Diffusive Boundary Layer Thickness Research Articles

Diatom elemental and morphological changes in response to iron limitation: a brief review with potential paleoceanographic applications

Diatoms are a major group of phytoplankton that account for approximately 40% of the ocean carbon fixation and the vast majority of biogenic silica production through the construction of their cell walls (termed frustules). These frustules accumulate and are partially preserved in the ocean sediments. Diatom growth and nutrient utilization in high-nitrate, low-chlorophyll regions of the world's oceans are mostly regulated by iron availability. Diatoms acclimate to iron limitation by decreasing cell size. The associated increase in surface area-to-volume ratio and decrease in diffusive boundary layer thickness may improve nutrient uptake kinetics. In parallel, cellular silicon (Si) contents are elevated in iron-limited diatoms relative to nitrogen (N) and carbon (C). Variations in degree of silicification and nutritional requirements of iron-limited diatoms have been hypothesized to account for higher cellular Si and/or lower cellular N and C, respectively. However, in some diatoms, frustule silicification does not significantly change when cells are iron-limited. Instead, changes in the Si-containing valve surface area relative to volume within these diatoms is hypothesized to be responsible for the variations in the cellular Si : N and Si : C ratios. In particular, some examined iron-limited pennate diatoms have reduced widths relative to their lengths (i.e. lower length-normalized widths, LNW) compared to iron-replete cells. In the pennate diatom Fragilariopsis kerguelensis, the mean LNWs of valves preserved in sediments throughout the Southern Ocean (a well-characterized iron-limited region) is positively correlated with satellite-derived, climatological net primary productivity in the overlying waters. Because of the specific morphological changes in pennate diatom frustules in response to iron availability, the valve morphometerics (e.g. LNWs) can potentially be used as a diagnostic tool for iron-limited diatom growth and relative changes in the Si : N (and Si : C) ratios in extant diatom assemblages as well as those preserved in the sediments.

Modeling of a three-compartment membrane electrodialysis in H 2SO 4–(NH 4) 2SO 4–NH 3·H 2O system

In this paper, a mathematic model of a three-compartment membrane electrodialysis in H 2SO 4–(NH 4) 2SO 4–NH 3·H 2O system has been developed to calculate the exit concentration of ammonium sulfate in the desalting cell. The model is established on the basis of electromigration and concentration diffusion, and it includes several parameters such as electrolyte solution diffusion coefficient, diffusion boundary layer thickness, current density as well as ionic transference number in the solution and in the membrane. These parameters can be deduced from a reliable procedure based on some experimental data. The model can predict the ammonium sulfate exit concentration according to actual operating conditions. In the context of this model, we discuss the current density effect on the exit concentration. The results showed that calculation data were in accordance with experimental data in large current density range, but deviated from them in a small current density range. The good agreement between experimental data and model data confirms the reliability of the model predictions.

Analysis of aerosol deposition in PHEBUS containment during FPT-1 experiment

The international PHEBUS-FP programme was initiated in 1988 and performed by the French Institute de Protection et de Sûreté Nucléaire (IPSN) to investigate the key phenomena of severe water reactor accident. The main objective of the programme is to study the release, transport and retention of fission products in an in-pile facility under conditions representative of a severe accident in a light water reactor. The Lithuanian Energy Institute has joined the programme in 2005 and most of the efforts were directed to investigation of containment phenomena. This paper presents overview of the analyses performed to investigate aerosol transport and deposition phenomena in PHEBUS containment during FPT-1 test. A lumped parameter code COCOSYS was used for the analysis. Parametric analyses were performed to investigate the influence of aerosol density, solubility and diffusive boundary layer thickness on the deposition rate and deposition distribution of particles in PHEBUS containment. The performed analysis showed only minor influence of the selected parameters on the results of FPT-1. Also it was observed that the diffusive boundary layer thickness should not be defined too small.

