Diffusion-limited Regime Research Articles

Nutrient diffusion and simple n th-order consumption in regenerative tissue and biocatalytic sensors

This contribution addresses intra-tissue molar density profiles for nutrients, oxygen, growth factors, and other essential ingredients that anchorage-dependent cells require for successful proliferation on biocompatible surfaces. One-dimensional transient and steady state models of the reaction–diffusion equation are solved to correct a few deficiencies in the first illustrative example of diffusion and zeroth-order rates of consumption in tissues with rectangular geometry, as discussed in Ref. [(Griffith and Swartz, 2006) 1]. The functional form of the molar density profile for each species depends on geometry and the magnitude of the species-specific intra-tissue Damköhler number. The tissue's central core is reactant starved at high consumption rates and low rates of intra-tissue diffusion when the Damköhler number exceeds its geometry-sensitive critical value. Ideal tissue engineering designs avoid the diffusion-limited regime such that attached cells are exposed to all of the ingredients required for proliferation everywhere within a regenerative matrix. Analytical and numerical molar density profiles that satisfy the unsteady state modified diffusion equation with pseudo-homogeneous n th-order rates of intra-tissue consumption (i.e., n = 0,1,2) allow one to (i) predict von Kármán–Pohlhausen mass transfer boundary layer thicknesses, measured inward from the external biomaterial surface toward its central core, and, most importantly, (ii) estimate the time required to achieve steady state conditions for regenerative tissue growth and biocatalytic sensing.

The RNA core weakly influences the interactions of the bacteriophage MS2 at key environmental interfaces

The effect of the RNA core on interfacial interactions of the bacteriophage MS2 was investigated. After removal of the RNA core, empty intact capsids were characterized and compared to untreated MS2. Electron density of untreated MS2 and RNA-free MS2 were characterized by transmission electron microscopy (TEM) and synchrotron-based small angle spectroscopy (SAXS). Suspensions of both particles exhibited similar electrophoretic mobility across a range of pH values. Similar effects were observed at pH 5.9 across a range of NaCl or CaCl2 concentrations. We compared key interfacial interactions (particle–particle and particle/air–water interface) between suspensions of each type of particle using time resolved dynamic light scattering (TR-DLS) to observe and quantify aggregation kinetics and axisymmetric drop shape analysis to measure adsorption at the air–water interface. Both suspensions showed insignificant aggregation over 4 h in 600 mM NaCl solutions. In the presence of Ca2+ ions, aggregation of both types of particles was consistent with earlier aggregation studies and was characterized by both reaction-limited and diffusion-limited regimes occurring at similar [Ca2+]. However, the removal of the RNA from MS2 had no apparent effect on the aggregation kinetics of particles. Despite some differences in the kinetics of adsorption to the air–water interface, the changes in surface tension which result from particle adsorption showed no difference between the untreated MS2 and RNA-free MS2. The interactions and structure of particles at the air–water interface were further probed using interfacial dilational rheology. The surface elasticity (Es) and surface viscosity (ηs) at the interface were low for both the untreated virus and the RNA-free capsid. This observation suggests that the factors that impact the adsorption kinetics are not important for an equilibrated interface.

Growth kinetics in position-controlled and catalyst-free InAs nanowire arrays on Si(111) grown by selective area molecular beam epitaxy

We investigated the interwire distance dependence on the growth kinetics of vertical, high-yield InAs nanowire arrays on Si(111) grown by catalyst-free selective area molecular beam epitaxy (MBE). Utilizing lithographically defined SiO2 nanomasks on Si(111) with regular hole patterns, catalyst-free and site-selective growth of vertically (111)-oriented InAs nanowires was achieved with very high yields of ∼90 percent. Interestingly, the yield of vertically ordered nanowires was independent of the interwire distance and the initial growth stages. Significant size variation in the nanowires was found to depend critically on the interwire distance and growth time. Two growth regimes were identified—(i) a competitive growth regime with shorter and thinner nanowires for narrow interwire distances and (ii) a diffusion-limited growth regime for wider distances, providing good estimates for the surface diffusion lengths. Surprisingly, despite these size-dependent effects the nanowire geometries remained unaltered with uniform, almost nontapered morphologies even over large variation in nanowire density (∼mid−106–109 cm−2 range). X-ray diffraction further confirmed the vertical (111) directionality with low crystal tilt by rocking curve widths (ω scans) as low as ∼0.6°. These findings demonstrate the capability to precisely tailor the position and size of well-oriented III-V semiconductor nanowires through noncatalytic MBE selective area growth and provide an important step toward fully integrated, uniform vertical III-V nanowire array-on-Si devices.

