A study of tablet dissolution by magnetic resonance electric current density imaging

The electric current density imaging technique (CDI) was used to monitor the dissolution of ion releasing tablets (made of various carboxylic acids and of sodium chloride) by following conductivity changes in an agar-agar gel surrounding the tablet. Conductivity changes in the sample were used to calculate spatial and temporal changes of ionic concentrations in the sample. The experimental data for ion migration were compared to a mathematical model based on a solution of the diffusion equation with moving boundary conditions for the tablet geometry. Diffusion constants for different acids were determined by fitting the model to the experimental data. The experiments with dissolving tablets were used to demonstrate the potential of the CDI technique for measurement of ion concentration in the vicinity of ion releasing samples.     

Multistep ion exchange processes of gradient refractive index rod lens

A mathematical model for research on the refractive index profile (RIP) of multistep ion exchange processes (IEPs) of gradient refractive index rod lenses (GRINs) is established by the different initial condition and boundary condition, based on the Fickian diffusion equation. GRIN rod lenses have been fabricated using the three-step IEPs. Research results indicate that the experimental deviations of refractive index (DRI) are in good agreement with the theoretical data. The DRI of three-step IEPs is superior to the one- and two-step IEPs and smaller than 10(-5).     

Acoustic enhancement of diffusion in a porous material

Lattice Boltzmann simulations are used to model the enhancement of diffusion which results from Eckart (attenuation driven) acoustic streaming in model porous material. Comparisons are made to Fickian diffusion where no flow is present and the diffusion when a fluid jet is used, which represents a more conventional method of enhancement. We show that streaming can produce a higher diffusion rate for the same average flow velocity and propose that this is the result of the continuation within the material of the driving force that produces the acoustic streaming.     

Diffusional inhomogeneity in cell cultures

Cell migrations in the cell cultures are found to follow non-Gaussian statistics. We recorded long-term cell migration patterns with more than six hundred cells located in 28 mm~2. Our experimental data support the claim that an individual cell migration follows Gaussian statistics. Because the cell culture is inhomogeneous, the statistics of the cell culture exhibit a non-Gaussian distribution. We find that the normalized histogram of the diffusion velocity follows an exponential tail.A simple model is proposed based on the diffusional inhomogeneity to explain the exponential distribution of locomotion activity in this work. Using numerical calculation, we prove that our model is in great agreement with the experimental data.     

Spatially resolved solvent interaction with glassy HPMC polymers studied by magnetic resonance microscopy

Magnetic resonance microscopy was used to study the interaction of an alkaline water solvent (pH=12) with hydroxypropylmethyl cellulose (HPMC) matrices with different molecular masses Mw=12,000, 86,000, and 120,000. The polymers in the form of cylinders were hydrated at 37 degrees C and monitored at equal time intervals with a 300MHz Bruker AVANCE. The spatially resolved spin-spin relaxations times T2 and diffusion coefficients D of the solvent molecules within the gel layer of HPMC samples, along with changes in the dimension of the glass core of the polymers were determined as a function of hydration times. The experimental data allows us to characterize the diffusion mechanism as being Fickian and to determine the mean diffusivity values D of the solvent molecules for each voxel within the gel of the studied polymers. The influence of the molecular mass of the HPMC polymers on swelling properties has been shown.     

Electrodynamic coupling of electric dipole emitters to a fluctuating mode density within a nanocavity

We investigate the impact of rotational diffusion on the electrodynamic coupling of fluorescent dye molecules (oscillating electric dipoles) to a tunable planar metallic nanocavity. Fast rotational diffusion of the molecules leads to a rapidly fluctuating mode density of the electromagnetic field along the molecules' dipole axis, which significantly changes their coupling to the field as compared to the opposite limit of fixed dipole orientation. We derive a theoretical treatment of the problem and present experimental results for rhodamine 6G molecules in cavities filled with low and high viscosity liquids. The derived theory and presented experimental method is a powerful tool for determining absolute quantum yield values of fluorescence.     

