Ordinary Diffusion Research Articles

Action of an electromagnetic pulse on a plasma with a high level of ion-acoustic turbulence. Field diffusion and subdiffusion

Specific features of the interaction of a relatively weak electromagnetic pulse with a nonisothermal current-carrying plasma in which the electron drift velocity is much higher than the ion-acoustic velocity, but lower than the electron thermal velocity, are studied. If the state of the plasma with ion-acoustic turbulence does not change during the pulse action, the field penetrates into the plasma in the ordinary diffusion regime, but the diffusion coefficient in this case is inversely proportional to the anomalous conductivity. If, during the pulse action, the particle temperatures and the current-driving field change due to turbulent heating, the field penetrates into the plasma in the subdiffusion regime. It is shown how the presence of subdiffusion can be detected by measuring the reflected field.

Continuous time random walk with linear force applied to hydrated proteins

An integro-differential diffusion equation with linear force, based on the continuous time random walk model, is considered. The equation generalizes the ordinary and fractional diffusion equations. Analytical expressions for transition probability density, mean square displacement, and intermediate scattering function are presented. The mean square displacement and intermediate scattering function can fit well the simulation data of the temperature-dependent translational dynamics of nitrogen atoms of elastin for a wide range of temperatures and various scattering vectors. Moreover, the numerical results are also compared with those of a fractional diffusion equation.

Chiral diffusion of rotary nanomotors

Neither a purely deterministic rotary nanomotor nor a purely orientational diffuser exhibits long-term translational motion, but coupling rotation to orientational diffusion yields translational diffusion. We demonstrate that this effective translational diffusion can easily dominate the ordinary thermal translational diffusion for experimentally relevant nanomotors, and that this effective diffusion is chiral. Unpowered chiral particles do not exhibit chiral diffusion, but a nanorotor has both handedness and an instantaneous direction of powered motion, thus-unlike an unpowered particle-its diffusional motion can distinguish left from right.

Self-sustained webs of polyvinylidene fluoride electrospun nanofibers at different electrospinning times: 2. Theoretical analysis, polarization effects and thermal efficiency

A novel theoretical model that considers the gas transport mechanisms through the inter-fiber space of self-sustained electrospun nanofibrous membranes (ENMs) is developed for direct contact membrane distillation (DCMD). The theoretical model involves the structural characteristics of the ENMs, the heat transfer mechanisms and the nature of mass transport through the self-sustained web. The permeate fluxes of different ENMs prepared with different electrospinning times and therefore different thicknesses were predicted for different feed temperatures and sodium chloride salt concentrations up to 60g/L. The used ENMs exhibit different parameters such as liquid entry pressure of water, inter-fiber space, void volume fraction, thickness, etc. In contrast to what reported in other theoretical MD studies considering Bosanquet equation with equal mass transport contributions for Knudsen diffusion and ordinary molecular diffusion, in this study the contribution of each mass transport mechanism was determined. It was found that the Knudsen contribution increases with the increase of the ratio of the mean electrospun fiber diameter to the inter-fiber space. The predicted permeate fluxes were compared with the experimental ones and reasonably good agreements between them were found. The temperature polarization coefficient (θ) and the vapor pressure polarization coefficient (ψ) both increase with the thickness of the ENMs, whereas the concentration polarization coefficient (β) decreases indicating the dominant effect of the temperature polarization effect. β was found to be higher for the ENMs having higher permeate fluxes and for greater feed temperatures, whereas it decreases slightly with the increase of the feed salt concentration. The thermal efficiency (EE) is enhanced with the increase of the feed temperature being in all cases for all studied ENMs greater than 78.8% and the heat transfer by conduction less than 20% of the total heat transferred through the ENMs.

