Mass Transport Dynamics Research Articles

Thermodynamics of stressed solids: Slow deformation and roughening of material interfaces

At every turn in nature we are confronted with complex patterns. Patterns often formed in multiphase systems by an intricate dynamics of mass transport, e.g. diffusion and/or advection, and mass exchange between individual phases. Here we consider instabilities of phase boundaries in idealized stressed multiphase systems. Specifically, we study the growth of small perturbations of surfaces by considering mass transport from regions, where the stress and chemical potential is high, to surrounding regions where the stress and chemical potential is low. We present a linear stability analysis for various stress configurations and their corresponding stability diagrams.

The Reynolds transport theorem: Application to ecological compartment modeling and case study of ecosystem energetics

The Reynolds transport theorem (RTT) from mathematics and engineering has a rich history of success in mass transport dynamics and traditional thermodynamics. This paper introduces RTT as a complementary approach to traditional compartmental methods used in ecological modeling and network analysis. A universal system equation for a generic flow quantity is developed into a generic open-system differential expression for conservation of energy. Nonadiabatic systems are defined and incorporated into control volume (CV) and control surface (CS) perspectives of RTT where reductive assumptions in empirical data are then formally introduced, reviewed, and appropriately implemented. Compartment models are abstract, time-dependent systems of simultaneous differential equations describing storage and flow of conservative quantities between interconnected entities (the compartments). As such, they represent a set of flexible and somewhat informal, assumptions, definitions, algebraic manipulations, and graphical depictions subject to influence and selectively parsed expression by the modeler. In comparison, RTT compartment models are more rigorous and formal integro-differential equations and graphics initiated by the RTT universal system equation, forcing an ordered identification of simplifying assumptions, ending with clearly identified depictions of the transfer and transport of conservative substances in physical space and time. They are less abstract in the rigor of their equation development leaving less ambiguity to modeler discretion. They achieve greater consistency with other RTT compartment style models while possibly generating greater conformity with physical reality. Characteristics of the RTT approach are compared with those of a traditional compartment model of energy flow in an intertidal oyster-reef community.

The origin of refractory minerals in comet 81P/Wild 2

Refractory Ti-bearing minerals in the calcium-, aluminum-rich inclusion (CAI) Inti, recovered from the comet 81P/Wild 2 sample, were examined using analytical (scanning) transmission electron microscopy (STEM) methods including imaging, nanodiffraction, energy-dispersive spectroscopy (EDX) and electron energy loss spectroscopy (EELS). Inti fassaite (Ca(Mg,Ti,Al)(Si,Al) 2O 6) was found to have a Ti 3+/Ti 4+ ratio of 2.0 ± 0.2, consistent with fassaite in other solar system CAIs. The oxygen fugacity ( log f O 2 ) of formation estimated from this ratio, assuming equilibration among phases at 1509 K, is −19.4 ± 1.3. This value is near the canonical solar nebula value (−18.1 ± 0.3) and in close agreement with that reported for fassaite-bearing Allende CAIs (−19.8 ± 0.9) by other researchers using the same assumptions. Nanocrystals of osbornite (Ti(V)N), 2–40 nm in diameter, are embedded as inclusions within gehlenite, spinel and diopside in Inti. Vanadium is heterogeneously distributed within some osbornite crystals. Compositions range from pure TiN to Ti 0.36V 0.64N. The possible presence of oxide and carbide in solid solution with the osbornite was evaluated. The osbornite may contain O, but C is not present at detectable levels. The presence of osbornite, likely a refractory early condensate, together with the other refractory minerals in Inti, indicates that the parent comet contains solids that condensed closer to the proto-sun than the distance at which the parent comet itself accreted. The estimated oxygen fugacity and the reported isotopic and chemical compositions are consistent with Inti originating in the inner solar system like other meteoritic CAIs. These results provide insight for evaluating the validity of models of radial mass transport dynamics in the early solar system. The oxidation environments inferred for the Inti mineral assemblage are inconsistent with an X-wind formation scenario. In contrast, radial mixing models that allow accretion of components from different heliocentric distances can satisfy the observations from the cometary CAI Inti.

