Characteristic Diffusion Time Research Articles

New Temporal Asymptotics of the Survival Probability in the Capture of Particles in Traps in Media with Anomalous Diffusion

The problem of capture of particles experiencing normal diffusion as well as anomalous subdiffusion to absorbing traps has been investigated. It is shown that two characteristic diffusion times (and, accordingly, three time intervals) emerge in such a problem. It is established that new temporal (power-law and fractional–exponential) asymptotic forms of the particle survival probability appear in these intervals, which are determined by the character of diffusion of particles in strongly anisotropic media.

The prediction of size and charge of particles formed from evaporation of charged droplets generated in an electrospray system

Electrospray systems are an effective methodology for generating uniform submicrometer sized charged droplets, initially containing a dissolved solute or nanoparticle inclusions, producing particles from the droplets. In this work, we develop a model for charged droplet drying to predict the final size and resultant charge of the particles. The model accounts for solvent evaporation, solute/nanoparticle diffusion, the collision and aggregation of nanoparticles, coulombic fission and ion evaporation processes. The competition among these subprocesses determines the final size and charge. The model equations are cast into nondimensional forms for generalization. The governing dimensionless parameters are derived and their influences on the final particle size and charge are investigated numerically. The most important parameters are the non-dimensional characteristic diffusion time, non-dimensional characteristic coagulation time, non-dimensional flow rate and coulombic fission related loss. An analytical solution is obtained in the case of slow drying.

A smoothed particle hydrodynamics study of the collapse for a cylindrical cavity.

In this study, we propose a mesh-free (particle-based) Smoothed Particle Hydrodynamics model for simulating a Rayleigh collapse. Both empty and gas cavities are investigates and the role of heat diffusion is also accounted for. The system behaves very differently according to the ratio between the characteristic time of collapse and the characteristic time of thermal diffusion. This study identifies five different possible behaviours that range from isothermal to adiabatic.

Taylor-diffusion-controlled combustion in ducts

An analysis is presented for the Burke–Schumann flame established when a fuel tank discharges with mean velocity U along a circular duct of radius a filled initially with air. Attention is focused on effects of interactions of shear with transverse diffusion resulting in enhanced longitudinal dispersion. The analysis accounts for preferential-diffusion effects arising for non-unity values of the fuel Lewis number , with the Peclet number based on the thermal diffusivity taken to be of order unity for generality. The solution to the associated Taylor-dispersion problem is described for times much larger than the characteristic diffusion time across the pipe , when the flame is embedded in a mixing region of increasing longitudinal extent moving with the mean velocity. At leading order in the limit , the longitudinal flame location, the burning rate, and the peak temperature are found to be a function of the effective Lewis number , whose value changes from for to for . As a result of this variation, the flame exhibits preferential-diffusion effects that depend fundamentally on , with important implications in designs of microcombustion devices employing narrow channels and pipes.

Effects of Particle Size on the Ignition of Static CH4/Air and H2/Air Mixtures by Hot Particles

ABSTRACT Understanding and characterizing the non-homogenous ignition of flammable mixtures by hot particles are important for industry safety. In this study, one-dimensional transient simulations considering detailed chemistry and transport are conducted for the ignition of static methane/air and hydrogen/air mixtures by hot particles with different radii. The objective is to assess the effects of particle size on the ignition delay time for the hot particle-induced ignition process. Unlike the nearly homogenous ignition in shock tubes or rapid compression machines, the non-homogeneous ignition caused by a hot particle depends on not only chemical kinetics but also transport of reactive species. It is found that 1D hot particle ignition is much slower than the 0D homogenous ignition (in which the mixture temperature is the same as the fixed particle temperature) since there is radical loss near the particle surface caused by mass diffusion. The ignition delay time for hot particle ignition is found to strongly depend on the particle radius and temperature. This is interpreted through the change of radical loss with particle radius and temperature. Moreover, to characterize the hot particle ignition, we introduce a Damköhler number which is the ratio between two characteristic times for chemical reaction and mass diffusion. The change of the normalized ignition delay time for 1D hot particle with the Damköhler number is discussed; and a linear relationship is observed for certain conditions.