Influence of the diffusive boundary layer on solute dynamics in the sediments of a seiche‐driven lake: A model study

The diffusive boundary layer (DBL) plays an important role in the transport of electron acceptors for mineralization and oxidation processes in highly reactive sediments. We used transient numerical modeling to characterize the effects of the DBL thickness on solute dynamics in the sediments of Lake Alpnach. Our model study shows that the DBL mainly influences short‐term sedimentary denitrification by resisting transport. The DBL also governs the reoxidation of reduced compounds by controlling the oxygen penetration depth in the sediment. An increase of the DBL thickness from 0.25 to 1.5 mm diminished the oxygen flux into the sediment by more than 30% from 15 to 9.5 mmol m−2d−1. At the same time, this change in DBL thickness had contrasting effects on the reoxidation of reduced solutes released in the anoxic sediment layers: While the rates of Fe(II) and Mn(II) oxidation decreased by up to 60%, the oxidation of methane changed by only 2%. Still, the contribution to the total oxygen uptake by these redox processes never exceeded 40%. Denitrification rates under steady state conditions were only 8% slower when the DBL was extended from 0.25 to 1.5 mm. The decreased nitrate supply was partially compensated by a stimulated denitrification process due to the lower oxygen penetration. However, fluxes of nitrogen species periodically deviated by more than 60% when an oscillating DBL thickness with periods of less than 6 h was modeled.

Hydrodynamic characterization and performance of an autonomous benthic chamber for use in coastal systems

A benthic chamber (covering 5030 cm2 of seafloor) with real‐time control of sampling and sensor data transmission has been developed for studying benthic fluxes in coastal sediments. Enclosed water is stirred by three submersible centrifugal pumps, which are connected to power circuits that regulate their input voltage, and thus, the current velocity inside the chamber. The complete mixing of the incubated water is achieved within 4 min. The 3‐D velocity field and the distribution of the diffusive boundary layer (DBL) inside the chamber were characterized at different pump rates in a laboratory tank with a bottom layer of sediment or a false bottom supporting alabaster dissolution plates. Two different outlet devices from the pumps were tested. For the one finally selected, averaged tangential velocities at 5 cm above the bottom ranged from 2.0 cm s−1 to 4.8 cm s−1, depending on the voltage applied to the pumps, providing averaged DBL thicknesses that ranged from 125 µm to 279 µm. Average tangential velocity and average DBL thickness were found to correlate according to: VH = 615 × [DBL]−1.02 (R2 = 0.97). Successful field chamber measurements were performed in two shallow coastal systems: Ría de Vigo (NW Spain) and Bay of Cádiz (SW Spain).

Oxygen transfer from flowing water to microbes in an organic sediment bed

Mass transfer of dissolved oxygen (DO) across a sediment–water interface was investigated using laboratory experiments and a numerical simulation model. DO concentration profiles and velocity profiles were measured with high resolution in a recirculating flume with water flowing at cross-sectional average velocities from 3.5 to 11.5 cm/s over a flat and hydrodynamically smooth organic sediment bed. Parameters extracted from the measurements included (1) the DO penetration depth, (2) the effective diffusion coefficient in the sediment layer, (3) the thickness of the turbulent diffusive boundary layer, and (4) the diffusion coefficients in the diffusive boundary layer. DO penetration depths were less than 1 mm, and diffusive boundary layer thicknesses were less than 8 mm. Diffusion in the sediment porewater system was shown to be essentially molecular. The laboratory data were compared to results from a deterministic simulation model. The model included explicit descriptions of (1) mass transfer through the diffusive boundary layer above the sediment/water interface, (2) the boundary layer development over the sediment bed of finite length, (3) diffusive transfer in the sediment porewater system, and (4) microbial uptake of DO in the sediment. The model included both water-side and sediment-side mass transport limitations. The control of DO flux could alternate between water-side and sediment-side without discontinuity. Monod-type kinetics was adopted for DO uptake in the sediment. Organic substrate availability in the sediment did not vary over the course of an experiment. A kinetic limitation for organic matter (substrate) was not considered, and microbial activity in the sediment was parameterized by biomass density. Measured and simulated DO concentration profiles showed satisfactory agreement, with some discrepancies at the interface caused by roughness and porosity effects of the sediment surface.

