Zone Mass Transfer Research Articles

Theoretical computation of the band broadening in micro-pillar array columns

We have investigated the possibility to establish a theoretical plate height expression for the band broadening in the most widely used micro-pillar array column format, i.e., a cylindrical pillar array wherein the pillar walls and the channel bottom are coated with a thin layer of meso‑porous material.Assuming isotropic diffusion in the shell-layer, it was found that the vertical diffusive transport along the porous shell-layer covering the pillar walls significantly suppresses the band broadening originating from the vertical migration velocity gradients. As the vertical transport in the shell-layer increases linearly with the retention equilibrium constant K, this leads to an anomalous dependency on the retention factor. Indeed, instead of increasing with k’’ and following the classic (1+ak’’+bk’’2)/(1 + k’’)2-dependency governing a classic Taylor-Aris system, the variation of the mobile zone mass transfer resistance term hCm in a 3D pillar array with bottom-wall retention goes through a maximum (resp. factor 1.5 (k’’=4) and 2 (k’’=16) difference between observed and classic Taylor-Aris behaviour). This effect increases with increasing pillar heights and increasing reduced velocities. Because of this complex k’’-dependency, it proves very cumbersome to establish a general plate height equation covering all conditions. Instead, a plate height expression was established that is limited up to k’’=4, but remains accurate for higher k’’-values for cases where the ratio of pillar height over inter-pillar distance remains below 5. It can however be anticipated the proposed analytical model is only valid in a rather limited range around the presently considered external porosity of ε=0.5.

Nonadditivity and Nonlinearity of Mobile and Stationary Zone Mass Transfer Resistances in Chromatography.

Using a two-zone moment analysis (TZMA) method based on Brenner's generalized dispersion theory for two-dimensional (2D) and three-dimensional (3D) periodic media, we investigated the mechanisms for dispersion in particulate media for liquid chromatography. This was done using a set of plate height data covering an unprecedented wide range of retention factors, diffusion coefficients, and velocities, all computed with unequaled accuracy. Applying Giddings' additivity test, based on alternatingly making the diffusion coefficient in the mobile and stationary zones infinitely large, the dispersion data clearly indicate a lack of additivity. Although this lack could be directly understood by identifying the existence of multiple parallel mass transfer paths, the additivity assumption interestingly overestimates the true C term band broadening (typically by more than 10%, depending on conditions and dimensionality of the system). However, Giddings originally asserted the occurrence of parallel paths would always lead to an underestimation of the dispersion. The origin of the lack of additivity is analyzed in detail and qualitatively explained. Finally, we also established a generic framework for the modeling of the effect of the reduced velocity and the retention coefficient on the C term in ordered chromatographic media. This led to the introduction of a new expression for the mobile zone mass transfer term, which, unlike the currently used literature expression, contains the complete k″ dependency.

Preface: Special Issue on Ophiolites and Oceanic Lithosphere

AbstractWith this Preface, we provide background information, a scientific overview of topics, and an annotated bibliography of the 63 papers published in the Journal of Geophysical Research (JGR) Special Issue on “Ophiolites and Oceanic Lithosphere, with a Focus on the Samail Ophiolite,” collected online at https://agupubs.onlinelibrary.wiley.com/doi/toc/10.1002/(ISSN)2169-9356.SAMAIL1. Topics covered in the Special Issue include formation and alteration of igneous ocean crust at submarine spreading centers, subduction zone mass transfer at the leading edge of the mantle wedge, the tectonic emplacement and evolution of ophiolites, processes of alteration and weathering of tectonically exhumed mantle peridotite, and the subsurface biosphere in the peridotite weathering environment. The bibliography, in the form of a supplementary Excel spreadsheet with links to each paper, is organized by topic, but can be sorted by first author, order of publication, specific Oman Drilling Project boreholes, and other factors.