DNA capture into a nanopore: Interplay of diffusion and electrohydrodynamics

We present a detailed analysis of the process of voltage driven capture of DNA molecules by nanopores. We show that ionic current generates a nonuniform electric field that acts on both the DNA and on its counterions and that the response of DNA to the electric field is affected by its electroosmotic coupling to the mobile counterions. We calculate the voltage and molecular mass dependence of the radius of capture and of the capture rate in the diffusion limited regime. We argue that electroosmotic flow through the DNA coil is suppressed in the vicinity of the pore and present a tentative estimate of the capture rate in the barrier limited regime.

Conformality of Plasma-Assisted ALD: Physical Processes and Modeling

For plasma-assisted atomic layer deposition (ALD), reaching conformal deposition in high aspect ratio structures is less straightforward than for thermal ALD due to surface recombination loss of plasma radicals. To obtain a detailed insight into the consequences of this additional radical loss, the physical processes in plasma-assisted ALD affecting conformality were identified and investigated through Monte Carlo simulations. The conformality was dictated by the recombination probability , the reaction probability , and the diffusion rate of particles. When recombination losses play a role, the saturation dose depended strongly on the value of . For the deposition profiles, a minimum at the bottom of trench structures was observed (before reaching saturation), which was more pronounced with larger values of . In turn, three deposition regimes could be identified, i.e., a reaction-limited regime, a diffusion-limited regime, and a new regime that is recombination-limited. For low values of , conformal deposition in high aspect ratio structures can still be achieved, as observed for several metal oxides, even for aspect ratios as large as 30. For high surface recombination loss probabilities, as appears to be the case for many metals, achieving a reasonable conformality becomes challenging, especially for aspect ratios .

Quantitative investigation of the influence of carbon surfactant on Ge surface diffusion and island nucleation on Si(100)

We investigated the surface diffusion and island nucleation of Ge on Si(100) in presence of a submonolayer coverage of carbon as surfactant by using scanning Auger microscopy and atomic force microscopy. Ge stripes have been deposited and lithographically etched on a Si substrate and used as sources for the surface diffusion of Ge promoted by annealing at 600, 650, and $700\text{ }\ifmmode^\circ\else\textdegree\fi{}\text{C}$. The diffusion coefficient has been determined by fitting the postannealing coverage profiles measured by Auger microscopy with a one-dimensional continuous model. The carbon coverage has been spatially modulated on a single sample, allowing the measurement of the diffusion coefficient as a function of the C thickness at $600\text{ }\ifmmode^\circ\else\textdegree\fi{}\text{C}$. We show that the reduction in the diffusion coefficient while increasing the surfactant coverage is described by a linear dependence of the diffusion activation energy on the C coverage. This dependence is discussed in terms of the chemical interactions among Si, C, and Ge, of the surface roughness and the local strain field induced by the C surfactant. Spontaneous nucleation of SiGe islands coexists with the continuous surface diffusion of Ge. The transition of the island nucleation as a function of the carbon coverage is observed to be continuous from the Stranski-Krastanov mode to the Volmer-Weber regime. We propose a consistent scenario correlating diffusion and nucleation parameters within a diffusion limited growth regime and show the existence of a threshold for C coverage below which no effect is observed.