Low-frequency impedance of an ion-exchange membrane system

A 1D mathematical description of low-frequency impedance is presented for a system including an ion-exchange membrane, two adjacent diffusion boundary layers (DBLs) and two layers of bulk solution. Electrolyte concentration may vary within the DBLs under the action of a direct current (DC) and a small sinusoidal current perturbation imposed on the DC. The description is based on the Nernst–Planck equations and the local electroneutrality assumption, which are believed correct at current densities lower than the limiting one. The results of calculations are compared with experimental data obtained for an AMX anion-exchange membrane installed in a cell with a well specified forced laminar flow of a 0.02 M NaCl solution. For each applied DC density, two fitting parameters, the DBL thickness and the ohmic resistance of the membrane and two bulk solution layers are found. It is shown that the experimental spectra are well described by the model. The hyperbolic tangent element, tanh α/ α, acts an important role in the impedance behavior of membrane system, similar as in electrode systems with an open diffusion layer of a finite thickness, or O element, which provides a “finite thickness porous Warburg” impedance. The relevant parameter found by fitting the experimental data is the thickness of depleted DBL, which increases slightly with increasing DC density, but remains close to Nernst's DBL thickness calculated by using the 2D convective-diffusion model. It is found that the main contributions to the impedance are the Donnan contribution, which is due to the variation of interfacial potential drops caused by boundary concentration variations, and the “conductivity” contribution becoming important at high currents. The last contribution, first considered in this paper, is due to the variation of the solution conductivity resulting from the concentration variation caused by an increment of alternative current (AC).

Application of chronopotentiometry to determine the thickness of diffusion layer adjacent to an ion-exchange membrane under natural convection

A brief review of the evolution of the diffusion boundary layer (DBL) conception inspired by the works of Nernst, Levich and Amatore is presented. Experimental methods for studying the DBL in electrode and membrane systems are considered. The electrochemical behaviour of a CM2 cation-exchange membrane in NaCl and KCl solutions is studied by chronopotentiometry at constant under-limiting current. Chronopotentiometric curves are described theoretically by applying the Kedem–Katchalsky equations in differential form to a three-layer system including the membrane and two adjoining DBLs. The conductance coefficients entering the equations are found by treating the results of membrane characterisation: the electrical conductivity, transport numbers of ions and water, electrolyte uptake, as functions of the equilibrium electrolyte solution. The two-phase microheterogeneous model is used for this treatment resulting in presentation of the conductance coefficients as functions of (virtual) electrolyte solution concentration in the membrane. The steady-state DBL thickness ( δ) is found by fitting experimental potential drop at sufficiently high times. It is found that δ is proportional to (Δ c) − 0.2 , where Δ c is the difference between the electrolyte concentration in the solution bulk and at the interface. This result differs from the Levich equation, which gives the power equal to − 0.25 for Δ c. This deviation is explained by the fact that the theory of Levich does not take into account microscopic chaotic convection motion recently described by Amatore et al. It is shown that the treatment of experimental chronopotentiometric curves with the model developed allows one to observe the role of streaming potential in the membrane. Different mechanisms of streaming potential and their effect on the shape of chronopotentiograms are discussed. A simple analytical solution of Navier–Stokes equations applied to natural convection near an infinite vertical ion-exchange membrane is found. It is shown that the formation of DBL induced by electric current is quasi-stationary. This fact allows the empirical expression found earlier and linking δ with Δ c under steady-state conditions to be used in transient regimes. The numerical solution of the non-stationary Kedem–Katchalsky equations together with this empirical expression results in quantitative description of the potential difference (pd) and δ as functions of time in chronopotentiometric experiments. The comparison of theoretical and experimental chronopotentiometric curves shows an excellent agreement, especially for the part after switching off the current. The reasons of a small deviation observed just before the curves attain steady state under a constant current applied are discussed.

OXYGEN LIMITATION IN MICROFLUIDIC BIOFUEL CELLS

Biofuel cells are devices that use biocatalysts (enzymes or microbes) to convert biochemical energy directly into electrical energy. Microfluidic biofuel cells exploit the lack of active mixing at microscale dimensions to eliminate the use of proton exchange membranes that separate anolyte and catholyte streams. Simulation of this system, by solving the governing 3-D conservation equations (flow, species transport), reveals that oxygen availability limits the performance of the cathode. An exponential decay in the availability of oxygen at the cathode is observed along the length of the microchannel, indicating that increasing the number of electrode pairs reduces the overall current density. This conclusion is consistent with experimental observations. Increasing electrolyte flow rates can reduce the mass transport limitations by decreasing the diffusion boundary-layer thickness, but disparity between the flow rates of the anolyte and catholyte can induce wastage of dissolved oxygen.