Welding dynamics in an atomistic model of an amorphous polymer blend with polymer–polymer interface

AbstractWe consider an atomistic model of thermal welding at the polymer‐polymer interface of a polyetherimide/polycarbonate blend, motivated by applications to 3D manufacturing in space. We follow diffusion of semiflexible chains at the interface and analyze strengthening of the samples as a function of the welding time tw by simulating the strain–stress and shear viscosity curves. The time scales for initial wetting, and for fast and slow diffusion, are revealed. It is shown that each component of the polymer blend has its own characteristic time of slow diffusion at the interface. Analysis of strain–stress demonstrates saturation of the Young's modulus at tw = 240 ns, while the tensile strength continues to increase. The shear viscosity is found to have a very weak dependence on the welding time for tw > 60 ns. It is shown that both strain–stress and shear viscosity curves agree with experimental data.

Extended Rate Constants Distribution (RCD) Model for Sorption in Heterogeneous Systems: 2. Importance of Diffusion Limitations for Sorption Kinetics on Cryogels in Batch.

Here we address the problem of what we can expect from investigations of sorption kinetics on cryogel beads in batch. Does macroporosity of beads indeed help eliminate diffusion limitations under static sorption conditions? Are sorption rate constants calculated using phenomenological kinetic models helpful for predicting sorption properties under dynamic conditions? Applying the rate constants distribution (RCD) model to kinetic curves of Cu(II) ions sorption on polyethyleneimine (PEI) cryogel and gel beads and fines, we have shown that diffusion limitations in highly swollen beads are very important and result in at least ten-fold underestimation of the sorption rate constants. To account for intraparticle diffusion, we have developed the RCD-diffusion model, which yields “intrinsic” kinetic parameters for the sorbents, even if diffusion limitations were important in kinetic experiments. We have shown that introduction of a new variable—characteristic diffusion time—to the RCD model significantly improved the reliability of sorption kinetic parameters and allowed prediction of the minimal residence time in column required for efficient uptake of the adsorbate under dynamic conditions. The minimal residence time determined from kinetic curves simulated using the RCD-diffusion model was in good agreement with experimental data on breakthrough curves of Cu(II) ion sorption on monolith PEI cryogel at different flow rates.

Anode Monitoring By Electrochemical Impedance Spectroscopy in Polymer Electrolyte Membrane Fuel Cells

Although widely used to study the operation of Polymer Exchange Membrane Fuel Cells (PEMFC), Electrochemical Impedance Spectroscopy (EIS) remains a complex tool: experimental data are somewhat delicate to interpret because of the wide range of physical phenomena occurring in Membrane Electrode Assemblies (MEA) and in the flow field plates. Therefore, impedance models are often based on oversimplified equations or conversely, include too many correlated parameters. A typical example of the complexity of the phenomena governing fuel cell electrical behavior are the oscillations of oxygen concentration resulting from the measuring signal, that propagate along the gas channels and makes more difficult the interpretation of the low frequency loop [1, 2, 3]. In addition, most of the impedance models assume Fickian oxygen diffusion although, at least in fuel cells fed with air, Stefan-Maxwell equations should be used as in most stationary models [4, 5]. In this regard, oxygen diffusion and thus the low frequency impedance are strongly dependent on the overall convective flux and as a result, on water management [6].However, due to the characteristic times of oxygen diffusion, these limitations do not apply to the high frequency region of the impedance spectra. The high frequency impedance of a PEMFC remains mostly governed by the cathode [7] but at least in some cases, considering the anode in the Electrical Equivalent Circuit (EEC) is necessary to improve the quality of the fit of the model to the experimental data (Figure). Since the anode has an impact on fuel cell impedance, this means that it becomes possible to monitor its ageing while performing Accelerated Stress Tests (AST). Since most of FC lifetime issues presumably originate from the cathode [8, 9] anode degradation has been rarely studied in the literature. Nevertheless, Schwämmlein et al. showed recently that it may be significant in the case of repeated start-up and shut-down - because of potential cycling - and have a measurable impact on FC performance [10].In this work, we performed AST combining potential and humidity cycles to be as representative as possible of the stressful conditions encountered by the FC in real operating conditions. Commercially available MEA with an initial voltage of the order of 0.7 V at 0.5 A/cm² showed a drop in performance comprised between 400 and 900 µV/h, and a significant degradation of the anode operation was observed by EIS (Figure), confirmed by an increase of its local potentials, and linked to Pt ElectroChemical Surface Area (ECSA) losses. Post-mortem physico-chemical analysis of MEA will be carried out to bridge the decrease of performance with the degradation mechanisms occurring at the anode catalytic layer. Note that these tests were carried out using a 30 cm² segmented cell with 5 straight parallel gas channels [11] (30×1 cm² active area) and that its overall performances may be lower than with regular cells.

