Analysis of commercial general engineering finite element software in electrochemical simulations

Versatile Tools for Understanding Electrosynthetic Mechanisms

Electrosynthesis is a popular, green alternative to traditional organic methods. Understanding the mechanisms is not trivial yet is necessary to optimize reaction processes. To this end, a multitude of analytical tools is available to identify and quantitate reaction products and intermediates. The first portion of this review serves as a guide that underscores electrosynthesis fundamentals, including instrumentation, electrode selection, impacts of electrolyte and solvent, cell configuration, and methods of electrosynthesis. Next, the broad base of analytical techniques that aid in mechanism elucidation are covered in detail. These methods are divided into electrochemical, spectroscopic, chromatographic, microscopic, and computational. Technique selection is dependent on predicted reaction pathways and electrogenerated intermediates. Often, a combination of techniques must be utilized to ensure accuracy of the proposed model. To conclude, future prospects that aim to enhance the field are discussed.

Modelling of packed bed and coated wall microreactors for methanol steam reforming for hydrogen production

A Computational Fluid Dynamics (CFD) study has been conducted to assess the performance of packed bed and coated wall microreactors for the steam reforming of methanol with a CuO/ZnO/Al₂O₃ based catalyst (BASF F3-01). The results obtained were compared to experimental data from the literature to assess the validity and robustness of the models, and a good validation has been obtained. The performance of the packed bed and coated wall microreactors is similar at a constant reforming temperature. It was found that methanol conversion is enhanced with increasing temperature, residence time, steam to methanol ratio, and catalyst coating thickness. Furthermore, internal and external mass transfer phenomena were investigated using the models, and it was found that there were no internal and external mass transfer resistances for this reactor configuration. Further studies demonstrated that larger catalyst pellet sizes led to the presence of internal mass transfer resistance, which in turn causes lower methanol conversions. The CFD models have exhibited a sound agreement with the experimental data, hence they can be used to predict the steam reforming of methanol in microreactors.

A Computational Fluid Dynamics (CFD) study has been conducted to assess the performance of packed bed and coated wall microreactors for the steam reforming of methanol with a CuO/ZnO/Al₂O₃ based catalyst (BASF F3-01).

Image-based modeling of kidney branching morphogenesis reveals GDNF-RET based Turing-type mechanism and pattern-modulating WNT11 feedback

Branching patterns and regulatory networks differ between branched organs. It has remained unclear whether a common regulatory mechanism exists and how organ-specific patterns can emerge. Of all previously proposed signalling-based mechanisms, only a ligand-receptor-based Turing mechanism based on FGF10 and SHH quantitatively recapitulates the lung branching patterns. We now show that a GDNF-dependent ligand-receptor-based Turing mechanism quantitatively recapitulates branching of cultured wildtype and mutant ureteric buds, and achieves similar branching patterns when directing domain outgrowth in silico. We further predict and confirm experimentally that the kidney-specific positive feedback between WNT11 and GDNF permits the dense packing of ureteric tips. We conclude that the ligand-receptor based Turing mechanism presents a common regulatory mechanism for lungs and kidneys, despite the differences in the molecular implementation. Given its flexibility and robustness, we expect that the ligand-receptor-based Turing mechanism constitutes a likely general mechanism to guide branching morphogenesis and other symmetry breaks during organogenesis.

Many organs develop through branching morphogenesis, but whether the underlying mechanisms are shared is unknown. Here, the authors show that a ligand-receptor based Turing mechanisms, similar to that observed in lung development, likely underlies branching morphogenesis of the kidney.