A 3D Hybrid Model for Tissue Growth: The Interplay between Cell Population and Mass Transport Dynamics

To provide theoretical guidance for the design and in vitro cultivation of bioartificial tissues, we have developed a multiscale computational model that can describe the complex interplay between cell population and mass transport dynamics that governs the growth of tissues in three-dimensional scaffolds. The model has three components: a transient partial differential equation for the simultaneous diffusion and consumption of a limiting nutrient; a cellular automaton describing cell migration, proliferation, and collision; and equations that quantify how the varying nutrient concentration modulates cell division and migration. The hybrid discrete-continuous model was parallelized and solved on a distributed-memory multicomputer to study how transport limitations affect tissue regeneration rates under conditions encountered in typical bioreactors. Simulation results show that the severity of transport limitations can be estimated by the magnitude of two dimensionless groups: the Thiele modulus and the Biot number. Key parameters including the initial seeding mode, cell migration speed, and the hydrodynamic conditions in the bioreactor are shown to affect not only the overall rate, but also the pattern of tissue growth. This study lays the groundwork for more comprehensive models that can handle mixed cell cultures, multiple nutrients and growth factors, and other cellular processes, such as cell death.

A Review of Solid Oxide Fuel Cell (SOFC) Dynamic Models

In this paper, state-of-the-art dynamic models for solid oxide fuel cells (SOFCs) in the open literature are reviewed. The review also includes the transient modeling of SOFC systems with reformers. In the transients of a SOFC, three characteristic time constants are observed. One of the challenges in transient modeling is to capture these characteristic times. The first characteristic time is on the order of milliseconds and is mostly neglected, because it is too small, from the viewpoint of practical applications. The second time constant is on the order of seconds and arises mainly because of the mass-transport dynamics. The third characteristic time is on the order of minutes or hours and is dependent on the energy transport characteristics of the system. These characteristic times are extremely system-specific and, therefore, must be identified on a case-to-case basis. In this paper, the existing literature on dynamic studies are reviewed, focusing mainly on the fidelity of the model that is required to capture these time constants. The dynamic modeling of SOFC is still not as rich as the steady-state modeling. Therefore, steady-state models are also reviewed, whenever required. The utility of the dynamic models in design, control, and operation is discussed. A dynamic model from the literature is chosen for this purpose.

Single-Cell Transfection by Electroporation Using an Electrolyte/Plasmid-Filled Capillary

Single-cell transfection of adherent cells has been accomplished using single-cell electroporation (SCEP) with a pulled capillary. HEPES-buffered physiological saline solution containing pEGFP plasmid at a low concentration (0.16 approximately 0.78 microg/microL) filled a 15 cm long capillary with a tip opening of 2 microm. The electric field is applied to individual cells by bringing the tip close to the cell and subsequently applying one or two brief electric pulses. Many individual cells can thus be transfected with a small volume of plasmid-containing solution (approximately 1 microL). The extent of electroporation is determined by measuring the percentage loss of freely diffusing thiols (chiefly reduced glutathione) that have been derivatized with the fluorogenic ThioGlo 1. A mass transport model is used to fit the time-dependent fluorescence intensity decay in the target cells. The fits, which are excellent, yield the electroporation-induced fluorescence loss at steady state and the mass transfer rate through the electroporated cell membrane. Steady-state fluorescence loss ranged approximately from 0 to about 80% (based on the fluorescence intensity before electroporation). For the cells having a loss of thiol-ThioGlo 1 fluorescence intensity greater than 10% and mass transfer rate greater than 0.03 s(-1), EGFP fluorescence is observed after 24 h. The EGFP fluorescence is increased at 48 h. With a loss smaller than 10% and a mass transfer rate smaller than 0.03 s(-1), no EGFP fluorescence is detected. Thus, transfection success is closely related to the small molecule mass transport dynamics as indicated by the loss of fluorescence from thiol-ThioGlo 1 conjugates. The EGFP expression is weaker than bulk lipid-mediated transfection, as indicated by the EGFP fluorescence intensities. However, the success with the single-cell approach is considerably greater than lipid-mediated transfection.

Modeling Growth and Quorum Sensing in Biofilms Grown in Microfluidic Chambers

Biofilms are highly organized structures coordinately formed by multiple species of bacteria. Quorum sensing (QS) is one cell-cell communication mechanism that is used by bacteria during biofilm formation. Biofilm formation is widely acknowledged to occur through a sequence of spatially and temporally regulated colonization events. While several mathematical models exist for describing biofilm development, these have been developed for open systems and are not applicable to closed systems where biofilm development and hydrodynamics are interlinked. Here, we report the development of a mathematical model describing QS and biofilm formation in a closed system such as a microfluidic channel. The model takes into account the effect of the external environment viz the mass and momentum transport in the microfluidic channel on QS and biofilm development. Model predictions of biofilm thickness were verified experimentally by developing Pseudomonas aeruginosa PA14 biofilms in microfluidic chambers and reflect the interplay between the dynamics of biofilm community development, mass transport, and hydrodynamics. Our QS model is expected to guide the design of experiments in closed systems to address spatio-temporal aspects of QS in biofilm development and can lead to novel approaches for controlling biofilm formation through disruption of QS spatio-temporal dynamics.