Diffusion in fluids with large mean free paths: Non-classical behavior between Knudsen and Fickian limits

Diffusion in fluids is analyzed at non-classical conditions, intermediate between the Knudsen and Fickian limits. The fluid is considered in the framework of the Einstein’s diffusion evolution equation involving expansions of the density distribution in powers of displacement and time. The standard truncation of these expansions results in the classical model of diffusion; however, higher-order terms lead to a departure from classical behavior. This has not been studied or discussed adequately in the literature previously.Here, we present an exact solution of the Einstein’s diffusion evolution equation without truncation of the density expansions. This solution illustrates limitations in the classical truncations and demonstrates non-classical effects due to large mean free paths, λ. In particular, this new solution shows that, at large λ, there are significant quantitative deviations from classical diffusion profiles. In addition, this solution demonstrates a dramatic change in the diffusion mechanism from the state where the molecular motions are predominantly ballistic to one of molecular chaos. This has implications for fundamentals of fluids between the Knudsen and Fickian limits, and for a variety of fields where evolution of a system includes random, multi-scale displacement of particles, such as nanotechnology, vacuum techniques, turbulence, and astrophysics.     

Phase transition kinetics of vanadium pentoxide II. Theoretical results

Experimental data on the phase transformation kinetics in vanadium pentoxide due to surface oxygen loss are analyzed theoretically. A model for the process as a one-dimensional problem with oxygen loss from the surface and coupled interface and diffusion controlled growth modes is described. This model appears to match well the experimental data with reasonable numbers for the surface loss rate and diffusion constant. In particular, the model reproduces changes in the number of phase fronts as a function of electron beam flux. In addition, the analysis confirms that the effective diffusion constant is electron beam flux dependent.     

Pattern formation and localized structures in monoatomic layer deposition

We study the nonlinear robust behaviors of a model for the deposition of a monolayer of molecules on a surface which takes into account the interactions of the adsorbed molecules. The transport properties of the model lead to non Fickian diffusion. It is shown that we have generically Turing structures coexisting with uniform concentrations and consequently localized structures through the pinning mechanism. The characteristic lengths are in the nanometer region in agreement with recent experiments.     

Ultrasound assisted hydration of navy beans (Phaseolus vulgaris)

The use of ultrasound to enhance the transport phenomena in food processes has been well recognised in recent times. The objective of this study was to evaluate the effect of sonication on hydration rate and pasting profile of navy beans. The hydration kinetics for control and ultrasound assisted soaking was mathematically described using mechanistic (Fickian diffusion) and empirical (Peleg’s equation, Weibull model and First Order equation) models. Ultrasound enhanced the rate of hydration which was evident from the plot of kinetic data and model parameters. The effective diffusivities for water transport without and with ultrasound application were estimated to be 1.36 × 10⁻¹⁰ m²/s and 2.19 × 10⁻¹⁰ m²/s respectively, considering Fickian diffusion. The Weibull model was concluded to best predict the hydration kinetics of navy beans in an ultrasonic field. Significant increase in peak viscosity of sonicated bean powder was observed compared to control.     

Vacancy-assisted diffusion in silicon: a three-temperature-regime model

In this Letter we report kinetic lattice Monte Carlo simulations of vacancy-assisted diffusion in silicon. We show that the observed temperature dependence for vacancy migration energy is explained by the existence of three diffusion regimes for divacancies. This characteristic has been rationalized with an analytical model. In the intermediate temperature regime the divacancy dissociation plays a key role and an effective migration energy E{v}{m} approximately 2 eV is predicted, computed from either full ab initio values or mixed with experimental ones. The exact position of this temperature regime strongly depends on vacancy concentration. Previous contradictory experimental results are revisited using this viewpoint.     

Turing bifurcation in a reaction-diffusion system with density-dependent dispersal

Motivated by the recent finding [N. Kumar, G.M. Viswanathan, V.M. Kenkre, Physica A 388 (2009) 3687] that the dynamics of particles undergoing density-dependent nonlinear diffusion shows sub-diffusive behaviour, we study the Turing bifurcation in a two-variable system with this kind of dispersal. We perform a linear stability analysis of the uniform steady state to find the conditions for the Turing bifurcation and compare it with the standard Turing condition in a reaction-diffusion system, where dispersal is described by simple Fickian diffusion. While activator-inhibitor kinetics are a necessary condition for the Turing instability as in standard two-variable systems, the instability can occur even if the diffusion constant of the inhibitor is equal to or smaller than that of the activator. We apply these results to two model systems, the Brusselator and the Gierer-Meinhardt model.     

