and infer an absolute energy scale for inflation—a priori, one of the more immediate corollaries of detecting primordial tensor modes—one necessarily makes reference to a particular choice of units, the natural choice for which is Planck units. In this note, we discuss various aspects of how inferring the energy scale of inflation is complicated by the fact that the effective strength of gravity as seen by inflationary quanta necessarily differs from that seen by gravitational experiments at presently accessible scales. The uncertainty in the former relative to the latter has to do with the unknown spectrum of universally coupled particles between laboratory scales and the putative scale of inflation. These intermediate particles could be in hidden as well as visible sectors or could also be associated with Kaluza–Klein resonances associated with a compactification scale below the scale of inflation. We discuss various implications for cosmological observables.

CATCH across Texas: Building a model for the diffusion of effective school-based health promotion programs

The impact of health promotion programs is related to both program effectiveness and the extent to which the program is implemented among the target population. The purpose of this dissertation was to describe the development and evaluation of a school-based program diffusion intervention designed to increase the rate of dissemination and adoption of the Child and Adolescent Trial for Cardiovascular Health, or CATCH program (recently renamed the Coordinated Approach to Child Health). ^ The first study described the process by which schools across the state of Texas spontaneously began to adopt the CATCH program after it was tested and proven effective in a multi-site randomized efficacy trial. A survey of teachers and administrator representatives of all schools on record that purchased the CATCH program, but were not involved in the efficacy trial, was used to find out who brought CATCH into the schools, how they garnered support for its adoption, why they decided to adopt the program, and what was involved in deciding to adopt. ^ The second study described how the Intervention Mapping framework guided the planning, development and implementation of a program for the diffusion of CATCH. An iterative process was used to integrate theory, literature, the experience of project staff and data from the target population into a meaningful set of program determinants and performance objectives. Proximal program objectives were specified and translated into both media and interpersonal communication strategies for program diffusion. ^ The third study assessed the effectiveness of the diffusion program in a case-comparison design. Three of the twenty Education Service Center regions in Texas were chosen, selected based on similar demographic criteria, and were followed for adoption of the CATCH curriculum. One of these regions received the full media and interpersonal channel intervention; a second received a reduced media-only intervention, and a third received no intervention. Results suggested the use of the interpersonal channels with media follow-up is an effective means to facilitate program dissemination and adoption. The media-alone condition was not effective in facilitating program adoption. ^

Experimental determination of barium isotope fractionation during diffusion and adsorption processes at low temperatures

Variations in barium (Ba) stable isotope abundances measured in low and high temperature environments have recently received increasing attention. The actual processes controlling Ba isotope fractionation, however, remain mostly elusive. In this study, we present the first experimental approach to quantify the contribution of diffusion and adsorption on mass- dependent Ba isotope fractionation during transport of aqueous Ba2+ ions through a porous medium. Experiments have been carried out in which a BaCl2 solution of known isotopic composition diffused through u-shaped glass tubes filled with silica hydrogel at 10 C and 25 C for up to 201 days. The diffused Ba was highly fractionated by up to -2.15‰ in d137/134Ba, despite the low relative difference in atomic mass. The time-dependent isotope fractionation can be successfully reproduced by a diffusive transport model accounting for mass-dependent differences in the effective diffusivities of the Ba isotope species (D137Ba/D134Ba = (m134/m137)^b). Values of b extracted from the transport model were in the range of 0.010–0.011. Independently conducted batch experiments revealed that adsorption of Ba onto the surface of silica hydrogel favoured the heavier Ba isotopes (a = 1.00015 ± 0.00008). The contribution of adsorption on the overall isotope fractionation in the diffusion experiments, however, was found to be small. Our results contribute to the understanding of Ba isotope fractionation pro- cesses, which is crucial for interpreting natural isotope variations and the assessment of Ba isotope ratios as geochemical proxies.