Determination of Diffusion Boundary Layers and Copper Thickness Uniformity in Plating Tools Designed for 3-D Interconnect and Packaging Applications

Limiting currents under mass transport limiting conditions were determined experimentally for two distinct types of electrochemical plating cells using voltammetric and chronoamperometric methods. The average limiting currents were used to estimate the thickness of the diffusion boundary layer that results from the novel cell configurations and agitation schemes. Additionally, the deposit thickness uniformity across the surface of copper plated substrates was experimentally determined and reported as the coefficient of variation (CV). Results show that optimization of the cell configurations and solution agitation within provides a thin uniform diffusion boundary layer thickness and low CVs for the metal thickness distribution indicating a uniform current distribution is achieved across the surface of the substrate.

Two dimensional simulation on immunoassay for a biosensor with applying electrothermal effect

For diffusion-limited proteins, the diffusion boundary layer on the reacting surface hinders the binding reaction. The authors performed finite-element simulations of the electrothermal effect on the reaction kinetics of C-reactive protein (CRP)–anti-CRP. The induced vortices stir the flow and enhance the transport rate of analytes. They attribute the enhancement to the reduction of the thickness of diffusion boundary layer. Significant interference patterns of the votices are observed by varying the position of the reacting surface. These patterns are utilized to optimize the enhancement factor, yielding 5.166 and 3.744 times for association and dissociation, respectively, under voltage (15Vrms) and frequency (100kHz).

EFFECT OF WATER VELOCITY AND BENTHIC DIATOM MORPHOLOGY ON THE WATER CHEMISTRY EXPERIENCED BY POSTLARVAL ABALONE

The water bathing postlarval abalone often lies within the diffusive boundary layer (DBL) so its chemistry is greatly influenced by the metabolism of the biofilm on which the abalone feed. This study used microelectrodes to investigate the influence of water velocity and diatom morphology on dissolved oxygen and pH in the DBL. Decreasing water velocity increased the thickness of the DBL, thereby increasing the amplitude of changes in oxygen concentration. Over a film of the prostrate diatom Nitzschia ovalis Arnot, DBL thickness averaged 71, 139, 177, and 406 μm at water velocities of 78, 15, 7, and 1 mm s−1 respectively. Corresponding oxygen concentrations at the biofilm surface under moderate light (75 μE m−2 s−1) and temperature (15°C) averaged 111%, 120%, 125%, and 151% of air saturation respectively, at the four velocities. The presence of a 1-mm tall diatom canopy (Achnanthes longipes Agardh) over a Nitzschia ovalis film thickened the DBL by 3-fold at 1 mm s−1 and 6-fold at ∼80 mm s−1. The thickened DBL and higher diatom biomass generated extreme conditions at the biofilm surface. Dissolved oxygen concentrations as high as 440% of air saturation, and pH as high as 9.8 were recorded beneath the canopy in moderate light (105 μE m−2 s−1) and temperature (15°C) at a water velocity of 1 mm s−1. Changes during darkness were less extreme, with 53% oxygen saturation and pH 7.7 the minima recorded. These measurements demonstrate the extreme water chemistry that can develop in the microhabitat of postlarval abalone. The changes will be amplified by the presence of filamentous diatoms, by increased light intensity, and by lack of water movement. Standard aeration will greatly reduce the extremes experienced by postlarvae by generating water movement sufficient to thin the DBL.

Development and Characterization of Plating Cell Geometry for PCB and Packaging Applications.

Plating cell geometry and uniform solution flow are the foundation for a uniform plating process for printed circuit board and electronic packaging applications. Currently, the plating cells used for copper metallization for these applications utilize a number of agitation methods to reduce the thickness of the diffusion boundary layer as well as fostering solution movement into and through small features. In order to achieve a uniform diffusion boundary layer, a requirement for uniform plating thickness, a uniform diffusion layer must be established by flow/agitation method within the cell. A novel plating cell geometry that provides a thin uniform diffusion boundary layer and consequently uniform plating thickness is disclosed. Results from cell characterization in terms of diffusion boundary layer thickness and deposit thickness uniformity is also reported.