Sorption and Desorption of PVA-Pyrene Chains in and out of Agarose Gel

In situ steady-state fluorescence (SSF) measurement technique was applied to investigation of pyrene labeled Poly(vinyl alcohol) (PVA-Py) molecules diffusion in and out of agarose gels. Gel samples with four different concentration of agarose were prepared. PVA-Py was synthesized by "click" chemistry method and dissolved in water to use in diffusion experiments. The results were analyzed by using Fickian type diffusion model, and it was found that sorption and desorption processes of PVA-Py molecules in and out of agarose gel have two distinct regions for short and long diffusion times. Sorption and desorption coefficients were measured and it was seen that the diffusion rates were much larger at short times and at lower agarose concentrations.     

Lattice-Boltzmann simulations of dynamic interfacial tension due to soluble amphiphilic surfactant

An amphiphilic Lattice-Boltzmann approach is adopted to model dynamic interfacial tension due to non-ionic surfactant. In the current system, the surfactant adsorption kinetics is diffusion dominated and the interface separates two immiscible fluids. A rotational relaxation time and a diffusive/viscous relaxation time are associated with the surfactant. The model results are compared with experimental data for the dynamic interfacial tension of a pendant oil droplet in water, with oil soluble surfactant. We demonstrate how to adapt and calibrate the model to capture the adsorption timescale of the surfactant and the magnitude of interfacial tension reduction due to surfactant. A scheme to overcome numerical instabilities due to the relatively low surfactant concentration, is devised. We are able to qualitatively match the Frumkin equation of state for the interfacial tension.     

Water molecules migration at oil–paper interface under the coupling fields of electric and temperature: a molecular dynamics study

Moisture is an important factor affecting the insulation properties of transformers. Due to the limitations of macroscopic experimental methods, the diffusion of water at oil–paper interface cannot be accurately measured. Therefore, molecular dynamics method was used in this work to establish oil–paper layer model of 10⁵ atoms. Through jointly analysing the aggregation degree, diffusion coefficient, free volume as well as radial distribution function of water molecules, the diffusion mechanism of water molecules at oil–paper interface was studied. The results show that when the initial water content in paper was high, water molecules would accumulate at oil–paper interface to form the local high-water region during heating. The polarisation of the electric field strengthened the hydrogen bonding interaction between water molecules and increased the probability of occurrence of the high-water region. Meanwhile, electric field reduced the free volume and diffusion coefficient of water molecules and rendered its diffusion coefficient anisotropic. What’s more, when the electric field was combined with the temperature field, the electric field played a leading role in the diffusion of water molecules while the temperature field was less affected. Diffusion coefficients of water molecules at different temperatures from molecular dynamics simulations were well consistent with experimental results, which verified the rationality of the model.     

Calculation of the effective diffusion coefficient for random wear surface migration on different scales

The paper considers the contact interaction of crystalline solids under shear deformation in the context of molecular dynamics. The interatomic interaction is specified by a potential calculated using the embedded atom method. The peculiarities of structural changes in a contact zone are studied for various materials of the contact pair. Based on the data extracted, the effective diffusion coefficient was estimated for random migration of the contact zone in a direction perpendicular to applied shear strains. The calculation results agree well with data of a microscopic contact model built around the method of movable cellular automata.     

Sorption and Diffusion of Supercritical Carbon Dioxide in a Biodegradable Polymer

A gravimetric method was used to study the sorption and diffusion of supercritical carbon dioxide in a temperature range from 40°C to 80°C and a pressure range from 8.0 to 18.0 MPa in a biodegradable polymer, namely poly(butylene adipate-co-terephthalate) (PBAT). The PBAT presented Fickian behavior and Fick's diffusion model was applied to determine the amount of carbon dioxide present in the samples after a predetermined exposure time as well as the diffusion coefficients. The variations of diffusion coefficients of CO₂ for the sorption under supercritical conditions and desorption at ambient conditions as well as equilibrium sorption amounts of CO₂ with variations of pressure and temperature were determined and compared.