In Situ Study of the Drug-Target Protein Interaction in Single Living Cells by Combining Fluorescence Correlation Spectroscopy with Affinity Probes.

The drug-target protein interaction is the basis of drug screening and precise therapy in modern clinical medicine. How to acquire the information about the drug-target protein interaction in single living cell is a great challenge due to the shortage of efficient methods. Here we propose a new strategy for in situ studying the drug-target protein interaction in single living cells based on the competition of candidate drugs to the fluorescent probe-target complexes and fluorescence correlation spectroscopy (FCS) with a microfluidic chip. In this study, we used ABL kinase (target) as a model and synthesized a fluorescent probe (Cy3-dasatinib) with an affinity to the target using ABL inhibitor dasatinib as a precursor. We systematically investigated the association of the probe with targets and the dissociation of the drug-target complexes in the presence of candidate drug. We presented a new parameter IC50 (τD) to assess the inhibitory effect of drugs on the basis of the changes in the characteristic diffusion time (τD) and the binding ratio (y) of fluorescent probes during the drug competition process in living cells. We found a remarkable difference of IC50 (τD) values in living cells and in solutions, suggesting it is quite necessary to evaluate the drug-target interactions in living cells. Compared with current methods, our approach can be used to in situ and real-time study the drug-target interaction in living cells, and it may become a promising and universal tool for in situ drug research at molecular level.

Enabling fast charging of lithium-ion batteries through secondary-/dual- pore network: Part II - numerical model

To increase the market share of electric vehicles, it is desirable to reduce the battery charge times, which are significantly limited by poor electrolyte transport. A high rate charging is achievable by using expensive and low energy density cells with thin electrodes. For higher energy density cells, new electrolytes with improved conductivity and diffusivity and/or electrodes with advanced architecture are required to boost the electrolyte transport, leading to a more uniform utilization of active materials. In our previous work, an analytical model was developed to investigate the effect of secondary pore network (SPN) on electrolyte transport and the configuration of SPN was optimized by enforcing equal characteristic diffusion times in through-plane and in-plane directions. To evaluate the effect of SPN on the fast-charging capability of lithium-ion batteries, a 2D physics-based electrochemical model is developed with SPN in either one or both electrodes. The effect of SPN on cell energy density and lithium plating is investigated for cells with different loadings and electrode porosities. Combining SPN with elevated charging temperatures, the model predicts that the volumetric discharge energy density of a 3 mA h/cm2 cell can reach 270 Wh/L after a 6C constant-current charging.

LES/TPDF investigation of the role of reaction and diffusion timescales in the stabilization of a jet-in-hot-coflow CH4/H2 flame

