Flow Solution Research Articles

Nonlinear dynamics of dissipative water conveying SWCNT/MWCNT/Ferro nanofluid subject to radiation: Thermal analysis by linear slope regression

Carbon nanotubes have gained significant attention due to their unique properties like small dimensions, high thermal conductivity, and unique architecture. These nanotubes have enormous potential in various fields such as nanomedicine, mechanical compound materials, sensor devices, bio-sensors, and many other applications. The present study investigates the impact of adding nanoparticles such as iron oxide (Fe3O4), single-walled carbon nanotubes (SWCNT), and multi-walled carbon nanotubes (MWCNT) on magnetohydrodynamics (MHD) oscillatory water-based flow over a porous medium. The aim is to examine the effect of heat and mass transfer rate and radiative viscous dissipation that interacts with Fe3O4 nanoparticles and carbon nanotubes. The governing equations of the dynamic nanofluid systems are transformed into a set of coupled nonlinear partial differential equations through suitable dimensionless transformations and further converted into ordinary differential equations by taking appropriate solutions for oscillatory-type nanofluid flow. The homotopy perturbation method is applied to solve the governing equations with oscillatory boundary conditions and the solution is also compared with the numerical solver bvp4c. The rate of increase in the temperature and Heat Transfer are computed by the linear slope regression method and results are computed for nanoparticles SWCNT, MWCNT, and Ferro. Also, Skin friction and rate of heat transfer are computed and compared for the nanoparticles with varying Peclet and Eckert numbers. The velocity profile and temperature profile of SWCNT/MWCNT/Ferro nanofluids are being compared. The heat transfer rate is observed to be high for Ferro nanoparticles compared to SWCNT and MWCNT.

Legendre wavelet integration operational matrix method for the numerical solution of unsteady MHD nanofluid flow between moving parallel plates

This study proposes a novel method based on Legendre wavelet integration operational matrix for solving a system of nonlinear ODE’s to model the two-phase, unsteady nanofluid flow and heat transfer between parallel plates in presence of magnetic field. To validate the applicability of proposed method, system of nonlinear BVP with exact solutions is employed as a test problem. Test problem results are compared with exact solution, and other numerical methods. The governing equations were then changed using similarity transformation into a set of nonlinear ODE’s. . Following this, the LWOMM is applied for the proposed problem. Findings demonstrated that, for a constant Reynolds number, skin friction coefficient value increases with rising Hartmann and squeezing numbers. Furthermore, it is demonstrated that Eckert number is a reducing function of the squeeze number and Nusselt number is an increasing function of Hartmann number.

Enhanced Electroactive Phases of Poly(vinylidene Fluoride) Fibers for Tissue Engineering Applications.

Nanofibrous materials generated through electrospinning have gained significant attention in tissue regeneration, particularly in the domain of bone reconstruction. There is high interest in designing a material resembling bone tissue, and many scientists are trying to create materials applicable to bone tissue engineering with piezoelectricity similar to bone. One of the prospective candidates is highly piezoelectric poly(vinylidene fluoride) (PVDF), which was used for fibrous scaffold formation by electrospinning. In this study, we focused on the effect of PVDF molecular weight (180,000 g/mol and 530,000 g/mol) and process parameters, such as the rotational speed of the collector, applied voltage, and solution flow rate on the properties of the final scaffold. Fourier Transform Infrared Spectroscopy allows for determining the effect of molecular weight and processing parameters on the content of the electroactive phases. It can be concluded that the higher molecular weight of the PVDF and higher collector rotational speed increase nanofibers' diameter, electroactive phase content, and piezoelectric coefficient. Various electrospinning parameters showed changes in electroactive phase content with the maximum at the applied voltage of 22 kV and flow rate of 0.8 mL/h. Moreover, the cytocompatibility of the scaffolds was confirmed in the culture of human adipose-derived stromal cells with known potential for osteogenic differentiation. Based on the results obtained, it can be concluded that PVDF scaffolds may be taken into account as a tool in bone tissue engineering and are worth further investigation.