Passive microfluidic pumping using coupled capillary/evaporation effects

Controlled pumping of fluids through microfluidic networks is a critical unit operation ubiquitous to lab-on-a-chip applications. Although there have been a number of studies involving the creation of passive flows within lab-on-a-chip devices, none has shown the ability to create temporally stable flows for periods longer than several minutes. Here a passive pumping approach is presented in which a large pressure differential arising from a small, curved meniscus situated along the bottom corners of an outlet reservoir serves to drive fluid through a microfluidic network. The system quickly reaches steady-state and is able to provide precise volumetric flow rates for periods lasting over an hour. A two-step mathematical model provides accurate predictions of fluid and mass transport dynamics in these devices, as validated by particle tracking in laboratory systems. Precise flow rates spanning an order of magnitude are accomplished via control of the microchannel and outlet reservoir dimensions. This flow mechanism has the potential to be applied to many micro-total analytical system devices that utilize pressure-driven flow; as an illustrative example, the pumping technique is applied for the passive generation of temporally stable chemical gradients.

Analysis of power and entropy generation in a chemical engine

We develop a thermodynamic theory for a difficult class of chemical processes undergoing in irreversible power-producing systems that yield mechanical work and are characterized by multiple (vectorial) efficiencies. Obtained efficiency formulas are applied for chemical machines working at maximum production of power. Steady-state model describes a chemical system in which two reservoirs are infinite, whereas an unsteady model treats a dynamical system with finite upper reservoir and gradually decreasing chemical potential of a key fuel component. In the considered chemical systems total power output is maximized at constraints which take into account dynamics of mass transport and efficiency of power generation. Dynamic optimization methods, in particular variational calculus, lead to optimal functions that describe integral power limits and extend reversible chemical work W rev to finite rate situations. Optimization results quantify effects of chemical rates and transport phenomena. Legendre transform of a local power function is an effective tool to obtain an optimal path in a dynamical process of power yield.

Mass transport dynamics of N 2 and O 2 in wood-based carbon molecular sieves affected by pre-treatments and comminution

Carbon honeycomb adsorbents having molecular sieve characteristics were prepared by controlled single-step carbonization from 1 × 1 × 1 cm 3 cubes of spruce wood. The carbonized xylem retained the original tracheal structure of the wood. The obtained three-dimensional frame exhibits low transport diffusional resistance due to the wide straight micron sized channels. The wood-based carbon molecular sieve (CMS) samples, synthesized in various ways, were characterized by their dynamic adsorption properties using the unique potentials of the frequency-response (FR) technique. The carbon honeycomb cubes exhibited significantly lower macropore diffusional resistance and higher kinetic selectivity in N 2 and O 2 separation than that of a commercial pelletized adsorbent (Takeda MSC-4A).

Dynamics of Ion Beam Stimulated Surface Mass Transport to Nanopores

AbstractWe explore the ion beam-induced dynamics of the formation of large features at the edges of nanopores in freestanding silicon nitride membranes. The shape and size of these “nanovolcanoes”, together with the rate at which the nanopores open or close, are shown to be strongly influenced by sample temperature. Volcano formation and pore closing slow and stop at low temperatures and saturate at high temperatures. Nanopore volcano size and closing rates are dependent on initial pore size. We discuss both surface diffusion and viscous flow models in the context of these observed phenomena.

Dynamics of Mass Transport and Magnetic Fields in Low-Wire-Number-ArrayZPinches

The dynamics of mass transport were observed in a wire array implosion with multiframe laser probing. Plasma bubbles arise at breaks in the wires. Interferometry shows that the leading edge of the bubbles brings material to the axis of the array. The speed of this material was measured to be > or =3 x 10(7) cm/s during the wire array implosion. A shock was observed during the collision of the bubbles with the precursor. The Faraday effect indicates current flowing in breaks on the wires. The current switches from the imploding mass to the on-axis plasma column at the beginning of the x-ray pulse.