Wanted: Scalable Tracers for Diffusion

Scalable tracers are potentially a useful tool to understand diffusion mechanisms and to predict diffusion coefficents, particularly for hindered diffusion in complex, heterogeneous, or crowded systems. Scalable tracers are defined as a homologous series of tracers varying in size but with the same shape, structure, surface chemistry, flexibility, and diffusion mechanism. Both chemical homology and constant dynamics are required. Specifically, branching must not vary with size, and there must be no transition between ordinary diffusion and reptation. Ideally the tracers would be uniform, monodisperse, metabolically inert cylinders in 2D or spheres in 3D with continuously variable radius and tunable surface properties. Scalable tracers would facilitate more rigorous diffusion measurements in which two types of measurements would be clearly distinguished: using scalable tracers to find the mean diffusion coefficient as a function of size, and using nonscalable tracers to find the variation due to differences in shape, surface properties, and the like. Candidate scalable tracers are discussed for 2D diffusion in membranes and 3D diffusion in cytoplasm and nucleoplasm. Specific recommendations for 3D measurements include the use of synthetic dendrimers or random hyperbranched polymers instead of dextran, and the use of core-shell quantum dots in which the shell thickness is used to vary the overall diameter. A set of scalable tracers varying in flexibility would also be useful. These would be made by varying the density of crosslinking in a polymer, to make say “reinforced Ficoll” or “reinforced hyperbranched polyglycerol.” (Supported by NIH grant GM038133.)

Time characteristics of Lévy flights in a steep potential well

Using the method previously developed for ordinary Brownian diffusion, we derive a new formula to calculate the correlation time of stationary Levy flights in a steep potential well. For the symmetric quartic potential, we obtain the exact expression of the correlation time of steady-state Levy flights with index α = 1. The correlation time of stationary Levy flights decreases with an increasing noise intensity and steepness of potential well.

Study of Diffusion Instability in Some Ternary Gas Mixtures at Various Temperatures

Within the linear theory of stability, the process of isothermal mixing of three-component gas mixtures in a channel of final dimensions in the absence of mass-transfer through its walls is considered. The comparison of experimental data with the results of theoretical calculations for the mixtures He+Ar-N2 and H2+N2-CH4 is shown, that a stable diffusion process as the temperature increased will remain the same and be described by the ordinary diffusion laws, but unstable one lost its intensity and tend to the stable diffusion.

Synthesis of platinum–polyaniline composite, its evaluation as a performance boosting interphase in the electrode assembly of proton exchange membrane fuel cell

Platinum formed on polyaniline (PANi) is used as the interlayer between porous gas diffusion layer and the catalyst layer with the aim to reduce the thickness of the ordinary gas diffusion layer and provide a performance boosting electrostatic layer. The doping tendency of PANi is utilized to incorporate platinum(IV) ion in its matrix by chemisorption followed by its reduction to metallic platinum. Platinum is deposited on polyaniline by a simple wet chemistry method. PANi is prepared by the chemical oxidative polymerization of aniline by ammonium persulphate while Pt deposition on PANi is achieved by a phase transfer method (water–toluene) to yield Pt nanoparticles on PANi. The composite is characterized by XRD, Scanning electron microscopy (SEM) with energy dispersive X-ray analysis (EDX), IR spectroscopy, cyclic voltammetry (CV), AC impedance studies, density and conductivity measurements. The Pt/PANi composite is assessed in the proton exchange membrane fuel cell (PEMFC) using H2/O2 gases at ambient pressure. The performance of the PEMFC with Pt/PANi composite interphase on cathode side of the gas diffusion layer (GDL) shows improvement at high current densities which is attributed to the increased capacitative current of Pt/PANi layer in the presence of O2 thereby improving the kinetics of subsequent reduction of O2.

Turbulent concentration diffusion in multiphase flow

In multifluid multiphase flow models, the velocity of each phase is determined by its own momentum equation, which is coupled to the other phases by pairwise interphase drag forces proportional to velocity differences. When the drag coefficients are large, the phase velocities become nearly equal and the relative motion of the phases becomes diffusional rather than inertial. The multifluid momentum equations then reduce to a single momentum equation for the mixture and a system of linear relations that determine the small residual velocity differences between the phases. We derive such diffusional relations in a very general form that applies to nearly all multiphase flow models of this type. The simplest such models then reduce to “drift flux” models that exhibit pressure diffusion but not ordinary (Fick's law) diffusion driven by concentration gradients. The question then arises of how to consistently account for turbulent concentration diffusion in models of this type. This question is resolved by specializing the general diffusional relations to a rather typical single-pressure multiphase flow model which includes turbulent momentum transport due to Reynolds stresses. This special case serves as a paradigm which illustrates that (a) turbulent concentration diffusion in multiphase flow is a direct consequence of the isotropic (turbulent pressure) part of the Reynolds stresses, provided the latter are expressed in their proper divergence form; and (b) the order of magnitude of the resulting turbulent diffusivities is just what one would anticipate on dimensional grounds. Properly formulated models of this type therefore automatically include turbulent concentration diffusion, and consequently require no further additions or modifications to introduce it.