Volatilization induced by impacts recorded in Zn isotope composition of ureilites

Ureilites are ultramafic achondrites formed by igneous processes early in the history of the Solar System. Ureilites are heavily depleted in volatile elements, probably by evaporation at the surface of the ureilite parent body; however the moderately volatile element Zn is an exception and its abundance is similar to CI. Volatilization can fractionate isotopes in a mass-dependent manner. Therefore, comparing the isotope composition of volatile elements in ureilites may better constrain the physical conditions during ureilite formation and the mechanism of origin of the variation of Zn content. For this study, we measured the Zn isotopic composition of 11 ureilites with a large range of Zn content. The elemental abundance of Zn is negatively correlated with δ 66Zn, which may reflect that isotopic fractionation occurred by evaporation during the heating event on the ureilite parent body. Simple Rayleigh distillation predicts isotopic fractionations much larger than what is actually observed, therefore, such a model cannot account for the observed Zn isotope fractionation in ureilites. We propose that the observed isotopic fractionation can be produced by evaporation in a diffusion-limited regime. In addition, the isotopic composition of Zn is shown to be correlated with the shock grade of the ureilites. This may indicate that the heating events responsible for the depletion in light isotopes in some ureilites were impacts.

Protein Phosphorescence Quenching: Distinction between Quencher Penetration and External Quenching Mechanisms

The accessibility of quenching solutes, Q, of various molecular sizes to buried Trp residues in proteins, as attested by dynamic quenching of their phosphorescence emission, is instrumental for probing structural fluctuations in these macromolecules. However, interpretation of quenching rates in terms of Q migration through the globular fold requires that alternative reaction pathways, such as long-range interactions with Q in the solvent, be ruled out. In theory, the external quenching rate can be estimated from the distance dependence of the through-space interaction by assuming compliance with the rapid diffusion limit regime. To validate the applicability of theoretical predictions to external quenching of protein phosphorescence, we compared the rate of quenching of the buried Trp residues of RNase T1 and parvalbumin by acrylamide and the bigger double-headed derivative bisacrylamide. The results showed that larger bisacrylamide is twice as efficient a quencher as acrylamide, implying that for these superficially buried residues the reaction is dominated by long-range interactions with acrylamide in the aqueous phase. To test the dependence of the quenching rate constant, k(q), on solvent viscosity, quenching studies were extended to glycerol-water solutions ranging in bulk viscosity from 1 to 120 cP. Apart from an initial about 2-fold increase, k(q) was found to be independent of solvent viscosity, thus demonstrating that external quenching rigorously complies with the rapid diffusion limit regime. Experiments were extended to larger acrylamide derivatives to evaluate the impact of Q size on the external quenching rate.

Modelling of Zry-4 cladding oxidation by air, under severe accident conditions using the MAAP4 code

In a nuclear power plant, a potential risk in some low probability situations in severe accidents is air ingress into the vessel. Air is a highly oxidizing atmosphere that can lead to an enhanced core oxidation and degradation affecting the release of Fission Products (FP), especially increasing that of ruthenium. This FP is of particular importance because of its high radio-toxicity and its ability to form highly volatile oxides. Oxygen affinity is decreasing between Zircaloy cladding, fuel and ruthenium inclusions in the fuel. It is consequently of great need to understand the phenomena governing cladding oxidation by air as a prerequisite for the source term issues. A review of existing data in the field of Zircaloy-4 oxidation in air-containing atmosphere shows that this phenomenon is quantitatively well understood. The cladding oxidation process can be divided into two kinetic regimes separated by a breakaway transition. Before transition, a protective dense zirconia scale grows following a solid state diffusion-limited regime for which experimental data are well fitted by a parabolic time dependence. For a given thickness, which depends mainly on temperature and the extent of pre-oxidation in steam, the dense scale can potentially breakdown. In case of breakaway combined with oxygen starvation, cladding oxidation can then be much faster because of the combined action of oxygen and nitrogen through a complex self sustaining nitriding-oxidation process. A review of the pre-existing correlations used to simulate zirconia scale growth under air atmospheres shows a high degree of variation from parabolic to accelerated time dependence. Variations also exist in the choice of the breakaway parameter based on zirconia phase change or oxide thickness. Several correlations and breakaway parameters found in the literature were implemented in the MAAP4.07 Severe Accident code. They were assessed by simulation of the QUENCH-10 test, which is a semi-integral test designed to study fuel bundle exposure to steam first and then to air. This paper deals with the main results obtained with MAAP4.07 when simulating QUENCH-10.

