Diffusive Transport Processes Research Articles

Optimal Control in Space and Time and the Management of Environmental Resources

We present methods and tools that can be used to study dynamic environmental resource management in a spatial setting, to explore spatially dependent regulation, and to understand pattern formation. In particular, we present the maximum principle and its use in the context of the emerging frontier of applications of optimal control of diffusive transport processes to environmental and resource economics. We show how optimal spatiotemporal control induces pattern formation and how deep uncertainty with a spatial structure can be handled with spatial robust control methods. Finally, we show how models with diffusive transport can be extended to allow for long-range effects and more general transport mechanisms.

THE EFFECT OF DRIFT ON THE EVOLUTION OF THE ELECTRON/POSITRON SPECTRA IN AN AXISYMMETRIC PULSAR WIND NEBULA

Charged particles propagating through a structured magnetic field are subject to drift motion. The primary aim of the present paper is therefore to investigate the effects of gradient, curvature, and neutral sheet drift on the evolution of the electron and positron spectra in a pulsar wind nebula, where the drift motion is a direct result of the magnetic field having an Archimedean spiral structure. In order to investigate the evolution of the spectra, the steady-state, axisymmetric Fokker-Planck transport equation is solved numerically using a finite-difference scheme. Apart from drift motion, the transport processes of convection and diffusion, along with the energy loss processes of adiabatic cooling and synchrotron radiation, are also included in the model. It is found that drift, particularly neutral sheet drift, can lead to a quantitative difference in the evolution of the electron and positron spectra. This difference may be of importance when interpreting the positron excess observed by PAMELA and AMS-02 near Earth.

Water pollution estimation based on the 2D transport–diffusion model and the Singular Evolutive Interpolated Kalman filter

In this paper, the 2D mathematical water pollution model describing the transport–diffusion processes of some contaminant substances in Thanh Nhan Lake in Hanoï is considered. The finite-volume method is used to solve the model equations. The Singular Evolutive Interpolated Kalman filter is applied to evaluate the pollution level at arbitrary mesh point based only on a small number of measurement points.

Some basic mathematical features of the simultaneous convection anomalous diffusion transport processes

The basic mathematical features of the anomalous diffusion processes are discussed in detail, together with some of the open research subdomains belonging to it. Due to its practical importance in engineering applications, the possibilities of the necessary mathematical refinements are proposed and justified for the general case of the simultaneous convection-anomalous diffusion processes taking place through porous bulk materials.

Effect of parallel segmented flow chromatography on the height equivalent to a theoretical plate II – Performances of 4.6 mm × 30 mm columns packed with 2.6 μm Accucore-C18 superficially porous particles

The reduced trans-column (or long-range eddy dispersion) height equivalent to a theoretical plate (HETP) of short and wide 4.6mm×30mm columns packed with 2.6μm Accucore-C18 superficially porous particles was measured under conventional (no split flow) and parallel segmented (outlet and inlet) flow chromatography. The overall reduced HETP was derived from the true moments of the recorded concentration profiles. The longitudinal diffusion HETP term was measured at a very small flow rate (0.05mL/min). The solid–liquid mass transfer resistance was derived from the shell diffusivity, using the composite Garnett–Torquato model of effective diffusion in a heterogeneous system made of a dense packing of core–shell particles immersed in a continuous matrix (the eluent). The trans-channel and short-range interchannel eddy dispersion HETP terms were assumed to be equal to the calculated h data after solving the Navier–Stokes equation and simulating the advection–diffusion transport process. Experimental results confirmed that the optimum efficiency of these short columns was increased by a factor of about two. The ratio of the detection sensitivities on the PSFC stream and on a regular stream increased from 1 to 1.45 when the retention factor decreases from about 10 to 0.5. These phenomena are due to a strong reduction of the trans-column eddy dispersion HETP term. The system loses about 60% of the sample mass when only outlet skimming is carried out when the flow rate ratio of 55% is applied, as was done in this work. It loses about 50% of the sample when inlet/outlet segmentation is applied. In gradient elution, the peak capacity is increased by only 15%, due to post-column band spreading, which should imperatively be minimized when the outlet flow is split.