Numerical solution of multi-component species transport in gases at any total number of components

In Böttcher [K. Böttcher, Numerical solution of a multi-component species transport problem combining diffusion and fluid flow as engineering benchmark, Int. J. Heat Mass Transfer 53 (1–3) (2010) pp. 231–240], one of us described an implementation of ternary multi-component species transport by diffusion and convection and presented benchmark cases and simulation results for these cases computed with software ENTWIFE. In this paper, an implementation of the Stefan–Maxwell equation into the ANSYS CFX software is described in combination with a procedure to numerically calculate the ordinary multi-component diffusion coefficients in gases at any total number of components. Finally, the benchmark for ternary mixtures is extended to a quarternary one. A comparsion to the benchmark results of Böttcher revealed an implementation mistake in Böttcher’s paper leading to wrong results in case of largely different molar masses. The correct benchmark results are presented here and furthermore compared to two different kinds of effective binary diffusion approaches in multi-component gas mixtures.

Three to six ambiguities in immittance spectroscopy data fitting

Several important ambiguities in immittance spectroscopy (IS) model data-fitting results are identified and illustrated by means of complex-nonlinear-least-squares (CNLS) fits of experimental and synthetic frequency response data. A well-known intrinsic ambiguity, following from Maxwell’s electromagnetic equations, arises from the indistinguishability in external measurements of conduction and displacement currents. Usual fit models for either dielectric or conductive-system situations, such as the Davidson–Cole one, only involve a strength parameter, a dielectric constant, a characteristic relaxation time, and a fractional exponent and lead to no additional ambiguities. But the situation is different for more powerful and useful general models, such as ordinary or anomalous diffusion Poisson–Nernst–Planck ones: PNP and PNPA, used here, whose historical background, current status, and applicability are described and discussed herein. They apply to two different kinds of experimental IS situations and involve several additional, potentially free fit parameters, such as the mobilities of positive and negative charge carriers, and generation–recombination parameters that determine the partial or complete dissociation of a neutral entity of concentration N0 into positive and negative charge carriers of equal concentration, c0. Then, several additional ambiguities appear that may require information about the material system involved for their adequate resolution.

Modeling and Optimization of Diffusive Layers in Potentiometric and Amperometric Electrochemical Gas Sensors

A physicochemical model of the behavior of electrochemical gas sensors based in a solid-state ion conducting electrolyte is presented and verified. The model focuses on air-referenced planar sensors with a porous, diffusive layer covering one of the electrodes. By assuming hypotheses of ergodicity, ordinary diffusion, near-equilibrium situation, high catalytic activity and steady-state mass conservation in the system layer/electrode/electrolyte/electrode, the model describes the current-voltage characteristics both in steady-state as in transient conditions. Numerical simulations, including finite element modelling, are used for obtaining the model preditions for I(V), I(t) and V(t) responses in front of binary O2-N2 mixtures and multi-component mixtures. The model is validated with our own-designed sensors with different diffusion layers.

Relation of astrophysical turbulence and magnetic reconnection

Astrophysical fluids are generically turbulent and this must be taken into account for most transport processes. We discuss how the preexisting turbulence modifies magnetic reconnection and how magnetic reconnection affects the MHD turbulent cascade. We show the intrinsic interdependence and interrelation of magnetic turbulence and magnetic reconnection, in particular, that strong magnetic turbulence in 3D requires reconnection and 3D magnetic turbulence entails fast reconnection. We follow the approach in Eyink et al. [Astrophys. J. 743, 51 (2011)] to show that the expressions of fast magnetic reconnection in A. Lazarian and E. T. Vishniac [Astrophys. J. 517, 700 (1999)] can be recovered if Richardson diffusion of turbulent flows is used instead of ordinary Ohmic diffusion. This does not revive, however, the concept of magnetic turbulent diffusion which assumes that magnetic fields can be mixed up in a passive way down to a very small dissipation scales. On the contrary, we are dealing the reconnection of dynamically important magnetic field bundles which strongly resist bending and have well defined mean direction weakly perturbed by turbulence. We argue that in the presence of turbulence the very concept of flux-freezing requires modification. The diffusion that arises from magnetic turbulence can be called reconnection diffusion as it based on reconnection of magnetic field lines. The reconnection diffusion has important implications for the continuous transport processes in magnetized plasmas and for star formation. In addition, fast magnetic reconnection in turbulent media induces the First order Fermi acceleration of energetic particles, can explain solar flares and gamma ray bursts. However, the most dramatic consequence of these developments is the fact that the standard flux freezing concept must be radically modified in the presence of turbulence.