Design and Finite Element Model of a Microfluidic Platform with Removable Electrodes for Electrochemical Analysis

A microfluidic platform for hydrodynamic electrochemical analysis was developed, consisting of a poly(methyl methacrylate) chip and three removable electrodes, each housed in 1/16" OD polyether ether ketone tube which can be removed independently for polishing or replacement. The working electrode was a 100-μm diameter Pt microdisk, located flush with the upper face of a 150 μm × 20 μm × 3 cm microchannel, smaller than previously reported for these types of removable electrodes. A commercial leak-less reference electrode was utilized, and a coiled platinum wire was the counter electrode. The platform was evaluated electrochemically by oxidizing a potassium ferrocyanide solution at the working electrode, and a typical limiting current behavior was observed after running linear sweep voltammetry and chronoamperometry, with flow rates 1-6 μL/min. While microdisk channel electrodes have been simulated before using a finite difference method in an ideal 3D geometry, here we predict the limiting current using finite elements in COMSOL Multiphysics 5.3a, which allowed us to easily explore variations in the microchannel geometry that have not previously been considered in the literature. Experimental and simulated currents showed the same trend but differed by 41% in simulations of the ideal geometry, which improved when channel and electrode imperfections were included.

Electrochemical impedance spectroscopy and finite element analysis modeling of a 4-electrode humidity sensor for natural gas transportation pipelines

Reliable corrosion monitoring of natural gas transmission lines is a major tool providing a foundation for safe management of natural gas infrastructures. Through the development of membrane-based electrochemical sensors which are able to function in low-conductivity gas environments, corrosion monitoring practices can be further strengthened by real-time monitoring of key risk factors such as relative humidity and corrosion rates of corrodible structures. In this work, we demonstrate and validate how a 4-electrode conductivity sensor can provide a means to monitor relative humidity in gases via electrochemical impedance spectroscopy through finite element analysis (FEA). For a relative humidity range of 5%-55%, the impedance response varied from 1 kΩ to 66 kΩ, showing a high sensitivity for gas humidity. To confirm that the measured impedance values reliably interpreted relative humidity, it was found that precise estimation of the sensor's cell constant was needed. FEA was used to assess how the cell constant depended on the electrode geometry, membrane geometry, and electrode placement within the sensor. Through this approach, assumptions about the characteristic area and length were validated using electrolyte equipotential and current density vector mapping. This reduced possible cell constant uncertainties by 70%. With a cell constant of 14.84 cm^-1, obtained via FEA, membrane conductivity values were in good agreement with published data.

Effect of Electrode Shape and Flow Conditions on the Electrochemical Detection with Band Microelectrodes

In this work, we report the analysis of the electrochemical detection of electroactive species with band microelectrodes that operate under controlled convection. The study focuses on the determination of the collection efficiency of the analyte as a function of inlet flow velocity and microband geometry (inlaid, bumped and recessed), also providing a straightforward method for the theoretical determination of the lower detection limit. The analysis has been carried out by simulating the dimensionless mass transport with the finite element method, delivering the stationary limiting current density. Simulations have been performed on systems consisting of single and double band electrodes to investigate the trail effect on the electrochemical detection. We show that the obtained dimensionless results can be easily turned into dimensional data, providing a tool for the design of devices. The proposed method is general and can easily be extended to systems with different geometry.

A hydrogel pen for electrochemical reaction and its applications for 3D printing

A hydrogel pen consisting of a microscopic pyramid containing an electrolyte offers a localized electroactive area on the nanometer scale via controlled contact of the apex with a working electrode. The hydrogel pen merges the fine control of atomic force microscopy with non-linear diffusion of an ultramicroelectrode, producing a faradaic current that depends on the small electroactive area. The theoretical and experimental investigations of the mass transport behavior within the hydrogel reveal that the steady-state current from the faradaic reaction is linearly proportional to the deformed length of the hydrogel pen by contact, i.e. signal transduction of deformation to an electrochemical signal, which enables the fine control of the electroactive area in the nanometer-scale regime. Combined with electrodeposition, localized electrochemistry of the hydrogel pen results in the ability to fabricate small sizes (110 nm in diameter), tall heights (up to 30 μm), and arbitrary structures, thereby indicating an additive process in 3 dimensions by localized electrodeposition.