Solute flow and particle transport in aquatic ecosystems: A review on the effect of emergent and rigid vegetation

In-channel vegetation is ubiquitous in aquatic environments and plays a critical role in the fate and transport of solutes and particles in aquatic ecosystems. Recent studies have advanced our understanding of the role of vegetation in solute flow and particle transport in aquatic ecosystems. This review summarizes these papers and discusses the impacts of emergent and rigid vegetation on the surface flow, the advection and dispersion of solutes, suspended load transport, bedload transport, and hyporheic exchange. The two competing effects of emergent vegetation on the above transport processes are discussed. On the one hand, emergent vegetation reduces mean flow velocity at the same surface slope, which reduces mass transport. On the other hand, at the same mean flow velocity, vegetation generates turbulence, which enhances mass transport. Mechanistic understanding of these two competing effects and predictive equations derived from laboratory experiments are discussed. Predictive equations for the mean flow velocity and turbulent kinetic energy inside an emergent vegetation canopy are derived based on force and energy balance. The impacts of emergent vegetation on the advection-dispersion process, the suspended load and bedload transport, and the hyporheic exchange are summarized. The impacts of other vegetation-related factors, such as vegetation morphology, submergence, and flexibility, are briefly discussed. The role of vegetation in transporting other particles, such as micro- and macro-plastics, is also briefly discussed. Finally, suggestions for future research directions are proposed to advance the understanding of the dynamic interplays among natural vegetation, flow dynamics, and sedimentary processes.

How borehole wall elasticity affects wellbore storage capacity in periodic hydraulic tests

Characterizing fluid transport and pore pressure diffusion is key for monitoring and understanding many natural (e.g., seismically active zones and volcanic systems) and engineered environments (e.g., enhanced geothermal reservoirs and CO2 underground storage). Borehole hydraulic testing allows for inferring relevant properties of the probed subsurface volume, such as, for example, its transmissivity and diffusivity, assessing the governing flow regime as well as detecting the presence of hydraulic boundaries. Periodic hydraulic tests (PHT) achieve these objectives using an oscillatory fluid injection procedure while measuring the fluid pressure response in monitoring boreholes. The relevant information on the pressure diffusion process occurring in a probed formation is retrieved from the phase shifts and amplitude ratios between the flow rate and the interval pressure. In general, the interpretation of PHT data relies on the assumption that the pressure diffusion process is largely unaffected by the deformation of the probed rock volume. To assess this assumption, we present a conceptual PHT model based on the theory of poroelasticity to investigate the role played by hydromechanical coupling (HMC) effects during PHT and to assess whether and to what extent additional mechanical information can be extracted from these tests. These effects include the influence of the borehole wall deformation on the wellbore storage coefficient Sw, which quantifies the difference between the injected flow rates and those actually entering the porous formation. We show that, in homogeneous formations, the commonly taken approach based on the uncoupled diffusion solution for radial flow reproduces the results of our HMC model. However, neglecting the deformation effect of the borehole wall on the storage capacity of the system during injection can lead to underestimations of both transmissivity and diffusivity, particularly at shorter oscillation periods. We present analytical expressions for the borehole wall deformation contribution to Sw, which depends on the shear modulus and does not change with the oscillatory period. We show that it is possible to obtain the effective Sw along with the transmissivity and diffusivity using observations at various oscillatory periods. In the presence of hydraulic boundaries, such as no-flow or constant-pressure boundaries, at a given distance from the injection borehole, Sw becomes period-dependent, introducing apparent variations in the inferred shear modulus of the formation if the associated HMC effects are not accounted for. Our results thus highlight the importance of accounting for HMC effects in PHT data interpretation, not only to reliably and accurately characterize and monitor hydraulic properties but also to fully exploit the potential of PHT to provide additional information on the mechanical behaviour of the probed rock volume.