Photoinduced Mass Transport by One-Dimensional Gaussian Beam Irradiation: Width and Polarization Dependence

Photoinduced mass transport dynamics for the irradiation of a one-dimensional (1D) Gaussian beam was investigated experimentally, and its width and polarization dependence were simulated according to our two models. One of our models is based on viscous fluid mechanics, in which the analytical function expressing the nature of the driving force of photoinduced mass transport has been defined a priori to suit the phenomenological characteristics. Antithetically, another newly developed model assumes that the force of mass transport could be attributed to electromagnetic interaction between dipoles of the molecules and the electromagnetic field of the excitation beam, and surface tension. The polymer is treated as a viscous fluid even in the new model, but the condition of inhomogeneous viscosity that depends on the irradiated light intensity has been additionally introduced in order to describe the phenomenon more precisely. The experimental results and the simulated results were compared and discussed from the viewpoint of the validity of the models.

Sulfate distribution in a multi-basin, saline lake

Devils Lake in northeastern North Dakota (USA) is a terminal lake of glacial origin with a substantial sulfate content. Since 1940, the lake water level has risen over 13.5m and salinity has decreased. Devils Lake consists of a series of interconnected basins with sulfate concentration increasing in an eastward direction from 450mg/l in West Bay to 3000mg/l in East Devils Lake. Using sulfate as a tracer and linking measurements of specific conductance with observed time series of water surface elevations, wind, and water velocity, this paper illustrates the magnitude and dynamics of mass transport and exchange processes between the multiple basins of Devils Lake. Measurements show small horizontal salinity gradients within the lake basins, but large salinity gradients in some of the exchange zones connecting basins. Vertical salinity gradients were observed in small basins and near exchange zones with strong horizontal salinity differentials. These instances of vertical stratification were associated with buoyancy driven exchange flows and wind sheltering. Exchange flow velocities between selected basins were correlated with wind direction and speed. Interbasin exchange flows were found to reverse direction frequently in response to the prevailing wind direction. Flow direction frequencies in one specific exchange zone were 31% west to east, 48% east to west, and 21% bidirectional (stratified). At the lake level observed in 2000, time averaged, measured interbasin exchange flow rates were 30--40m3/s compared to tributary inflow rates to the lake of 3--9m3/s.

03/01932 Incorporation of fibres in geothermal well cements: Berndt, M. L. and Philippacopoulos, A. J. Geothermics, 2002, 31, (6), 643–656

Refractory Ti-bearing minerals in the calcium-, aluminum-rich inclusion (CAI) Inti, recovered from the comet 81P/Wild 2 sample, were examined using analytical (scanning) transmission electron microscopy (STEM) methods including imaging, nanodiffraction, energy-dispersive spectroscopy (EDX) and electron energy loss spectroscopy (EELS). Inti fassaite (Ca(Mg,Ti,Al)(Si,Al)2O6) was found to have a Ti3+/Ti4+ ratio of 2.0 ± 0.2, consistent with fassaite in other solar system CAIs. The oxygen fugacity (logfO2) of formation estimated from this ratio, assuming equilibration among phases at 1509 K, is −19.4 ± 1.3. This value is near the canonical solar nebula value (−18.1 ± 0.3) and in close agreement with that reported for fassaite-bearing Allende CAIs (−19.8 ± 0.9) by other researchers using the same assumptions. Nanocrystals of osbornite (Ti(V)N), 2–40 nm in diameter, are embedded as inclusions within gehlenite, spinel and diopside in Inti. Vanadium is heterogeneously distributed within some osbornite crystals. Compositions range from pure TiN to Ti0.36V0.64N. The possible presence of oxide and carbide in solid solution with the osbornite was evaluated. The osbornite may contain O, but C is not present at detectable levels. The presence of osbornite, likely a refractory early condensate, together with the other refractory minerals in Inti, indicates that the parent comet contains solids that condensed closer to the proto-sun than the distance at which the parent comet itself accreted. The estimated oxygen fugacity and the reported isotopic and chemical compositions are consistent with Inti originating in the inner solar system like other meteoritic CAIs. These results provide insight for evaluating the validity of models of radial mass transport dynamics in the early solar system. The oxidation environments inferred for the Inti mineral assemblage are inconsistent with an X-wind formation scenario. In contrast, radial mixing models that allow accretion of components from different heliocentric distances can satisfy the observations from the cometary CAI Inti.