An interplay of geometry and signaling enables robust lung branching morphogenesis

Early branching events during lung development are stereotyped. Although key regulatory components have been defined, the branching mechanism remains elusive. We have now used a developmental series of 3D geometric datasets of mouse embryonic lungs as well as time-lapse movies of cultured lungs to obtain physiological geometries and displacement fields. We find that only a ligand-receptor-based Turing model in combination with a particular geometry effect that arises from the distinct expression domains of ligands and receptors successfully predicts the embryonic areas of outgrowth and supports robust branch outgrowth. The geometry effect alone does not support bifurcating outgrowth, while the Turing mechanism alone is not robust to noisy initial conditions. The negative feedback between the individual Turing modules formed by fibroblast growth factor 10 (FGF10) and sonic hedgehog (SHH) enlarges the parameter space for which the embryonic growth field is reproduced. We therefore propose that a signaling mechanism based on FGF10 and SHH directs outgrowth of the lung bud via a ligand-receptor-based Turing mechanism and a geometry effect.

Feedback, receptor clustering, and receptor restriction to single cells yield large Turing spaces for ligand-receptor-based Turing models

Turing mechanisms can yield a large variety of patterns from noisy, homogenous initial conditions and have been proposed as patterning mechanism for many developmental processes. However, the molecular components that give rise to Turing patterns have remained elusive, and the small size of the parameter space that permits Turing patterns to emerge makes it difficult to explain how Turing patterns could evolve. We have recently shown that Turing patterns can be obtained with a single ligand if the ligand-receptor interaction is taken into account. Here we show that the general properties of ligand-receptor systems result in very large Turing spaces. Thus, the restriction of receptors to single cells, negative feedbacks, regulatory interactions among different ligand-receptor systems, and the clustering of receptors on the cell surface all greatly enlarge the Turing space. We further show that the feedbacks that occur in the FGF10-SHH network that controls lung branching morphogenesis are sufficient to result in large Turing spaces. We conclude that the cellular restriction of receptors provides a mechanism to sufficiently increase the size of the Turing space to make the evolution of Turing patterns likely. Additional feedbacks may then have further enlarged the Turing space. Given their robustness and flexibility, we propose that receptor-ligand-based Turing mechanisms present a general mechanism for patterning in biology.

Electroanalysis at the nanoscale

This article reviews the state of the art of silicon chip-based nanoelectrochemical devices for sensing applications. We first describe analyte mass transport to nanoscale electrodes and emphasize understanding the importance of mass transport for the design of nanoelectrode arrays. We then describe bottom-up and top-down approaches to nanoelectrode fabrication and integration at silicon substrates. Finally, we explore recent examples of on-chip nanoelectrodes employed as sensors and diagnostics, finishing with a brief look at future applications.

Inter-dependent tissue growth and Turing patterning in a model for long bone development

The development of long bones requires a sophisticated spatial organization of cellular signalling, proliferation, and differentiation programs. How such spatial organization emerges on the growing long bone domain is still unresolved. Based on the reported biochemical interactions we developed a regulatory model for the core signalling factors IHH, PTCH1, and PTHrP and included two cell types, proliferating/resting chondrocytes and (pre-)hypertrophic chondrocytes. We show that the reported IHH-PTCH1 interaction gives rise to a Schnakenberg-type Turing kinetics, and that inclusion of PTHrP is important to achieve robust patterning when coupling patterning and tissue dynamics. The model reproduces relevant spatiotemporal gene expression patterns, as well as a number of relevant mutant phenotypes. In summary, we propose that a ligand-receptor based Turing mechanism may control the emergence of patterns during long bone development, with PTHrP as an important mediator to confer patterning robustness when the sensitive Turing system is coupled to the dynamics of a growing and differentiating tissue. We have previously shown that ligand-receptor based Turing mechanisms can also result from BMP-receptor, SHH-receptor, and GDNF-receptor interactions, and that these reproduce the wildtype and mutant patterns during digit formation in limbs and branching morphogenesis in lung and kidneys. Receptor-ligand interactions may thus constitute a general mechanism to generate Turing patterns in nature.