A Cellular Automata Breccia Simulator (CABS) and its application to rounding in hydrothermal breccias

Dissolution processes are ubiquitous in surficial and hydrothermal environments. Solution breccias are formed when dissolution processes dominate and are widely observed in hydrothermal systems. Distinct fragment shapes develop during dissolution and can be used as diagnostic tools for characterizing the nature of the process. This paper presents a new simulator for hydrothermal breccias based on a 3D cellular automata model—thus called CABS (Cellular Automata Breccia Simulator)—that simulates various processes in virtual rocks, including dissolution, metosomatic exchange and precipitation. The code for this simulator is publicly available. The evolution of fragment shape complexity (boundary fractal dimension) during dissolution is evaluated using CABS. Results show that shape complexity increases for both surface-independent (kinetic regime) and dependant processes (diffusion-limited regime). In the case of a lognormal relationship between the probability of dissolution and the surface available for dissolution within the diffusion-limited regime, complexity remains constant and is accompanied by progressive rounding of the fragments. Increased porosity accelerates the rate of the process. The dissolution regime thus plays a crucial role in determining the relative importance of hydromorphic or clastic transport mechanism.

Spectroscopy and optical characterization of thulium doped TZN glasses

This paper reports on the spectroscopic properties of the 3H4 and 3F4 Tm3+ levels in a TZN glass host with a concentration range from 0.82 to 22 × 1020 cm−3. Precise refractive index measurements are performed on five different wavelengths by the prism coupling method. Judd–Ofelt intensity parameters have been determined in order to obtain transition rate, branching ratio and radiative lifetime. Spectroscopic measurements show the most promising concentration for the1.8 µm short cavity laser emission at 6.84 × 1020 cm−3 Tm3+ with a 24% quantum efficiency and upper limit concentration of 11 × 1020 cm−3 Tm3+. Energy transfer microparameters and critical ion distance are determined for both emission levels within the framework of diffusion-limited regime and dipole–dipole interaction.

Fabrication of Fractal Surfaces by Electron Beam Lithography

We describe a method based on electron beam lithography to fabricate patterns of fractal islands on a surface. The island morphology resembles that of a random deposition of particles in a diffusion-limited aggregation regime in 2-D, which is often encountered in the growth of atoms and molecules upon ultrahigh vacuum sublimation. With our fabrication protocol, the morphological parameters of the fractal islands (correlation length, fractal dimension, coverage, and roughness) can be controlled. The fabricated structures can be used as templates for investigating the interplay of self-affinity on thin film nucleation and growth, the adsorption of functional molecules, and the anchoring of living cells. Also they can be exploited as masters for nanoimprinting lithography and replica molding.

Milk Gelation Studied with Small Angle Neutron Scattering Techniques and Monte Carlo Simulations

The sol-gel transition of fat-free milk by acidification was studied with neutron scattering experiments and Monte Carlo simulations. Spin-echo small angle neutron scattering (SESANS) and ultrasmall angle neutron scattering (USANS) experiments were performed to measure the static structure of milk and yogurt, as well as the aggregation kinetics. Colloidal gelation was simulated from a reaction limited domain (RLCA) to the diffusion limited regime (DLCA) as cluster-cluster aggregation of adhesive, hard spheres on a three-dimensional lattice. Comparisons were drawn between experimental and numerical correlation functions. Milk was modeled as a suspension of casein micelles in water, and its structure was described with a dilute system of solid spheres with a log-normal distribution of sizes. The structure and formation of yogurt were described with a self-affine model, used for systems containing heterogeneities with a wide range of sizes. Simulation speed was increased by 1 order-of-magnitude using a new algorithm to eliminate dead time. Observations by SESANS and USANS of milk particle sizes and yogurt length scales were consistent and agreed well with literature. Kinetic USANS data yielded reliable information about the growth of typical length scale during aggregation. The simulation model predicted the measurement data qualitatively best staying close to the RLCA regime until large structures had formed. Correlation lengths were in good quantitative agreement, but longest simulated length scales were a of factor 2(1)/(2) below experimental findings. We conclude that small, mobile aggregates are formed during the first 3 h, mostly influencing the dimensionality of the system and that large, inert structures are formed from 2 up to 8 h, which determine the typical length scale.