Quaternary channels within the Northeast German Basin and their relevance on double diffusive convective transport processes: Constraints from 3‐D thermohaline numerical simulations

Key Points Thermohaline convection evolves within the Northeast German Basin Thermohaline convection is characterized by a helical flow pattern

JOVIAN STRATOSPHERE AS A CHEMICAL TRANSPORT SYSTEM: BENCHMARK ANALYTICAL SOLUTIONS

We systematically investigated the solvable analytical benchmark cases in both one- and two-dimensional (1D and 2D) chemical-advective-diffusive systems. We use the stratosphere of Jupiter as an example but the results can be applied to other planetary atmospheres and exoplanetary atmospheres. In the 1D system, we show that CH_4 and C_2H_6 are mainly in diffusive equilibrium, and the C_2H_2 profile can be approximated by modified Bessel functions. In the 2D system in the meridional plane, analytical solutions for two typical circulation patterns are derived. Simple tracer transport modeling demonstrates that the distribution of a short-lived species (such as C_2H_2) is dominated by the local chemical sources and sinks, while that of a long-lived species (such as C_2H_6) is significantly influenced by the circulation pattern. We find that an equator-to-pole circulation could qualitatively explain the Cassini observations, but a pure diffusive transport process could not. For slowly rotating planets like the close-in extrasolar planets, the interaction between the advection by the zonal wind and chemistry might cause a phase lag between the final tracer distribution and the original source distribution. The numerical simulation results from the 2D Caltech/JPL chemistry-transport model agree well with the analytical solutions for various cases.

Controls on the spacing and geometry of rill networks on hillslopes: Rain splash detachment, initial hillslope roughness, and the competition between fluvial and colluvial transport

Rill networks have been a focus of study for many decades, but we still lack a complete understanding of the variables that control the spacing of rills and the geometry of rill networks (e.g., parallel or dendritic) on hillslopes. In this paper, we investigate the controls on the spacing and geometry of rill networks using numerical modeling and comparison of the model results to terrestrial‐laser‐scanner‐derived topographic data from rill networks formed in physical experiments. The landscape evolution model accounts for the transport of sediment due to rain splash and fluvial entrainment as well as the deposition of sediment being advected by the overland flow. In order to develop realistic rill networks in the model, we find that it is necessary to incorporate the effects of raindrop impact within the fluvial sediment transport process. Model results are only consistent with those of experiments when raindrop‐aided fluvial sediment transport is accounted for. Dendritic networks are often predicted by the model in cases of high initial topographic roughness and high rates of advective (fluvial) sediment transport relative to diffusive (colluvial) transport. Parallel networks form within numerical experiments in low‐roughness cases under a wide range of relative advective and diffusive transport rates as well as in high roughness cases in which diffusive sediment transport is high relative to advective transport. The transition from dendritic to parallel rill networks is shown to occur gradually rather than being associated with a particular threshold. Finally, based on a balance between diffusive and advective sediment transport processes, we predict that the mean spacing between parallel rills scales with the square root of the ratio of diffusivity to channel erodibility.

Dissolved inorganic carbon and alkalinity fluxes from coastal marine sediments: model estimates for different shelf environments and sensitivity to global change

Abstract. We present a one-dimensional reactive transport model to estimate benthic fluxes of dissolved inorganic carbon (DIC) and alkalinity (AT) from coastal marine sediments. The model incorporates the transport processes of sediment accumulation, molecular diffusion, bioturbation and bioirrigation, while the reactions included are the redox pathways of organic carbon oxidation, re-oxidation of reduced nitrogen, iron and sulfur compounds, pore water acid-base equilibria, and dissolution of particulate inorganic carbon (calcite, aragonite, and Mg-calcite). The coastal zone is divided into four environmental units with different particulate inorganic carbon (PIC) and particulate organic carbon (POC) fluxes: reefs, banks and bays, carbonate shelves and non-carbonate shelves. Model results are analyzed separately for each environment and then scaled up to the whole coastal ocean. The model-derived estimate for the present-day global coastal benthic DIC efflux is 126 Tmol yr−1, based on a global coastal reactive POC depositional flux of 117 Tmol yr−1. The POC decomposition leads to a carbonate dissolution from shallow marine sediments of 7 Tmol yr−1 (on the order of 0.1 Pg C yr−1. Assuming complete re-oxidation of aqueous sulfide released from sediments, the effective net flux of alkalinity to the water column is 29 Teq. yr−1, primarily from PIC dissolution (46%) and ammonification (33%). Because our POC depositional flux falls in the high range of global values given in the literature, the reported DIC and alkalinity fluxes should be viewed as upper-bound estimates. Increasing coastal seawater DIC to what might be expected in year 2100 due to the uptake of anthropogenic CO2 increases PIC dissolution by 2.3 Tmol yr−1and alkalinity efflux by 4.8 Teq. yr−1. Our reactive transport modeling approach not only yields global estimates of benthic DIC, alkalinity and nutrient fluxes under variable scenarios of ocean productivity and chemistry, but also provides insights into the underlying processes.