Kidney branching morphogenesis under the control of a ligand-receptor-based Turing mechanism

The main signalling proteins that control early kidney branching have been defined. Yet the underlying mechanism is still elusive. We have previously shown that a Schnakenberg-type Turing mechanism can recapitulate the branching and protein expression patterns in wild-type and mutant lungs, but it is unclear whether this mechanism would extend to other branched organs that are regulated by other proteins. Here, we show that the glial cell line-derived neurotrophic factor-RET regulatory interaction gives rise to a Schnakenberg-type Turing model that reproduces the observed budding of the ureteric bud from the Wolffian duct, its invasion into the mesenchyme and the observed branching pattern. The model also recapitulates all relevant protein expression patterns in wild-type and mutant mice. The lung and kidney models are both based on a particular receptor-ligand interaction and require (1) cooperative binding of ligand and receptor, (2) a lower diffusion coefficient for the receptor than for the ligand and (3) an increase in the receptor concentration in response to receptor-ligand binding (by enhanced transcription, more recycling or similar). These conditions are met also by other receptor-ligand systems. We propose that ligand-receptor-based Turing patterns represent a general mechanism to control branching morphogenesis and other developmental processes.

Digit patterning during limb development as a result of the BMP-receptor interaction

Turing models have been proposed to explain the emergence of digits during limb development. However, so far the molecular components that would give rise to Turing patterns are elusive. We have recently shown that a particular type of receptor-ligand interaction can give rise to Schnakenberg-type Turing patterns, which reproduce patterning during lung and kidney branching morphogenesis. Recent knockout experiments have identified Smad4 as a key protein in digit patterning. We show here that the BMP-receptor interaction meets the conditions for a Schnakenberg-type Turing pattern, and that the resulting model reproduces available wildtype and mutant data on the expression patterns of BMP, its receptor, and Fgfs in the apical ectodermal ridge (AER) when solved on a realistic 2D domain that we extracted from limb bud images of E11.5 mouse embryos. We propose that receptor-ligand-based mechanisms serve as a molecular basis for the emergence of Turing patterns in many developing tissues.

Branch mode selection during early lung development

Many organs of higher organisms, such as the vascular system, lung, kidney, pancreas, liver and glands, are heavily branched structures. The branching process during lung development has been studied in great detail and is remarkably stereotyped. The branched tree is generated by the sequential, non-random use of three geometrically simple modes of branching (domain branching, planar and orthogonal bifurcation). While many regulatory components and local interactions have been defined an integrated understanding of the regulatory network that controls the branching process is lacking. We have developed a deterministic, spatio-temporal differential-equation based model of the core signaling network that governs lung branching morphogenesis. The model focuses on the two key signaling factors that have been identified in experiments, fibroblast growth factor (FGF10) and sonic hedgehog (SHH) as well as the SHH receptor patched (Ptc). We show that the reported biochemical interactions give rise to a Schnakenberg-type Turing patterning mechanisms that allows us to reproduce experimental observations in wildtype and mutant mice. The kinetic parameters as well as the domain shape are based on experimental data where available. The developed model is robust to small absolute and large relative changes in the parameter values. At the same time there is a strong regulatory potential in that the switching between branching modes can be achieved by targeted changes in the parameter values. We note that the sequence of different branching events may also be the result of different growth speeds: fast growth triggers lateral branching while slow growth favours bifurcations in our model. We conclude that the FGF10-SHH-Ptc1 module is sufficient to generate pattern that correspond to the observed branching modes.

Most organs of higher organisms, such as the vascular system, lung, kidney, pancreas, liver and glands, are heavily branched structures. The branching process during lung development has been studied in great detail and is remarkably stereotyped. The branched tree is generated by the sequential, non-random use of three geometrically simple modes of branching. While the branching sequence is identical in mice of identical genetic background it differs between mouse strains. This suggests that the positioning of branch points and the type of branching sensitively depends on information encoded in the genome. Encoding every branching point independently in the genome would require a large number of genes, and it is more likely that a recursive, self-organized process exists that determines the patterning. While many regulatory molecules have been identified an integrated understanding of the regulatory network (program) is missing. Based on available experimental data we have developed a model for lung branching. The model correctly predicts branching phenotypes in mutants and suggests that also the growth speed of the lung tip can affect the positioning and type of the next branching event.