Effect of an inclined magnetic field on dispersion of solute in a pulsatile flow through a channel of absorptive porous walls

The present investigation gives an insight to comprehend the complex mechanism of species transport through porous walls, which has applications for crude oil refining, oil reservoir engineering, and separation of metal from fluids. The paper analyzes the impact of an inclined magnetic field on mass transport phenomena of solute through an unsteady, viscous, incompressible, and electrically conducting fluid flowing between two parallel plates. Both plates are permeable, and the flow is driven by a periodic pressure gradient. At both channel walls, the first order boundary reaction is applied. The governing time depending advection and diffusion equation is solved numerically based on Aris's method of moments. To determine the axial mean concentration distribution of solute, the first four central moments are used in a Hermite polynomial representation. It is significant to note that the dispersion of tracer is more significant for the low frequencies rather than the high frequencies. The behavior of the dispersion process of the tracer is studied for various flow parameters such as the angle of inclination of the magnetic field (α), Hartmann number (M), absorption parameter (β), suction Reynolds number (R), injection Reynolds number (R′), Womersley number (ω), and dispersion time (t) for both purely oscillatory and combined flows. It is significant to note that with the increment of R, α, and M, the amplitude of the dispersion coefficient of the solute reduces. On the other hand, an opposite phenomenon is observed for R′. It is seen that the transport coefficient moves cyclically with a double frequency period for all values of R and R′. Also, it is found that the peak of the mean concentration distribution enhances with the increment of α and M because the flow velocity decreases.

Analytical solutions for unsteady fractional maxwell nanofluid flow and mass transfer between two rigid spheres with periodic oscillations

In this paper, we develop axisymmetric squeeze flow and mass transfer of incompressible Maxwell nanofluid between two rigid spheres. The position of the boundary between the two rigid spheres varies periodically with time and space, and the unsteady magnetic field is considered. Analytical solutions are derived for velocity and concentration by using the method of Laplace integral variation. In addition, the radial velocity and concentration distributions are imaged and the relevant parameters are analyzed.

Investigation of physics-informed deep learning for the prediction of parametric, three-dimensional flow based on boundary data

The placement of temperature sensitive and safety-critical components is crucial in the automotive industry. It is therefore inevitable, even at the design stage of new vehicles, that these components are assessed for potential safety issues. However, with increasing number of design proposals, risk assessment using Computational Fluid Dynamics (CFD) quickly becomes expensive. We therefore present a parameterized surrogate model for the prediction of three-dimensional flow fields in aerothermal vehicle simulations. The proposed physics-informed neural network (PINN) design is aimed at learning families of flow solutions according to a geometric variation. The novelty of our method compared to existing works in the field of PINN lies in the extension of parametric flow prediction to three-dimensional space by applying a mini-batch based Quasi-Newton optimization. We contribute a parametric minibatch training algorithm which enables the utilization of the large datasets necessary for the three-dimensional flow modeling. Further, we introduce a continuous resampling algorithm that allows to represent domain variations, while operating on one static dataset of reduced size. In scope of this work, we could show that our nondimensional, multivariate scheme can be efficiently extended to predict the velocity and pressure distribution in three-dimensional space for different design scenarios and geometric scales. Every feature of our methodology is tested individually and verified against conventional CFD simulations. Finally, we apply our proposed method in context of an exemplary real-world automotive application.

Multiparameter optimization of non-thermal plasma-driven synthesis of carbohydrate-stabilized rhenium nanoparticles towards enhancement of their catalytical activity for reduction of nitroaromatic compounds