Effects of Magnetic Field Directed Orthogonally to Surfaces on Electrochemical Processes

The study provides a model for the effect on electrochemical processes of a magnetic field that is directed perpendicular to a planar electrode surface. The analysis assumes the formation of a hydrodynamic boundary layer of the fluid motion that is generated above a semi-infinite electrode as a result of magnetic force action. For a uniform magnetic field, the model predicts the decrease of the diffusion boundary layer thickness upon increasing either the magnetic field strength, B, or the reagent bulk concentration, C, with the power dependence corresponding to C 4/3B 2/3. The limiting current density, iL, is formulated as iL ≈ 0.5χm1/3(μoρ)-1/3R5/3D5/9ν-2/9nFC 4/3B 2/3. This permits semiquantitative interpretation of the enhanced mass transfer at electrode surfaces for electrochemical reactions and predicts a magnetic field effect on mass transfer-limited heterogeneous reactions of magnetic species. The results imply that the perpendicular magnetic field will affect any mass transport limited transforma...

In Situ Measurements of Metal Complex Exchange Kinetics in Freshwater

Trace metals were measured in situ in a freshwater river draining a peat catchment (DOC = 15 mg L(-1)) using diffusive gradients in thin-films (DGT) devices with a range of gel layer thicknesses (0.16-2.0 mm). The reciprocal of the accumulated mass of each metal varied linearly with the thickness of the diffusive layer. These plots allowed calculation of the thickness of an apparent diffusive boundary layer (ADBL). A constant value was obtained from the plots of Cd, Pb, and Zn. The observed increase in the ADBL for the other metals (Mn<Co<Ni<Cu<AI<Fe) was consistent with increasing kinetic limitation of metal supplied from complexes with humic substances. The results could be presented as a kinetic signature, which reflects the nature of the binding ligands available in the water. A theoretical basis for deriving kinetic constants from the DGT measurements was developed. The derived association rate constants for Ni, Mn, and Cu were consistent with values calculated by assuming that the Eigen mechanism holds and that the mean stability constants of the complexes are related to the binding constants of each metal with fulvic acid. These first in situ measurements of dissociation rate constants provided larger values than those obtained by different techniques in the laboratory, suggesting that trace metal complexes in natural waters may be more labile than previously thought.

Effect of the diffusive boundary layer on benthic mineralization and O2 distribution: A theoretical model analysis

On the basis of a dynamic diagenetic model, we evaluate and discuss the effect of the diffusive boundary layer (DBL) on benthic O2 exchange and O2 consuming pathways. The analysis documents that the DBL has only minor importance for the annual O2 uptake of coastal cohesive sediments. Imposing static DBL thicknesses of 300‐900 mm decreased the annual O2 uptake by only 2–10% in comparison to a situation without any DBL. Lower O2 availability as imposed by a thicker DBL, however, markedly reduced the aerobic heterotrophic respiration but enhanced aerobic reoxidation of solutes released by the stimulated anaerobic respiration. The 2–10% decrease in the annual O2 uptake was caused mainly by higher benthic release rates of NH4+ and Mn2+. The overall carbon degradation rate—and thus the carbon preservation—remained unaffected by the DBL thickness. Dynamic modeling revealed that abrupt changes in the DBL thickness caused an instantaneous change in the interstitial O2 distribution and in the benthic O2 uptake rate. However, conditions quickly reversed as the porewater profiles of reduced solutes and distribution of reduced solids readjusted even though full steady state was obtained only after several months. In nature the DBL is constantly changing, and thus in situ O2 microprofiles are transient by nature. Dynamic modeling showed that the benthic O2 concentration and the O2 uptake in Aarhus Bay could vary by 30% or more on time scales of a few hours or days solely because of changes in the DBL thickness. The integrated annual O2 uptake remained unaffected by these fluctuations.