Virtual-bound, filamentary and layered states in a box-shaped quantum dot of square potential form the exact numerical solution of the effective mass Schrodinger equation

The effective mass Schrodinger equation of a QD of parallelepipedic shape with a square potential well is solved by diagonalizing the exact Hamiltonian matrix developed in a basis of separation-of-variables wavefunctions. The expected below bandgap bound states are found not to differ very much from the former approximate calculations. In addition, the presence of bound states within the conduction band is confirmed. Furthermore, filamentary states bounded in two dimensions and extended in one dimension and layered states with only one dimension bounded, all within the conduction band which are similar to those originated in quantum wires and quantum wells coexist with the ordinary continuum spectrum of plane waves. All these subtleties are absent in spherically shaped quantum dots, often used for modeling.

Effective intercellular communication distances are determined by the relative time constants for cyto/chemokine secretion and diffusion

A cell’s ability to effectively communicate with a neighboring cell is essential for tissue function and ultimately for the organism to which it belongs. One important mode of intercellular communication is the release of soluble cyto- and chemokines. Once secreted, these signaling molecules diffuse through the surrounding medium and eventually bind to neighboring cell’s receptors whereby the signal is received. This mode of communication is governed both by physicochemical transport processes and cellular secretion rates, which in turn are determined by genetic and biochemical processes. The characteristics of transport processes have been known for some time, and information on the genetic and biochemical determinants of cellular function is rapidly growing. Simultaneous quantitative analysis of the two is required to systematically evaluate the nature and limitations of intercellular signaling. The present study uses a solitary cell model to estimate effective communication distances over which a single cell can meaningfully propagate a soluble signal. The analysis reveals that: (i) this process is governed by a single, key, dimensionless group that is a ratio of biological parameters and physicochemical determinants; (ii) this ratio has a maximal value; (iii) for realistic values of the parameters contained in this dimensionless group, it is estimated that the domain that a single cell can effectively communicate in is ≈250 μm in size; and (iv) the communication within this domain takes place in 10–30 minutes. These results have fundamental implications for interpretation of organ physiology and for engineering tissue function ex vivo.

Coupled heat and mass transfer in concrete exposed to fire

The first investigation of this study is concerned with the reasonableness of the assumptions related to diffusion of water vapour in concrete and with the development of a diffusivity equation for heated concrete. It has been demonstrated that diffusion of water vapour does occur in concrete at all temperatures and that the type of diffusion is concrete is Knudsen diffusion. Neglecting diffusion leads to underestimating the pressure. It results in a maximum pore pressure of less than 1 MPa. It has also been shown that the assumption that diffusion in concrete is molecular is unreasonable even when the tortuosity is considered. Molecular diffusivity leads to overestimating the pressure. It results in a maximum pore pressure of 2.7 MPa of which the vapour pressure is 1.5 MPa while the air pressure is 1.2 MPa. Also, the first diffusivity equation, appropriately named 'concrete diffusivity', has been developed specifically for concrete that determines the effective diffusivity of any gas in concrete at any temperature. In thick walls and columns exposed to fire, concrete diffusivity leads to a maximum pore pressures of 1.5 and 2.2 MPa (along diagonals), respectively, that are almost entirely due to water vapour pressure. Also, spalling is exacerbated, and thus higher pressures may occur, in thin heated sections, since there is less of a cool reservoir towards which vapour can migrate. Furthermore, the reduction of the cool reservoir is affected not only by the thickness, but also by the time of exposure to fire and by the type of exposure, i.e. whether the concrete member is exposed to fire from one or more sides. The second investigation is concerned with examining the effects of thickness and exposure time and type. It has been demonstrated that the build up of pore pressure is low in thick members, since there is a substantial cool zone towards which water vapour can migrate. Thus, if surface and/or explosive spalling occur on a thick member, then such spalling must be due to high thermal stresses, but corner spalling is likely to be pore pressure spalling. However, depending on the exposure time and type, the pore pressures can be more than twice those occurring in thick members and thought to be the maximum that can occur so far, and thus the enhanced propensity of pore pressure spalling occurring on thin sections heated on opposite sides has been conclusively demonstrated to be due to the lack of a cool zone towards which moisture can migrate. Expressions were developed for the determination of the maximum pore pressures that can occur in different concrete walls and columns exposed to fire and of the corresponding times of exposure.