An explicit expression for the retention factor and velocity dependency of the mobile zone mass transfer band broadening in packed spheres beds used in liquid chromatography

The present study proposes a ready-to-use analytical expression to calculate the mobile zone mass transfer contribution (hCm) in packed bed columns. For this purpose, first high-accuracy computations of the band broadening in a perfectly ordered sphere array (fcc-arrangement, external porosity ε=0.40) were made using computational fluid dynamics (CFD), covering a broad range of zone retention factors (2≤k’’≤18) and reduced velocities (0≤νi≤48). Subsequently, these data were used to determine the value of the geometrical constants in a number of possible analytical expressions for the hCm-contribution. This fitting exercise showed the traditional literature approach, using the Wilson-Geankoplis correlation to calculate the dimensionless Sherwood (Sh) number for the mass transfer, leads to fitting errors on the hCm-term as large as 150%. Instead, a new correlation for Sh is established. In addition, we also explored the difference in fitting accuracy between hCm-expressions based on either a plug-flow or a laminar flow profile assumption. Surprisingly, no significant difference in fitting accuracy between both assumptions was observed. Finally, a best-fit analytical expression is proposed that can represent the CFD-computed band broadening data with an average absolute fitting error of Δh=0.005, corresponding to a relative error of 2.5% on the hCm-term and of only 0.3% on the total plate height in a perfectly ordered sphere packing. Defining the presently investigated fcc-ordered sphere array with external porosity=40% as the reference geometry for a perfect sphere packing, the established expression can be used as a new yardstick expression against which the degree of eddy-dispersion can be measured.

Mathematical Modelling of Mass Transfer in Zones of Complete and Incomplete Saturation under the Action of Systematic Combined Drainage

The mathematical model of a processes mass transfer in saturated and unsaturated porous media to the filtertrap in isothermal conditions to the system of vertical drains is presented. The numerical solution of the respective boundary value problem was obtained by the method of finite differences using the numerical method of conformal mappings in an inverse statement.

Electrolytic fluid speciation by Gibbs energy minimization and implications for subduction zone mass transfer

The number of solute species required to describe the thermodynamic behavior of electrolytic fluids is a hindrance to the incorporation of aqueous geochemistry in petrological Gibbs energy minimization procedures. An algorithm is developed to overcome this problem. Beginning from the solute-free limit, chemical potentials, and phase stability are determined by minimization, the solute speciation and bulk fluid properties consistent with these chemical potentials are then computed and the procedure repeated until the chemical potentials converge. Application of the algorithm to a model for metamorphism of subducted sediment shows that accounting for solute chemistry does not change the conclusion based on molecular fluid models that a pervasive water flux from the subjacent mantle is required to explain island-arc carbon emissions by fluid-mediated slab decarbonation. This putative flux would deplete the sediment in potassium, limiting the capacity of the slab to transport water to greater depth and rendering it refractory to melting.

Static Mixers for Water Ozonation: Mechanisms, Advantages, Types, Applications and Mathematical Modelling - A Review

Static mixers have been successfully employed in water and wastewater treatment, particularly in water ozonation for disinfection and oxidation purposes. Producing higher concentration of ozone requires new contactors that operate efficiently at low gas/liquid ratio. The Kenics static mixer can meet these requirements and therefore enhance the ozone mass transfer rate [1]. This paper summarise the field of static mixers in water ozonation including comparison with other gas/liquid contactors. This study also reviews recent conceptual and technological innovations in static mixers: Current industrial applications, advantages and types are discussed, focusing on mixing and mass transfer performance. The work is complemented by a review of mixing fundamentals, knowledge of which allows the development of mathematical models which are crucial for the analysis of experimental data. Moreover, it reviews the recent advances of the mathematical models of zone mass transfer in static mixer: back flow cell model (BFCM), Axial diffusion model (ADM) and the continuous flow stirred tanks in series (CFSTR’s in series). Both the steady state and the transient BFCMs were validated with experimental data by Tizaoui and Zhang and it was found that they accurately predicted the outlet ozone concentration and the impulse RTD curves of gas-liquid system respectively along height of the static mixer[2].