A high-resolution method for the depth-integrated solute transport equation based on an unstructured mesh

This paper presents a high-resolution numerical method for solving mass transport problems involving advection and anisotropic diffusion in shallow water based on unstructured mesh. An alternating operator-splitting technique is adopted to advance the numerical solution with advection and diffusion terms solved separately in two steps. By introducing a new r-factor into the Total Variation Diminishing (TVD) limiter, an improved finite-volume method is developed to solve the advection term with significant reduction of numerical diffusion and oscillation errors. In addition, a coordinate transformation is introduced to simplify the diffusion term with the Green-Gauss theorem used to deal with the anisotropic effect based on unstructured mesh. The new scheme is validated against three benchmark cases with separated and combined advection and diffusion transport processes involved. Results show that the scheme performs better than existing methods in predicting the advective transport, particularly when a sharp concentration front is in presence. The model also provides a sound solution for the anisotropic diffusion phenomenon. Anisotropic diffusion has been largely neglected by existing flow models based on unstructured mesh, which usually treat the diffusion process as being isotropic for simplicity. Based on the flow field provided by the ELCIRC model, the developed transport model was successfully applied to simulate the transport of a hypothetical conservative tracer in a bay under the influence of tides.

Microtopography alters self‐organized vegetation patterns in water‐limited ecosystems

In terrestrial systems limited by water availability the spatial distribution of vegetation can self‐organize into a mosaic of vegetated patches and bare soil. Spatially extensive competition for water and short‐range facilitation underpin many models that describe the process of vegetation pattern formation. Earlier studies investigating this self‐organized patchiness have largely considered smooth landscapes. However, topographic variations can significantly alter the redistribution of surface water flow and therefore the pattern‐forming process. Here, we consider how microtopographic variations, at the scale of individual plants, alters self‐organized vegetation patterns with the use of a simple ecohydrological model. We show that increasing microtopography can induce a change from banded vegetation, oriented across the slope, to irregular drainage patterns, oriented in the downslope direction. The mechanism responsible is shown to be a change in the spatial redistribution of infiltration around plants and plant patches. Only small increases in microtopography are required to cause banded systems with weak facilitation to change to downslope‐oriented patterns. When non‐periodic boundary conditions were considered, band orientation tended to become oblique to the topographic contour and in some circumstances their migration upslope ceased. These results suggest that diffusive sediment transport processes may be essential for the maintenance of regular periodic vegetation patterns, which implies that erosion may be critical for understanding the susceptibility of these ecosystems to catastrophic shifts.

Scaling exponents for a monkey on a tree: Fractal dimensions of randomly branched polymers

We study asymptotic properties of diffusion and other transport processes (including self-avoiding walks and electrical conduction) on large, randomly branched polymers using renormalized dynamical field theory. We focus on the swollen phase and the collapse transition, where loops in the polymers are irrelevant. Here the asymptotic statistics of the polymers is that of lattice trees, and diffusion on them is reminiscent of the climbing of a monkey on a tree. We calculate a set of universal scaling exponents including the diffusion exponent and the fractal dimension of the minimal path to two-loop order and, where available, compare them to numerical results.

Conditional model for sorption in porous media with fractal properties

In this study, the conditional moment closure approach, which is proven to be very useful for modelling of reactions in turbulent flows, is extended to characterise adsorbing, desorbing or reacting flows in porous media. A complete specification of the porous distance conditioned moment closure model, which is formulated in terms of single-conditioned expectations, is presented. The closure of the model equations is obtained assuming the diffusion approximation for fluxes of the reactive species. The model simulates complex multi-cascade processes of convective and diffusive transport of species between pores in a continuous and consistent manner and is a generalisation of dual (or triple) porosity concept. The model addresses the major difficulty of describing transport, entrapment and sorption processes in porous media with fractal properties, where distant transport occurs in the largest pores or fractures, while the adsorbing or desorbing surface is mainly allocated in small pores. The model is able to simulate various regimes of methane replacement by CO2 in a coal sample, which makes it useful for optimising the design and parameters of enhanced coal bed methane recovery operations. It is demonstrated that the power-low decrease in downstream methane concentration, which has been observed experimentally, can be accurately reproduced by the model.