Isotopic fractionation of Cu in tektites

Tektites are terrestrial natural glasses of up to a few centimeters in size that were produced during hypervelocity impacts on the Earth's surface. It is well established that the chemical and isotopic composition of tektites is generally identical to that of the upper terrestrial continental crust. Tektites typically have very low water content, which has generally been explained by volatilization at high temperature; however, the exact mechanism is still debated. Because volatilization can fractionate isotopes, comparing the isotopic composition of volatile elements in tektites with those of their source rocks may help to understand the physical conditions during tektite formation. Interestingly, volatile chalcophile elements (e.g., Cd and Zn) seem to be the only elements for which isotopic fractionation is known so far in tektites. Here, we extend this study to Cu, another volatile chalcophile element. We have measured the Cu isotopic composition for 20 tektite samples from the four known different strewn fields. All of the tektites (except the Muong Nong-types) are enriched in the heavy isotopes of Cu (1.98 < delta(61)Cu < 6.99) in comparison to the terrestrial crust (delta(65)Cu approximate to 0) with no clear distinction between the different groups. The Muong Nong-type tektites and a Libyan Desert Glass sample are not fractionated, (delta(65)Cu approximate to 0) in comparison to the terrestrial crust. To refine the Cu isotopic composition of the terrestrial crust, we also present data for three geological reference materials (delta(65)Cu approximate to 0). An increase of delta(65)Cu with decreasing Cu abundance probably reflects that the isotopic fractionation occurred by evaporation during heating. A simple Rayleigh distillation cannot explain the Cu isotopic data and we suggest that the isotopic fractionation is governed by a diffusion-limited regime. Copper is isotopically more fractionated than the more volatile element Zn (delta(66/64)Zn up to 2.49 parts per thousand). This difference of behavior between Cu and Zn is predicted in a diffusion-limited regime, where the magnitude of the isotopic fractionation is regulated by the competition between the evaporative flux and the diffusive flux at the diffusion boundary layer. Due to the difference of ionic charge in silicates (Zn(2+) vs. Cu(+)), Cu has a diffusion coefficient that is larger than that of Zn by at least two orders of magnitude. Therefore, the larger isotopic fractionation in Cu than in Zn in tektites is due to the significant difference in their respective chemical diffusivity. (C) 2009 Elsevier Ltd. All rights reserved.

Kramers-like turnover in load-dependent activated dynamics

Recent advancement of experimental techniques at the single molecule level has demonstrated how an external load affects a chemical reaction which controls the transport of biological motor proteins. Majority of these studies are concerned with thermodynamically open systems. We have examined a prototype model reaction in terms of inertial Brownian motion of a particle in a force field subjected to an overdamped motion of a viscous load coupled harmonically to the particle. A general analytical expression for the rate constant has been derived to demonstrate that depending on the strength of harmonic coupling and drag coefficient of the load a Kramers-like turnover can be realized in the spatial diffusion-limited regime. The turnover reduces to a crossover between the two states characterized by zero-load and finite load conditions.