Importance of molecular interaction description on the hydrodynamics of gas mixtures

The aim of this study is to analyze the hydrodynamics of gas mixtures invoking a recently proposed multifluid model. The model consists of a separate equation set for one component species of the system and an equation set for average quantities of the mixture. Thereby, it provides details of the flow fields for each of the constituents separately. The new model also computes transport coefficients from some kinetic relations without the requirement of being input externally. Moreover, it automatically describes diffusion processes excluding the use of any coefficients for ordinary, pressure and thermal diffusion, which are generally required during Navier–Stokes computation of gas mixture flows.In the present paper, the model that was applied with hard-sphere molecules is extended to include more realistic molecular interaction descriptions (i.e. Maxwell repulsive potential and Lennard-Jones 12–6 potential). Moreover, the contribution of external forces is incorporated in the multifluid balance equations. Afterwards, the resulting equations are solved for some gas mixture problems in the context of a converging-diverging nozzle, and the importance of the molecular interaction description on the hydrodynamics of the mixtures is analyzed.

Recurrent host mobility in spatial epidemics: beyond reaction-diffusion

Human mobility is a key factor in spatial disease dynamics and related phenomena. In computational models host mobility is typically modeled by diffusion in space or on metapolulation networks. Alternatively, an effective force of infection across distance has been introduced to capture spatial dispersal implicitly. Both approaches do not account for important aspects of natural human mobility, diffusion does not capture the high degree of predictability in natural human mobility patters, e.g. the high percentage of return movements to individuals’ base location, the effective force of infection approach assumes immediate equilibrium with respect to dispersal. These conditions are typically not met in natural scenarios. We investigate an epidemiological model that explicitly captures natural individual mobility patterns. We systematically investigate generic dynamical features of the model on regular lattices as well as metapopulation networks and show that generally the model exhibits significant dynamical differences in comparison to ordinary diffusion and effective force of infection models. For instance, the natural human mobility model exhibits a saturation of wave front speeds and a novel type of invasion threshold that is a function of the return rate in mobility patterns. In the light of these new findings and with the availability of precise and pervasive data on human mobility our approach provides a framework for a more sophisticated modeling of spatial disease dynamics.

An object-oriented approach of generic diffusion computing for three dimensional ultrasound volumetric images

Medical image information representation using two dimensional image planes have major drawbacks on the grounds that the there are technical constrains in providing the optimized spatial orientation and physical limitations. In comparison, three dimensional imaging shows higher degree of versatility in clinical application. Conventional anisotropic diffusion and speckle removal might have promising performance on 2D ultrasonic images, but it is not effective in 3D ultrasonic images. In this paper, we have developed extension algorithms for 3D diffusion in ultrasonic volume rendering using open source visualization toolkits. Investigations have been conducted on 3D volume rendering based on visualization toolkit (VTK) generic computing and the simulation results were compared with ordinary 2D diffusion in 3D ultrasonic image. Obstructive effect was eliminated with the proposed technique by conserving information between neighboring 2D slices. The experimental results show the significant improvement of 3D diffusion on 3D ultrasound volume rendering. Key words: Three dimensional, ultrasound, volume, diffusion, rendering, visualization toolkit (VTK), open sources.