This study aims to optimize the synthesis of carbohydrate-stabilized rhenium nanoparticles (ReNPs) utilizing cold atmospheric pressure plasma (CAPP), specifically direct current atmospheric pressure glow discharge (dc-APGD), hypothesizing that controlling synthesis parameters will enhance catalytic efficiency in the reduction of nitroaromatic compounds (NACs). The dc-APGD system operated in flowing liquid cathode (FLC-dc-APGD) and flowing liquid anode (FLA-dc-APGD) modes. Design of experiments (DOE) and response surface methodology (RSM) were employed for the first time to optimize ReNPs synthesis. This included optimizing the concentration of ReO4- in ReNPs precursor solution, solution flow rate as well as discharge current. ReNPs were characterized using high-resolution transmission electron microscopy (HRTEM), dynamic light scattering (DLS), and X-Ray photoelectron spectroscopy (XPS). In turn, optical emission spectroscopy (OES) was employed for the identification of reactive species generated in plasma phase that contributed to the synthesis of ReNPs. The resultant sizes, surface charges, and phase compositions were linked with synthesis parameters and then with catalytic activities revealed by the variety of ReNPs. HRTEM photomicrographs revealed spherical and spherical-like morphologies of obtained ReNPs synthesized using FLC-dc-dc-APGD and FLA-dc-APGD modes with the actual sizes of 7.28 ± 2.90nm and 3.24 ± 0.57nm, respectively. Optimized conditions yielded ReNPs with exceptional catalytic activity, reducing 94.9% (FLC-dc-APGD) and 90.5% (FLA-dc-APGD) of 4-nitrophenol (4-NP) with the apparent rate constants (k1) 0.269 and 0.107min-1, respectively. Further, the conversions of 90% were achieved over FLC-dc-APGD-based ReNPs for nitrobenzene (NB), 2,4,6-trinitrophenol (2,4,6-TNP), 2,4-dinitrophenol (2,4-DNP), and 4-nitroaniline (4-NA). In these cases, the k1 values were 0.235, 0.174, 0.070, 0.001min-1 for, respectively. The results allowed to find a correlation between ReNP size distribution, oxidation state, and catalytic activity that suggested a potential for tailored Re nanocatalysts in environmental remediation.

Simulation of non-Newtonian fluid flow in a horizontal pipe

Microchannel reactors exhibit distinct gas-liquid two-phase flow behaviors compared to macro-scale channels, offering advantages like efficient heat and mass transfer, compact size, and low energy consumption. Sodium carboxymethyl cellulose (CMC) emerges as a potent stabilizer, enhancing mixing, homogenization and pipeline transport. Its judicious application reduces equipment strain, amplifies homogenization efficiency and finds diverse utility in food processing and beyond. However, incorrect employment bears the risk of compromised outcomes, potentially leading to product wastage. Consequently, investigating N2-CMC solution flow in microchannels holds paramount significance for elevating efficacy, minimizing usage, refining product quality and bolstering yield. In this study, we simulated the N2-CMC solution flow dynamics within an interleaved T-shaped microchannel using FLUENT which is a numerical simulation software. The simulation delved into alterations in gas-liquid two-phase flow patterns and pressure drops. We examined the impacts of liquid concentration and gas-liquid flow rate ratio on flow patterns, pressure drops and bubble lengths. The simulation results exhibited congruence with experimental data. Notably, elevated liquid concentrations correlated with higher pressure drops and elongated bubble lengths. Conversely, augmenting the gas-liquid flow rate ratio led to diminished pressure drops while elongating bubble lengths. These findings furnish insights into flow patterns and pressure drop behaviors for gas-non-Newtonian fluids within microchannels, forming a pivotal reference for microfluidic system design.

A handy analytical approximate solution for the magnetohydrodynamic flow of blood in a porous channel

This work presents a new version of the Picard method, known as the boundary values problems Picard method (BVPP), to obtain an analytical approximate solution for a highly complex nonlinear differential equation that models the magnetohydrodynamic flow of blood through a porous channel. The proposed method is versatile and can produce compact and easily evaluated analytical expressions that accurately capture the scientific phenomena being studied, making it ideal for practical applications. BVPP transforms a differential equation into an integral equation and utilizes an iterative algorithm like that of the basic Picard method. However, unlike the basic method, BVPP allows for the selection of an appropriate initial function and involves several adjustable parameters that can be optimized to obtain a precise analytical approximate solution with minimal effort. Overall, BVPP represents a significant advancement in the analysis of complex nonlinear differential equations, particularly in the field of biomedical engineering.