Estimation of diffusive boundary layer thickness in studies involving diffusive gradients in thin films (DGT)

Recent laboratory experiments and field investigations involving diffusive gradients in thin films (DGT) have shown that the thickness (delta) of the diffusive boundary layer (DBL), which can affect the accuracy of the technique, is generally not negligible. Accordingly, the determination of delta has become a matter of considerable practical importance. Though the problem has been addressed in the recent literature, there is room for some improvement. An expression for estimation of delta is presented here, and a practical procedure for determining delta and the concentration of DGT-labile species from sparse experimental data is proposed and illustrated by analyzing data from four experiments with DGT samplers of different diffusive gel thicknesses.

Application of chronopotentiometry to study the diffusion layer thickness adjacent to an ion-exchange membrane under natural convection

The diffusion boundary layer (DBL) arisingat an electrode or an ion-exchange membraneaffects significantly the mass transfer in electro-chemical systems. There is a great interest in lit-erature as for determination of DBL parametersand development of the real meaning of thisconcept [1]. In this paper, the chronopotentiom-etry is applied to determine the DBL thickness das a function of the time and the applied currentdensity near a CM2 cation-exchange membraneseparating two identical KCl solutions undernatural convection, the membrane being invertical position.

Accuracy of the Diffusive Gradients in Thin-Films Technique: Diffusive Boundary Layer and Effective Sampling Area Considerations

When using the diffusive gradients in thin-films (DGT) technique in well-stirred solutions, the diffusive boundary layer has generally been ignored on the assumption that it is negligibly thin compared to the total thickness of delta g, i.e., the sum of the thickness of the prefilter and diffusive gel. Deployment of devices with different diffusive layer thicknesses showed that the thickness of the DBL was approximately 0.23 mm in moderate to well-stirred solutions, but substantially thicker in poorly or unstirred solutions. Measurement of the distribution of Cd in the DGT resin gel at high spatial resolution (100 microm) using laser ablation inductively coupled plasma mass spectrometry showed that the effective sampling window had a larger diameter (2.20 cm) than the geometric diameter of the exposure window (2.00 cm). Lateral diffusion in the gel, which had previously been neglected, therefore increased the effective surface area of the device by approximately 20%. The concentrations measured by DGT agreed well with the known concentrations in standard solutions for all diffusion layer thicknesses, when the effective area and the appropriate diffusive boundary layer (DBL) were used. The extent of the error associated with neglecting the DBL and using the geometric window area depends on the gel layer thickness and the true thickness of the DBL, as determined by the deployment geometry and flow regime. When DGT measurements were made in well-stirred solutions using a 0.80-mm diffusive gel, the effect of neglecting the DBL and using the inappropriate geometric area offset each other, with the error being <+/-10%. For precise measurements, and especially work involving speciation or kinetic measurements, where DGT devices with different diffusive gel layer thicknesses are deployed, it is necessary to use the effective area and the appropriate DBL thickness in the full DGT equation, which allows for the use of layer-specific diffusion coefficients.

The effects of waves and morphology on mass transfer within branched reef corals

Rates of mass transfer in coral reefs are governed both by the physical flow environment and the morphology of the coral. Laboratory experiments were conducted to estimate mass transfer in unidirectional and oscillatory flows by measuring the rate of dissolution of gypsum cylinders (clods) placed within the branching structure of three morphologically distinct coral species. Unidirectional flows were varied between 2.9 and 14.1 cm s 21 and, as expected, mass transfer rates increased with increasing flow and a more open branch spacing. Depending on morphology and flow, mass transfer rates within the interior of the branching structure were 50 to 75% of that measured outside the coral in free-stream conditions. Oscillatory conditions showed relative mass transfer rates 1.6 to 2.9 times greater than equivalent unidirectional currents. This ratio increased with increasing wave frequency, likely due to the corresponding decrease in the diffusive boundary layer thickness. The ratio also increased with a greater compactness in branch spacing, with mass transfer rates within the coral structure up to 130% of free-stream conditions. We used planar laser-induced fluorescence imaging to study the instantaneous structure of mass advection through the coral. Oscillatory flow acts as a dominant forcing mechanism to generate water motion within the coral structure at levels not attainable with comparable unidirectional currents.