Upscaling of the advection–diffusion–reaction equation with Monod reaction

The need for reliable models for the reactive transport of contaminants in the subsurface is well recognized. The predictive power of these models is determined by the accurate description of bioavailability of contaminants to microorganisms in porous media. Among many other factors influencing bioavailability, diffusive mass transfer processes may limit the substrate availability at the pore scale and hence reduce the effective degradation rate considerably. In this study we used a combination of analytical and numerical methods to upscale surface catalyzed Monod-type reaction rates within a single pore, to obtain effective rate expression at a larger scale. Results show that in the upscaled description Monod kinetics lead to a concentration dependent transition between a reaction and diffusion-limited regime. Strictly, the effective rate repression does not follow Monod-type kinetics. However, we can present appropriate effective parameters relations, which provide an acceptable approximation of degradation dynamics using an effective Monod-type reaction rate.

Computational modeling for cell spreading on a substrate mediated by specific interactions, long-range recruiting interactions, and diffusion of binders

A continuum model was proposed to study cell spreading on a flat substrate mediated by specific interaction, long-range recruiting interaction, and the diffusion of binders. Specific interactions between the mobile receptors embedded in the cell membrane and ligands coated on the substrate surface result in cell adhesion to the substrate surface. This receptor-ligand interaction was described by a chemical reaction equation. Long-range recruiting interactions between the receptors and the substrate were simplified by a traction-separation law. The governing equations and boundary conditions were formulated for the entire process of cell spreading and solved using a finite element scheme. Parametric studies were conducted to investigate the effect of system parameters on the cell spreading kinetics. It is shown that kinetic factors play an important role in cell adhesion and three regimes, that is, the binder reaction limited regime, long-range recruiting force-driven binder recruitment limited regime, and the concentration gradient-driven diffusion limited regime, were identified.

Non-ideal absorption effects on hydrogen permeation through palladium–silver alloy membranes

Current theoretical models for the permeation behavior of hydrogen through palladium and palladium alloys predict that low temperature operation of thin membranes will result in permeation which is no longer controlled by the diffusion of hydrogen through the metal lattice. Specifically, the process of desorption from the downstream surface is predicted to become the dominant resistance to mass transfer. However, these models neglect the non-ideal absorption behavior of hydrogen in palladium which typically occurs at temperatures below 300 °C. In this work a model is developed which accounts for the non-ideal behavior of hydrogen in palladium–silver alloys (25% silver by weight) which are typically used for hydrogen purification. This model predicts that the diffusion-limited regime should be characterized by an increase in the activation energy to ∼32 kJ/mol at temperatures below 200 °C. This prediction is supported by data available in the literature for thick (>125 μm) palladium–silver alloy membranes.

Impact of peripheral fragmentation on the steam gasification of an isolated wood charcoal particle in a diffusion-controlled regime

This study focuses on the effect of peripheral fragmentation during gasification of an isolated wood charcoal particle in the regime of diffusional limitations. In fact, all the models available in the literature fail to reproduce the specific changes in biomass charcoals for which conversion increases quasi linearly versus time, whatever the particle size. We assumed this discrepancy is partly due to the fragmentation phenomenon, i.e. the detachment of fragments from the surface of the particle, which is not usually taken into account in models. The classical assumption in percolation models is a critical value of porosity beyond which fragmentation occurs. We compared our model results with experimental data. We demonstrated that in the diffusion-limited regime, the direct extrapolation of such a method to a continuum model is not satisfying. A new criterion of fragmentation based on a critical porosity and a critical porosity gradient is proposed which considerably improves modelling of gasification charcoal particles.

Hydrogen gas-driven permeation through the membrane with asymmetric surface conditions

Permeation through the membrane with different surface conditions on the inlet and outlet sides is analyzed. Two regime parameters characterizing the rates of processes on two sides of the membrane with respect to the rate of bulk diffusion are introduced. These regime parameters determine the concentration profile and the permeation rate. General equations for the concentration and the permeation flux are obtained. Three basic limit regimes are considered as partial limit cases of the general equations. These are diffusion limited regime (DLR), outlet surface limited regime (OLR), and inlet surface limited regime (ILR). The latter has two modes with qualitatively different concentration profiles. Boundaries between the regimes and approximation formulas for the permeation rates in these regimes have been found. Features of permeation in the limit cases and in intermediate regions are analyzed.