Comprehensive analysis of compositional interface fluctuations in planar lipid bilayer membranes

In this paper we present a comprehensive analysis of line tension-driven compositional interface fluctuations in planar lipid bilayer membranes. Our starting point is the advective Cahn-Hilliard equation for the local lipid composition in symmetric membranes, which explicitly incorporates both advective and diffusive lipid transport processes, and which is coupled to the continuum hydrodynamic equations governing the flow behavior of the membrane and surrounding solvent with finite subphase thickness. In order to extract the interface dynamics from the continuum phase-field formalism, we first derive the appropriate sharp-interface limit equations. We then carry out a linear perturbation analysis for the relaxational dynamics of small-amplitude sinusoidal interface fluctuations to yield the general dispersion relation ω(k) as a function of perturbation wave number k. The resulting expression incorporates the effects of diffusive and advective lipid transport processes within the membrane, viscous or viscoelastic membrane properties, coupling between membrane and solvent, and inertial effects within the membrane and solvent. It is shown that previously considered scenarios naturally emerge as limiting cases of the general result. Furthermore, we discuss two additional scenarios amenable to analysis, one in which the inertia of the solvent is relevant, and another one in which the membrane displays significant viscoelastic properties. Finally, we numerically evaluate the general dispersion relation for three representative model membrane systems.

Assessment of Material By-Product Fate from Bioresorbable Vascular Scaffolds

Fully bioresorbable vascular scaffolds (BVS) are attractive platforms for the treatment of ischemic artery disease owing to their intrinsic ability to uncage the treated vessel after the initial scaffolding phase, thereby allowing for the physiological conditioning that is essential to cellular function and vessel healing. Although scaffold erosion confers distinct advantages over permanent endovascular devices, high transient by-product concentrations within the arterial wall could induce inflammatory and immune responses. To better understand these risks, we developed in this study an integrated computational model that characterizes the bulk degradation and by-product fate for a representative BVS composed of poly(L-lactide) (PLLA). Parametric studies were conducted to evaluate the relative impact of PLLA degradation rate, arterial remodeling, and metabolic activity on the local lactic acid (LA) concentration within arterial tissue. The model predicts that both tissue remodeling and PLLA degradation kinetics jointly modulate LA fate and suggests that a synchrony of these processes could minimize transient concentrations within local tissue. Furthermore, simulations indicate that LA metabolism is a relatively poor tissue clearance mechanism compared to convective and diffusive transport processes. Mechanistic understanding of factors governing by-product fate may provide further insights on clinical outcome and facilitate development of future generation scaffolds.

A volume averaging approach for asymmetric diffusion in porous media

Asymmetric diffusion has been observed in different contexts, from transport in stratified and fractured porous media to diffusion of ions and macromolecular solutes through channels in biological membranes. Experimental and numerical observations have shown that diffusion is facilitated in the direction of positive void fraction (i.e., porosity) gradients. This work uses the method of volume averaging in order to obtain effective medium equations for systems with void fraction gradients for passive and diffusive mass transport processes. The effective diffusivity is computed from the solution of an associated closure problem in representative unit cells that allow considering porosity gradients. In this way, the results in this work corroborate previous findings showing that the effective diffusivity exhibits important directional asymmetries for geometries with void fraction gradients. Numerical examples for simple geometries (a section with an obstacle and a channel with varying cross section) show that the diffusion asymmetry depends strongly on the system configuration. The magnitude of this dependence can be quantified from the results in this work.