Moderate or Intense Low oxygen Dilution (MILD) combustion is a promising technology to meet the ever-stringent emission regulation while maintain high thermal efficiency. In this study, large eddy simulation (LES) in conjunction with transported probability density function (TPDF) method has been carried out for the first time to investigate the impact of reaction and diffusion timescales on the stabilization process of the jet-in-hot-coflow (JHC) CH4/H2 flame emulating MILD conditions. First it is demonstrated that the LES/TPDF simulations yield improved predictions of the species and temperature fields due to its capability in capturing finite-rate chemistry and resolving molecular transport at the filter scale. Then the impact of reaction and diffusion timescales on the stabilization process are investigated. It is found that the attenuation of chemical kinetics results in larger stabilization heights and unstable flame bases. More importantly the variation of stabilization height is found to be linearly proportional to that of auto-ignition delay time, illustrating the crucial importance of chemical kinetics during flame stabilization. The results show that the flame is initiated from the lean mixture away from the shear layer, which implies the importance of molecular transport during flame stabilization. Particle-level budget analysis further shows that the resolved molecular diffusion is important for flame base dynamics by contributing more than half of the overall conditional diffusion rate. Finally, a scaling rule for the characteristic flame stabilization time is proposed based on the auto-ignition delay time and characteristic time of diffusion, and it works reasonably well for all the cases considered. These findings shed light on the key physico-chemical mechanisms of the stabilization process for JHC flames under the MILD combustion mode. Moreover, the assessment on subgrid mixing and resolved molecular diffusion reveals that the simulation exhibits low sensitivity to the mixing model and mixing timescale while being highly sensitive to the resolved molecular diffusion, highlighting the key modelling aspects related to LES/TPDF simulation of this flame.

Evaluation of local heating in Doppler-broadening thermometry based on cavity ring-down spectroscopy

We report on an optical and thermal model that allows one to quantify the local heating effect in a cavity ring-down spectroscopy (CRDS) experiment. The effect is due to the intracavity absorption of the laser radiation propagating inside the optical cavity, when this latter is filled with an absorbing gas. The local heating generates a temperature profile into the volume probed by the laser radiation, thus leading to a systematical deviation in temperature measurements by means of Doppler-broadening gas thermometry. Exploiting the representation of the cavity as a linear system for the electric field in the frequency domain, we were able to determine the spatial and temporal behaviors of the heating source and solve the inhomogeneous Fourier heat transfer equation using the method of the Green's functions. The local heating effect is strongly dependent on several parameters characterizing the CRDS experiment, including the geometrical size of the cavity, the two mirrors' reflectivity and loss, the absorption coefficient of the intracavity gaseous medium, the incident power, and the intracavity beam waist. The dynamical behavior of the gas temperature was calculated in three experimental regimes, depending on the laser switch-on time interval as compared to the cavity decay time and heat diffusion characteristic time. In the worst case, the local heating provides a systematical shift in Doppler broadening thermometry of about one part per million.

Estimating the internal and surface oxidation of soot agglomerates

Oxidation of soot takes place inside and on the surface of its constituent primary particles at a rate that depends on temperature, T, and O2 concentration. Even though accurate oxidation kinetics are essential in both industrial uses and environmental impact of soot, they are often derived neglecting internal particle oxidation and the structure of such soot agglomerates. Here, the detailed evolution of the fractal-like agglomerate soot mass, m, and mobility diameter, dm, during both internal and surface oxidation is determined by a moving sectional model. The model predictions are in excellent agreement with oxidation data of mature ethylene soot dm for T = 900–1200 K. The oxidation mode index, a, given by the ratio of the characteristic O2 reaction and diffusion times is used to quantify the contributions of internal and surface oxidation of soot. At low Τ (e.g., < 1100 K), O2 diffuses into the primary particles and reacts with bulk soot, hardly altering the dm and yielding a > 3. As T increases, surface oxidation becomes dominant, decreasing both dm and a. The common assumption that soot agglomerates are spheres underestimates their dm up to 50 % during oxidation. Coupling this detailed moving sectional model with soot mobility size distributions can yield realistic soot oxidation rates. Accounting for soot morphology and internal oxidation shows that the classic NSC rate increasingly underestimates (by 3–7 times) the oxidation rate of soot (from ethylene and toluene flames) with decreasing temperature (900–1800 K) and/or oxygen concentration (0.2–21 vol %).

Fluctuation correlation spectroscopy and its applications in homogeneous analysis

Fluctuation correlation spectroscopy (FCS) is a single-molecule/particle detection technique based on measuring signal fluctuations in a highly focused detection volume. Multiple-parameter information can be obtained from the FCS measurement including the amplitude, characteristic diffusion time of correlation curve, and brightness of the adopted probes. The multiple-parameter change is related with physical or chemical change occurring in the probes. Meanwhile, the detection method has advantages such as short sample time in seconds, sample volume with low limit in femtoliters, and mixing to detection without any separations. These advantages make the FCS technique suitable for homogeneous analysis. In this review, we summarized recent novel applications of FCS and its variants in homogeneous analysis including nucleic acid analysis, protein analysis, enzyme activity assay, direct characterization of nanoparticles in solution, and others. Graphical abstract.