Can Arbuscular Mycorrhizal Fungi Enhance Crop Productivity and Quality in Hydroponics? A Meta-Analysis

Finding environmentally friendly solutions for crop growth and productivity has been gaining more attention recently. This meta-analysis aims to understand the combined application of arbuscular mycorrhizal fungi (AMF) and hydroponic systems compared to AMF in conventional (soil) systems. The analysis of up-to-date studies revealed that the root colonization, calculated as the proportion of colonized root segments relative to the total root length, by AMF in conventional (soil-based) culture exceeded hydroponic (or soilless) culture systems by 16.8%. The mean root colonization by AMF was determined to be 52.3% in hydroponic systems and 61.1% in conventional systems. Within hydroponic systems, the root colonization ranged from 2% to 20% after 10 days of inoculation, and notably, it exceeded 50% after 30 to 65 days, depending on the growing substrate and species. Under hydroponics, AMF application had a higher (compared to none-inoculated) positive effect on crop biomass and yield than fruit and leaf quality (antioxidants, phenols, and sugars) as well as leaf nutrients. However, AMF do not always have the potential to improve crop growth, quality and productivity in hydroponics. Among the studies analyzed in this review, approximately 34% (no effect: 29%; negative: 5%) reported no discernible positive effect on biomass or yield, 37% (no effect: 16%; negative: 21%) on fruit or leaf quality, and 60% (no effect: 47%; negative: 13%) on nutrient levels within plant tissues. To improve the performance of AMF in hydroponic systems, the meta-analysis recommended maintaining phosphorus levels in the nutrient solution within the range of 0.15 to 15.5 mg L−1 as elevated levels (40–75 mg L−1) were found to significantly reduce AMF colonization. Additionally, it was observed that certain hydroponic techniques, such as the presence of air bubbles generated by air pumps in floating hydroponic systems (Deep Flow technique) and continuous circulation of the nutrient solution (Ebb and Flow systems), may create dynamic conditions that could potentially hinder the introduction of AMF spores into hydroponic systems and potentially compromise the integrity of the spores and hyphae.

A fractional Darcian model‐based analytical solution for non‐Darcian flow toward a fully penetrating well in a confined aquifer

AbstractThe Forchheimer and Izbash equations have been long employed to investigate the behavior of non‐Darcian flow toward a well in various aquifer systems, but both two equations inevitably introduce problems such as more or less empirical nature, and dimensional unbalance. Therefore, this work makes the attempt to introduce the fractional Darcian model for characterizing the non‐Darcian behavior flow toward a fully penetrating well in a confined aquifer instead of the Forchheimer and Izbash equations. In this study, a fractional Darcian model‐based analytical solution in the time domain is obtained by means of Laplace transform and linearization approximation. The proposed analytical solution of this study can be readily reduced to the classical Theis solution for Darcian flow. Meanwhile, the late‐times and steady‐state analytical solutions for non‐Darcian flow described using the fractional Darcian model are also developed. Moreover, a comparison with previous analytical solutions shows that the newly derived analytical solution in this study is sufficiently accurate at later times. The influences of different parameters on transient drawdown are investigated. The results indicate that the fractional derivative order and hydraulic conductivity have a large influence on drawdown compared with other parameters. The introduction of fractional Darcian model in this study could also provide potential application for further investigations of non‐Darian flow behavior toward fully or partially penetrating wells in different aquifer systems, which can be very beneficial for hydrology and other related fields.