Estimation of the global amount of submarine gas hydrates formed via microbial methane formation based on numerical reaction-transport modeling and a novel parameterization of Holocene sedimentation

This study provides new estimates for the global offshore methane hydrate inventory formed due to microbial CH 4 production under Quaternary and Holocene boundary conditions. A multi-1D model for particular organic carbon (POC) degradation, gas hydrate formation and dissolution is presented. The novel reaction-transport model contains an open three-phase system of two solid compounds (organic carbon, gas hydrates), three dissolved species (methane, sulfates, inorganic carbon) and one gaseous phase (free methane). The model computes time-resolved concentration profiles for all compounds by accounting for chemical reactions as well as diffusive and advective transport processes. The reaction module builds upon a new kinetic model of POC degradation which considers a down-core decrease in reactivity of organic matter. Various chemical reactions such as organic carbon decay, anaerobic oxidation of methane, methanogenesis, and sulfate reduction are resolved using appropriate kinetic rate laws and constants. Gas hydrates and free gas form if the concentration of dissolved methane exceeds the pressure, temperature, and salinity-dependent solubility limits of hydrates and/or free gas, with a rate given by kinetic parameters. Global input grids have been compiled from a variety of oceanographic, geological and geophysical data sets including a new parameterization of sedimentation rates in terms of water depth. We find prominent gas hydrate provinces offshore Central America where sediments are rich in organic carbon and in the Arctic Ocean where low bottom water temperatures stabilize methane hydrates. The world’s total gas hydrate inventory is estimated at 0.82 × 10 13 m 3 – 2.10 × 10 15 m 3 CH 4 (at STP conditions) or, equivalently, 4.18–995 Gt of methane carbon. The first value refers to present day conditions estimated using the relatively low Holocene sedimentation rates; the second value corresponds to a scenario of higher Quaternary sedimentation rates along continental margins. Our results clearly show that in-situ POC degradation is at present not an efficient hydrate forming process. Significant hydrate deposits in marine settings are more likely to have formed at times of higher sedimentation during the Quaternary or as a consequence of upward fluid transport at continental margins.

Introduction to Production, Transport, and Emission of Trace Gases from the Vadose Zone to the Atmosphere

Rising concerns about global warming as a consequence of increased anthropogenic greenhouse gas emissions have markedly strengthened scientific, political, and even public interest in issues surrounding human-induced climate change. This has resulted in fundamental economic and ecologic debates

Preparation and characterization of hydrophilic, spectroscopic, and kinetic properties of hydrogels based on polyacrylamide and methylcellulose polysaccharide

AbstractHydrogels with potential technological applications has been prepared using polyacrylamide (PAAm) and methylcellulose (MC) polymers by free radical polymerization reaction. The spectroscopic, morphological, swelling, and kinetic properties were investigated by solid state 13C VACP‐MAS nuclear magnetic resonance (NMR), fourier transform infrared spectroscopy (FTIR), scanning electron microscopy (SEM), water uptake (WU) measurements, respectively. FTIR and NMR analysis confirmed the formation of semi‐IPN structured hydrogel. Data from WU and SEM revealed that the addition of MC into the solution‐forming hydrogel leads to increase in average pore size and hydrophilicity. By varying of AAm, MC, pH and ionic‐strength of swelling medium, it was possible to obtain hydrogels with hydrophilic properties controlled and optimized. The water uptake mechanism is dependent of the AAm concentration, which can follow the Fickian diffusion and anomalous transport process. In this way, PAAm‐MC hydrogels are promising materials for technological applications, such as agricultural field. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011

Determination of kinetics and controlling regimes for H2 oxidation on Pt/Al2O3 monolithic catalyst using high space velocity experiments

Recently developed criteria [S.Y. Joshi, M.P. Harold, V. Balakotaiah, Chemical Engineering Science 65 (2010) 1729–1747] are used to characterize the various controlling regimes (kinetic, pore diffusion and mass transfer controlled) during H2 oxidation on Pt/Al2O3 monolithic catalyst. The hydrogen conversion was measured over a wide range of temperatures and space velocities. Experiments at typical space velocities (104–105h−1) revealed that complete conversion can be achieved at ambient temperature, a result of fast catalytic kinetics. The high activity complicates the analysis of the relative importance of reaction, washcoat diffusion and mass transfer. High space velocity operation with accompanying theoretical analysis enabled an efficient determination of the intrinsic catalytic kinetics, quantification of the heat and mass transport coefficients and determination of the resistances due to reaction, washcoat diffusion and external mass transport processes. Specifically, we investigated the effects of catalyst aging, space velocity and catalyst temperature on the regime transition. The analysis reveals that washcoat diffusion regime is dominant over a wide range of temperatures for the aged catalyst whereas the monolith transitions to a mass transfer controlled regime above 90°C for the high dispersion fresh catalyst. The analysis also reveals that the aging of the catalyst due to sintering of Pt crystallites not only reduces the pre-exponential factor but also the observed activation energy.