Diffusive–stochastic–viscoelastic model for specific adhesion of viscoelastic solids via molecular bonds

A diffusive–stochastic–viscoelastic model is proposed for the specific adhesion of viscoelastic solids via stochastically formed molecular bonds. In this model, it is assumed that molecular-level behaviors, including the diffusion of mobile adhesion molecules and stochastic reaction between adhesion molecules and binding sites, are Markovian stochastic processes, while the mesoscopic deformation of the viscoelastic media is governed by continuum mechanics. Systematic Monte Carlo simulations of this model are used to investigate how competition between the time scales of molecular diffusion, reaction, and deformation creep of the solids may influence the lifetime and dynamic strength of their adhesion. The results reveal that there exists an optimal characteristic time for molecular diffusion corresponding to the longest lifetime and greatest adhesion strength, which is in good agreement with experimentally observed characteristic time scales of molecular diffusion in cell membranes. In addition, the results show that the viscosity of the media can significantly increase the lifetime and dynamic strength, since deformation creep and stress relaxation can effectively reduce the concentration of interfacial stress and increase the rebinding probability of molecular bonds.

Predicting Homogeneous Bubble Nucleation in Rhyolite

AbstractBubble nucleation is the critical first step during magma degassing. The resultant number density of bubbles provides a record of nucleation kinetics and underlying eruptive conditions. The rate of bubble nucleation is strongly dependent on the surface free energy associated with nucleus formation, making the use of bubble number density for the interpretation of eruptive conditions contingent upon a sound understanding of surface tension. Based on a suite of nucleation experiments with up to &gt;1016 bubbles per unit volume of melt, and using numerical simulations of bubble nucleation and growth during each experiment, we provide a new formulation for surface tension during homogeneous nucleation of H2O bubbles in rhyolitic melt. It is based on the Tolman correction with a Tolman length of δ = 0.32 nm, which implies an increase in surface tension of bubbles with decreasing nucleus size. Our model results indicate that experiments encompass two distinct nucleation regimes, distinguishable by the ratio of the characteristic diffusion time of water, τdiff, to the decompression time, td. Experiments with &gt;1013 m−3 bubbles are characterized by τdiff/td≪ 1, wherein the nucleation rate predominantly depends on the interplay between decompression and diffusion rates. Nucleation occurs over a short time interval with nucleation rate peaks at high values. For experiments with comparatively low bubble number density the average distance between adjacent bubbles and the diffusion timescale is large. Consequently, τdiff/td≫ 1 and nucleation is nearly unaffected by diffusion and independent of decompression rate, with bubbles nucleating at an approximately constant rate until the sample is quenched.

Diffusion in Nanopore Connected Bilayer Networks

A biomimetic model of cell-cell communication was developed to probe the passive molecular transport across ion channels inserted in synthetic lipid bilayers formed between contacting droplets arranged in a linear array. Diffusion of a fluorescent probe across the array was measured for different pore concentrations. The diffusion characteristic time scale is found to vary non-linearly with the pore concentration. Our measurements are successfully modeled by a continuous time random walk description, whose waiting time is the first exit time from a droplet through a cluster of pores. The size of the cluster of pores is found to increase with their concentration. Our results provide a direct link between the mesoscopic permeation properties and the microscopic characteristics of the pores such as their number, size and spatial arrangement.