Effect of aircraft landing angle on hydrodynamics characteristics during wave landing

In order to study the effect of different courses on the landing performance of aircraft when landing in waves, a Computational Fluid Dynamics (CFD) method is developed to investigate the landing performance of the NACA TN 2929 A aircraft model. The solution of fluid flow is based on the Reynolds-averaged Navier-Stokes equations with the shear stress transport (SST) k−ω turbulence model, and the numerical scheme employed is the Finite Volume Method (FVM). The fifth-order Stokes wave is generated by using the velocity inlet wave-making method. In the work, the slamming load, pitch change and motion response of the aircraft landing at different wave positions are analyzed. The landing characteristics of aircraft landing parallel to the wave, perpendicular to the wave and at the yaw angle are studied. It is found that the landing characteristics of the aircraft at the 1/2 π phase are better than those at other ones, with the maximum load at the π phase. When the aircraft lands parallel to the wave, yaw displacement generated at 1/2 π phase and 3/2 π phase is equal in magnitude and opposite in direction in the initial short time. These results are important for reducing slamming loads and improving the airworthiness of the aircraft structure when landing on a wave surface.

Flat flow solution to the mean curvature flow with volume constraint

Abstract In this paper I will revisit the construction of a global weak solution to the volume preserving mean curvature flow via discrete minimizing movement scheme by Mugnai, Seis and Spadaro [L. Mugnai, C. Seis and E. Spadaro, Global solutions to the volume-preserving mean-curvature flow, Calc. Var. Partial Differential Equations 55 2016, 1, Article ID 18]. This method is based on the gradient flow approach due to Almgren, Taylor and Wang [F. Almgren, J. E. Taylor and L. Wang, Curvature-driven flows: a variational approach, SIAM J. Control Optim. 31 1993, 2, 387–438] and Luckhaus and Sturzenhecker [S. Luckhaus and T. Sturzenhecker, Implicit time discretization for the mean curvature flow equation, Calc. Var. Partial Differential Equations 3 1995, 2, 253–271] and my aim is to replace the volume penalization with the volume constraint directly in the discrete scheme, which from practical point of view is perhaps more natural. A technical novelty is the proof of the density estimate which is based on second variation argument.

Optimal Frequency determination for Wind-Hydro hybrid unit using Telegrapher’s Method for Low frequency transmission lines

This study addresses the optimal load flow problem for low-frequency transmission lines connected to wind farms and pumped storage Hydropower (PSH). The losses in LF-HVac system and the voltage stability index heavily dependent on the operating frequency. Therefore, an optimal load flow (OLF) method must be incorporated to determine the proper solutions for these systems. This system analyses the load flow solutions in which newton Raphson with STATCOM requires large vector calculations with variables. So, to reduce the mathematical calculation a two-port equivalent model for transmission lines based on solutions to Telegrapher’s method has been proposed. The proposed OLF method is tested with other algorithms and implemented in IEEE 39-BUS system. The results obtained indicate that the LF method with the proposed metaheuristic algorithm gives optimal frequency for low-frequency HVac systems while maintaining the stability of system.

Analytical solution of the Poiseuille flow of a De Kee viscoplastic fluid

We provide an explicit analytical solution of the planar Poiseuille flow of a viscoplastic fluid governed by the constitutive equation proposed by De Kee and Turcotte (1980). Formulae for the velocity and the flow rate are derived, making use of the Lambert W function. It is shown that a solution does not always exist because the flow curve is bounded from above and hence the rheological model can accommodate stresses only up to a certain limit. In fact, the flow curve reaches a peak at a critical shear rate, beyond which it exhibits a negative slope, giving rise to unstable solutions.