Dynamic Cr(III) uptake by Macrocystis pyrifera and Undaria pinnatifida biomasses

Background: The increased industrial activity has resulted in the discharge of large amount of pollutants including non-degradable metals into the environment. Chromium is produced in several industrial processes and it can be found in the environment in two stable oxidation states, Cr(VI) and Cr(III). Cr(VI) is more hazardous due to its carcinogenic and mutagenic effects on living organisms. Although much less toxic, Cr(III) can also exert genotoxic effects under prolonged or severe exposure. It can be separated from the solution by precipitation but biosorption using brown algae seems to be an effective and sustainable treatment technique owing to its cost-effectiveness and environmental friendly characteristics. Macrocystis pyrifera and Undaria pinnatifida are two marine brown macroalgae with high capability of removing heavy metals including Cr(III) in batch mode of operation. In this work packed bed biosorption of Cr(III) by M. pyrifera and U. pinnatifida biomasses was evaluated. Results: The shapes of the breakthrough curves were rather different for each biomaterial. Parameters like the breakthrough time ( t b ) and zone mass transfer ( MTZ ) showed that U. pinnatifida has greater affinity for Cr(III). The maximum adsorption capacity at the exhaustion operating time ( t e ) demonstrated that M. pyrifera has higher retention capacity of Cr(III). The experimental data were fitted to Thomas, Yoon-Nelson and Dose-Response models. The best correlation coefficient (0.94 or 0.96) was obtained with Dose-Response that accurately describes the uptake behaviour of Cr(III) on the seaweed biomasses under different experimental conditions. The FT-IR spectra evidenced that Cr(III) adsorption occurred mainly by interaction between metal and carboxylate groups present on both the seaweed surfaces. Conclusions: M. pyrifera and U. pinnatifida biomasses are efficient biosorbents for Cr(III) adsorption under a continuous mode of operation although differences between uptake capacities suggest different mechanisms involved in the biosorption.

Modeling of lead (II) biosorption by residue of allspice in a fixed-bed column

Residue of allspice (Pimenta dioica L. Merrill) obtained as a by-product from the essential oil supercritical extraction process, has been evaluated as a biosorbent for removing lead (II) from aqueous solutions in batch studies, but not in a practical system like a fixed bed column [12,13]. In this paper, the effects of flow rate (20 and 40mL/min), bed depth (8 and 15cm) and influent lead concentration (15 and 25mg/L) on the adsorption capacity of the residue of allspice in a fixed-bed column were investigated. The highest adsorption capacity (99.2%) on a 15mg/L Pb(II) solution was achieved within a flow rate of 20mL/min and a bed depth of 15cm. The experimental data obtained from the adsorption process was successfully correlated with the Thomas, Adams–Bohart, Yoon–Nelson, Bed Depth Service Time (BDST), and Dose Response models. A rigorous model based on the differential balance mass transfer was also used to describe the adsorption process in the column. The results of the parameters zone mass transfer, diffusion and mass transfer coefficients obtained with modeling the continuous process could be applied to scale up the process to an actual industrial column.

New insights in the velocity dependency of the external mass transfer coefficient in 2D and 3D porous media for liquid chromatography

Numerical calculations of the mobile zone mass transfer rate in a variety of ordered 2D and 3D structures are presented. These calculations are in line with earlier theoretical and experimental findings made in the field of chemical engineering and suggest that the Sherwood-number (Shm) appearing in the mobile phase mass transfer term of the general plate height expression of liquid chromatography is not correctly predicted by the Wilson–Geankoplis – or the Kataoka – or the penetration model expression that have been used up to now to in the field of LC, and that at least more research is needed before these expressions can be continued to be used with confidence. The aforementioned expressions were obtained by neglecting the effect of axial dispersion on the mass transfer process, and it seems that they therefore underestimate the true Shm-number by a factor of 2–5 around the minimum of the van Deemter-curve. New correlations describing the variation of the Shm-coefficient as a function of the reduced velocity for a number of other packing geometries (tetrahedral monolith, 2D pillar array) are proposed. These correlations are in agreement with earlier theoretical and experimental studies showing that at low velocities the local-driving force-based Shm-value is of the order of 10–20 in a packed bed column with an external porosity on the order of 35–40%.