Upscaling of Mixing‐Limited Bimolecular Chemical Reactions in Poiseuille Flow

AbstractWe consider the fast irreversible bimolecular chemical reaction in the Poiseuille flow through a channel, in which A displaces B. This system allows to systematically study the impact of the interaction of interface deformation and diffusion on mixing and reactive transport. At early times, the reaction is diffusion controlled. With increasing time, advection begins to dominate and we find enhanced reaction efficiency due to the deformation of the interface between the two reactants. For times larger than the characteristic diffusion time across the channel, mixing and reaction are quantified by the Taylor dispersion coefficient. Predictions based on Taylor dispersion may significantly overestimate the reaction efficiency at preasymptotic times, when the system is characterized by incomplete mixing. This type of behaviors of incomplete mixing and reaction have been observed in heterogeneous systems across different scales. Channel flow allows to study them in detail for a well‐controlled system. We propose a dispersive lamella approach based on the concept of effective dispersion which accurately predicts the full evolution of the product mass. Specifically, this approach captures the impact of interface deformation and diffusive coalescence, which marks the transition to the Taylor regime. It gives insight into the mechanism of incomplete mixing and its consequences for reactive transport in more general porous media flows.

Microfluidic ballistic regime for the generation of linear gradients inside a capillary column: Proof-of-concept and application to the miniaturized acid-base volumetric titration

This work details a simple and original approach for the generation of linear gradients inside straight cylindrical microchannels such as a capillary column. The concept takes advantage of an oft-overlooked regime of dispersion of flowing liquids inside narrow channels: the ballistic regime. The ballistic regime is a pure convective regime and is produced by imposing a high velocity flow in a pre-filled capillary thus limited diffusion takes place. This is obtained by forcing the injection of a plug of solution on a short time scale t, much shorter than t<110×D/r2, D is the diffusion coefficient and r the capillary radius. The result is a stretched solution of a given length or depth of penetration, inside the capillary column. This leads to a linear mean concentration field through the mixing zone forming a linear gradient. In miniaturized systems, this transient regime is followed by mainly radial diffusion of the solution inside the capillary due to the short characteristic diffusion time of narrow channels. A convection-diffusion simulation was used to model the gradient formed under this ballistic regime. A specific experimental prototype set-up was designed to investigate this ballistic regime and the formation of a linear gradient of titrant NaOH solution inside a capillary tubing of 500 µm inner diameter and 35-cm total length pre-filled with nitric acid solution. With this prototype, the linear gradient was then pushed in a non-ballistic regime over a confocal fluorescence point detection system in order to measure the fluorescence emission of a fluorescent dye added to the solutions. Considering strong acid-base reaction, fluorescein was used due to its strong fluorescence dependency with pH near its pKa, i.e 6.4. A first set of experiments was realized to demonstrate the validity of such an approach and to determine the optimal condition for the formation of a linear gradient over 300 mm of the 350-mm capillary length. An injection pressure of 1000-mbars over 0.75 s was chosen. The first result was the stability of the system in its ability to produce reproducible linear gradients. As further proofs of feasibility, samples of different nitric acid concentrations were titrated with a 0.25 M NaOH solution. The result was rapid and reproducible titration curves obtained with a fully automated system that consumes less than approximately 70 µL of sample solution.

Coarse-grained models for diffusion in oil-filled hydrogel microbeads

Diffusion of digestive enzymes in oil-filled hydrogel microbeads is a highly complex process which is difficult to model, particularly for systems with high volume fractions of incorporated nano-droplets. In this paper coarse-grained models for this process are compared. The results show that the interplay between adsorption at the oil-water interface and diffusion through the matrix of the bead can lead to a front-like motion of the enzyme. This motion can be described by combining the mass balance for the enzyme with a Maxwell-Cattaneo type equation for the mass flux vector. Solutions of the resulting partial differential equation show that when τ<<td (where τ and td are characteristic times for adsorption and diffusion) the time evolution of the enzyme concentration is identical to the profile calculated using Fick's law. For τ>>td and time t≤τ the enzyme migrates through the hydrogel as a sharp front. The position of the front changes linearly with time, and this corresponds well with findings of a recent experimental study (van Leusden et al. (2018), Food Hydrocolloids, 85, 242–247). The effects of poly-dispersity of the interior oil droplet phase were described using a multi-mode generalization of the Maxwell-Cattaneo model, and the results show that a widening of the droplet size distribution leads to smoothing of the front. The results show that this level of coarse-grained modelling can capture the dynamics of these complex systems quite accurately.