Submarine landslides and tsunami genesis in Sagami Bay, Japan, caused by the 1923 Great Kanto earthquake

AbstractThe 1923 Great Kanto earthquake occurred on September 1, in Japan, and caused severe damage mainly in the Kanto region. Tsunamis were observed over wide regions from the east coast of the Izu Peninsula to the west coast of the Boso Peninsula, and particularly, the damage in Atami was devastating. Many earthquake fault models including those of Kanamori (1971) and Ando (1971) were proposed based on the records of land deformation. However, such fault models cannot sufficiently explain the tsunami elevation and its initial sea-level motion on the coasts. Hence, the detailed mechanisms remain elusive. This study examines the possibility that a leading mechanism of the tsunami in the 1923 Great Kanto earthquake was a large-scale submarine landslide that occurred at Sagami Bay and at the mouth of Tokyo Bay based on the records of depth data measured by the Imperial Japanese Navy (1924) before and after the earthquake. We first show that the tsunami calculated by each fault model was inconsistent with the waveform at Yokosuka, the coastal tsunami elevations, and initial sea-level motion. Then, based on statistical analysis of the depth changes at the 1923 Great Kanto earthquake, we found that the seafloor bathymetric changes represented large-scale submarine landslides that may correspond to long-runout submarine liquefied sediment flows. The seafloor gradient over a 40 km flow-out distance was equal to or less than 0.4$$^\circ$$ ∘ . Through the identification of the submarine landslide source by tsunami backpropagation analysis and utilizing an analytical solution of a high-density gravity flow and a sensitivity analysis, we conducted a range of numerical simulations of the 1923 Great Kanto earthquake tsunamis using a fault model and a submarine landslide tsunami source model due to a high-density liquefied gravity flow. The results quantitatively accounted for the discrepancy between the observed tsunami records with maximum tsunami elevations over 12 m and the fault-model–based simulations with maximum tsunami elevations of 2 to 5 m and explained consistently the maximum tsunami elevation distributions as well as the time-series tsunami waveforms. These results may thus facilitate and deepen our understanding of the earthquake-induced submarine landslide tsunami risk as cascading multi-geohazards.

Filter paper as electrolyte flow transport using vaporized methanol as fuel in a microfluidic fuel cell: Experimental and numerical simulation

In this work, we present a design of a paper-based microfluidic fuel cell (μFC), which employs the spontaneous capillary flow of reactant solutions in a filter paper to accomplish passive conveyance of the fuel and oxidant. This self-pumping device uses methanol vapor as a fuel. The gas phase in the microfluidic fuel cell increases the fuel supply to the anode due to a higher diffusion coefficient of 1.5 ​× ​10−5 ​m2 ​s−1 compared with 5 ​× ​10−9 ​m2 ​s−1 for liquid phase. An air-breathing cathode is incorporated to paper-based μFC through which atmospheric oxygen is continuously supplied. The paper-based μFC performance is studied by polarization curves and chronoamperometry to determinate the power output and stability. Peak power of 1.49 ​mW and a stable current of 1.35 ​mA at 0.35 ​V for 28 ​h can be achieved with this prototype under room temperature. To interpret the device performance a numerical model is developed and validated with the experimental polarization curve. The fuel and oxidant concentration profiles in the electrodes from the model demonstrates a constant species availability at the cathode and anode and explains the stable current obtained in the experimental measurements. Subsequently, a stack of four MμFCFP was developed and evaluated in both series and parallel connections. In the parallel configuration, a maximum open circuit potential (OCP) of 0.69 ​V with a maximum current and power output of 34.53 ​mA and 4.14 ​mW are delivered, respectively. Conversely, in the series connection, a total current of 7.35 ​mA, an OCP of 2.39 ​V and a maximum power of 3.57 ​mW are reached. As a proof of concept, the stack successfully operates a 3 green LEDs array, each requiring a 2.1–2.5 ​V and 4.2–5 ​mW power to function, for a continuous duration of 3 ​h.

Nonlinear aggregation-diffusion equations with Riesz potentials

We consider an aggregation-diffusion model, where the diffusion is nonlinear of porous medium type and the aggregation is governed by the Riesz potential of order s. The addition of a quadratic diffusion term produces a more precise competition with the aggregation term for small s, as they have the same scaling if s=0. We prove existence and uniqueness of stationary states and we characterize their asymptotic behavior as s goes to zero. Moreover, we prove existence of gradient flow solutions to the evolution problem by applying the JKO scheme.