The skeletal isomerization of n-butene over ferrierite catalysts

Abstract The catalytic properties of H-ferrierite zeolites, prepared by hydrothermal and dry-state synthesis, were compared in the skeletal isomerization of 1-butene. The activity was found to be strongly influenced by the presence of extra-framework Al (EFAl) species in the zeolite micropores and by the carbonaceous deposit formed during the reaction. The dynamics of mass transport in the zeolite crystallites were studied by the frequency-response (FR) method using acetylene, propane, n - and i -butane as probe molecules. The selectivity of n -butene conversion showed correlation with the dynamics of the n -butane sorption process. Either the diffusion or the sorption was the rate-controlling slowest step of n -butane mass transport, depending on the amount and the distribution of the EFAl species in the sample. In the catalyst sample, free of EFAl, the transport was found to be controlled by the rate of sorption. At an EFAl content of about 0.5–1.0 EFAl/unit cell the diffusion resistance of the micropores governed the n -butane transport rate.

Dynamics of multicomponent mass transport with complex reaction in a porous catalyst

Numerical simulations of the water-gas shift reaction over an industrial catalyst ICI 52-1 were performed. The analysis of the system was focused on the mutual influence of intraparticle mass transport and catalytic reaction. Responses of the WK cell on step changes of an inlet stream composition were modelled. The amount of information being important for reliable comparison of experiments and simulations was evaluated for several responses on the concentration step changes. The advantage of the WK cell in comparison with flow reactors was discussed in terms of sensitivities of system responses with respect to inlet stream parameters. The asymmetric feeding of reactants when the WK cell worked similarly like a membrane reactor was considered as most suitable. The related system of parabolic partial differential equations was solved by the method-of-lines integration technique with a fully adaptive time and space grid control.

Evolution of an Ensemble of Nanoparticles in a Colloidal Solution: Theoretical Study

The evolution of a nanosized particle in colloidal solution has been studied theoretically. The model developed is based on the size dependence of the activation energies of the growth and dissolution processes and takes into account the mass transport dynamics. Using this model, Monte Carlo simulations of the evolution of an ensemble of growing nanoparticles during Ostwald ripening have been performed, and conditions leading to either “focusing” or “defocusing” of the particle size distribution were found. The stationary particle size distribution inherent to the Ostwald ripening process in ensembles of nanoparticles less than 5 nm in radius is narrower and more symmetric than that predicted by the Lifshitz−Slyozov−Wagner theory valid for ensembles of larger (>20 nm in radius) colloidal particles. The growth of nanoparticles in the diffusion-controlled regime results in better final size distributions as compared with those grown in the reaction-controlled regime. The dependence of the particle size dist...

23] Limiting-current-type microelectrodes for quantifying mass transport dynamics in biofilmst

This chapter demonstrates the use of limiting-current-type microelectrodes for evaluating the mass transport coefficient, effective diffusivity, and flow velocity in space occupied by biofilms. It presents many concepts and experimental results generated by the Biofilm Structure and Function Research Group at the Center for Biofilm Engineering. Limiting-current-type microelectrodes are remarkably versatile when applied to the measurement of mass transport rates in biofilms. Local mass transport coefficient, local effective diffusivity, and local flow velocity can all be measured. When the results of these measurements are superimposed on the results of nutrient uptake dynamics, the intricate interplay between mass transport dynamics and microbial activity in biofilms becomes visible, at least in simple experimental systems. The most controversial part of the limiting current techniques, when applied to biological systems, is the choice of cathodic reactants. Ideally, such a reactant would not be toxic to the microorganisms, would not serve as a substrate in metabolic reactions, and would not react chemically with the biomass. At the same time it should exhibit acceptable electrochemical properties, reversible kinetics, and low overpotential on the selected electrode.

Thermodynamic framework for work-assisted unit operations

We construct thermodynamic criteria for optimization of sequential work-assisted unit operations, especially for heating, evaporation and drying. Constraints take into account dynamics of heat and mass transport and rate of real work consumption. Finite-rate, endoreversible models are used. By definition, they refer to systems which have separated in space their internal reversible parts, such as Carnot engines or heat pumps, from their (external) purely irreversible parts, such as thermal resistances. Consequently these models can quantify irreducible losses of classical exergy caused by the resistances. Extremum performance functions for optimal work, which incorporate residual minimum entropy production, are determined in terms of end states, duration and (in discrete processes) number of stages. Analogies between entropy production expressions for work-assisted operations and those without work help to formulate optimization models of the former. Our theory also answers the question whether work production is at all possible in a given system.