A six-zone simulation model for HCCI engines with a non-segregated solver of zone state

A new six-zone simulation model for the calculation of changes in an HCCI engine has been developed and tested. The model uses comprehensive chemical kinetics and a non-sequential solver of zone states. This means that the state vector comprises the states in all zones, and that the changes in states in all zones are calculated simultaneously. In this manner, physical accuracy during the calculation of a new state is maintained at the expense of the calculation time. The model comprises the wall heat transfer, zone heat transfer and zone mass transfer as means of zone interactions. The cylinder is divided into two central zones, three boundary layer zones and one crevice zone. Since the model calculates only the high pressure part of an engine cycle, it has been connected with the cycle simulation software AVL Boost. In this way, a relatively easy-to-use, higher accuracy, simulation tool for HCCI engines has been obtained. The model was tested by comparing simulation results with experimental ones. The comparison was made with a single cylinder engine running on isooctane. The calculated pressure and net rate of heat release correspond to the experimental results very well in the entire operating region. By using the six-zone simulation model, a big improvement, compared to the single zone simulation, is obtained in operating points where combustion efficiency is over 90%. Results of emissions of unburned HC and CO show that predictions of these species are greatly improved, but it has also been noticed that these emissions are still slightly underpredicted. Predictions of emissions that come from crevice regions are good, but emissions that come from the corners of boundary layers are not captured very well. A detailed description of the simulation model is given, and validation results and possibilities of a further development are discussed.

A numerical study of the assumptions underlying the calculation of the stationary zone mass transfer coefficient in the general plate height model of chromatography in two-dimensional pillar arrays

The present study investigates the validity of one of the key assumptions underlying the general plate height model of chromatography, i.e., the presumed independency of the individual band broadening contributions. More precisely, it is investigated under which conditions the mass transfer inside the stationary zone (e.g., porous pillars) is independent from the axial transport of species outside this zone, and how strongly any such dependency would affect the validity of the general plate height model of chromatography. For this purpose, detailed calculations of the species concentration distribution inside and outside the porous pillars of a computer-mimic of a porous pillar array column have been made. These simulations revealed a clear interplay between the mass transfer inside and outside the pillars, manifesting itself as an asymmetry of the species concentration distribution inside the pillars. The latter is in disagreement with the basic assumption used to calculate the value of the C s-term of the general plate height model. The asymmetry-effect is largest at low reduced velocities, high retention factors and high intra-pillar diffusion coefficients. Fortunately, these are conditions where the C s-term is relatively small, which might explain why the general plate height model of chromatography (and based on the symmetry assumption) can represent the band broadening in a porous pillar array within an accuracy on the order of some 1–2%.

Bayesian modeling of the assimilative capacity component of nutrient total maximum daily loads

Implementing stream restoration techniques and best management practices to reduce nonpoint source nutrients implies enhancement of the assimilative capacity for the stream system. In this paper, a Bayesian method for evaluating this component of a total maximum daily load (TMDL) load capacity is developed and applied. The joint distribution of nutrient retention metrics from a literature review of 495 measurements was used for Monte Carlo sampling with a process transfer function for nutrient attenuation. Using the resulting histograms of nutrient retention, reference prior distributions were developed for sites in which some of the metrics contributing to the transfer function were measured. Contributing metrics for the prior include stream discharge, cross‐sectional area, fraction of storage volume to free stream volume, denitrification rate constant, storage zone mass transfer rate, dispersion coefficient, and others. Confidence of compliance (CC) that any given level of nutrient retention has been achieved is also determined using this approach. The shape of the CC curve is dependent on the metrics measured and serves in part as a measure of the information provided by the metrics to predict nutrient retention. It is also a direct measurement, with a margin of safety, of the fraction of export load that can be reduced through changing retention metrics. For an impaired stream in western Oklahoma, a combination of prior information and measurement of nutrient attenuation was used to illustrate the proposed approach. This method may be considered for TMDL implementation.

Diffusion inside particles in HPLC columns

The stationary zone mass transfer coefficient (C5) in the reduced plate height equation has been determined experimentally for an adsorption and a partition system generated on the same column. Longitudinal diffusion terms (B-terms) were measured on these systems by applying the arrested elution method.