Oxygen reduction reaction on a mini gas diffusion electrode

A mini gas diffusion electrode (M-GDE) which is accessible to gaseous reactants and electrolyte has been developed for studying fuel cell catalysts and reactions by simply depositing catalyst ink onto a gas diffusion substrate of around a millimeter in diameter. Analogous to traditional gas-diffusion electrodes, the M-GDE comprises a carbon-paper gas diffusion layer and a catalyst-ink derived catalyst layer but with considerably decreased geometric surface area. The M-GDE has been characterized using electrochemical oxygen reduction reaction ( orr) on carbon-supported platinum in sulfuric acid solution as a probe reaction. On the steady-state voltammograms, no diffusion-limiting currents are observed over a wide potential range of 0.7–0.95 V which is relevant to fuel cell operations. The absence of the diffusion limiting currents suggests that the interfacial oxygen mass transport is fast and the measured currents could be directly used for kinetic analysis without the need of mass transport correction. The Tafel plot exhibits two linear regions—a wide region with a slope of around 2RT/ F followed by a narrow region with a slope of around 2 × 2 RT/ F at higher overpotentials. This Tafel behavior is similar to literature results for the orr on ordinary gas diffusion electrodes. The mass activities and specific activities of the carbon-supported platinum for the orr directly measured from the steady-state voltammograms are consistent with literature data measured under similar conditions. All these facts strongly indicate that the M-GDE is a promising technique for the investigations of fuel cell reactions and nanosized catalysts at gas–catalyst–electrolyte interfaces. It retains the advantages of gas diffusion electrodes and provides the convenience of a microelectrode.

Mobility of Nonsticky Nanoparticles in Polymer Liquids

We use scaling theory to derive the time dependence of the mean-square displacement 〈Δr2〉 of a spherical probe particle of size d experiencing thermal motion in polymer solutions and melts. Particles with size smaller than solution correlation length ξ undergo ordinary diffusion (〈Δr2 (t)〉 ~ t) with diffusion coefficient similar to that in pure solvent. The motion of particles of intermediate size (ξ < d < a), where a is the tube diameter for entangled polymer liquids, is sub-diffusive (〈Δr2 (t)〉 ~ t1/2) at short time scales since their motion is affected by sub-sections of polymer chains. At long time scales the motion of these particles is diffusive and their diffusion coefficient is determined by the effective viscosity of a polymer liquid with chains of size comparable to the particle diameter d. The motion of particles larger than the tube diameter a at time scales shorter than the relaxation time τ e of an entanglement strand is similar to the motion of particles of intermediate size. At longer time scales (t > τ e ) large particles (d > a) are trapped by entanglement mesh and to move further they have to wait for the surrounding polymer chains to relax at the reptation time scale τrep. At longer times t > τrep, the motion of such large particles (d > a) is diffusive with diffusion coefficient determined by the bulk viscosity of the entangled polymer liquids. Our predictions are in agreement with the results of experiments and computer simulations.

Nonlinear Diffusion and Transient Osmosis

We investigate both analytically and numerically the concentration dynamics of a solution in two containers connected by a narrow and short channel, in which diffusion obeys a porous medium equation. We also consider the variation of the pressure in the containers due to the flow of matter in the channel. In particular, we identify a phenomenon, which depends on the transport of matter across nano-porous membranes, which we call “transient osmosis". We find that nonlinear diffusion of the porous medium equation type allows numerous different osmotic-like phenomena, which are not present in the case of ordinary Fickian diffusion. Experimental results suggest one possible candidate for transiently osmotic processes.

A new thermal model for bone drilling with applications to orthopaedic surgery

This paper presents a new thermal model for bone drilling with applications to orthopaedic surgery. The new model combines a unique heat-balance equation for the system of the drill bit and the chip stream, an ordinary heat diffusion equation for the bone, and heat generation at the drill tip, arising from the cutting process and friction. Modeling of the drill bit-chip stream system assumes an axial temperature distribution and a lumped heat capacity effect in the transverse cross-section. The new model is solved numerically using a tailor-made finite-difference scheme for the drill bit-chip stream system, coupled with a classic finite-difference method for the bone. The theoretical investigation addresses the significance of heat transfer between the drill bit and the bone, heat convection from the drill bit to the surroundings, and the effect of the initial temperature of the drill bit on the developing thermal field. Using the new model, a parametric study on the effects of machining conditions and drill-bit geometries on the resulting temperature field in the bone and the drill bit is presented. Results of this study indicate that: (1) the maximum temperature in the bone decreases with increased chip flow; (2) the transient temperature distribution is strongly influenced by the initial temperature; (3) the continued cooling (irrigation) of the drill bit reduces the maximum temperature even when the tip is distant from the cooled portion of the drill bit; and (4) the maximum temperature increases with increasing spindle speed, increasing feed rate, decreasing drill-bit diameter, increasing point angle, and decreasing helix angle. The model is expected to be useful in determination of optimum drilling conditions and drill-bit geometries.