A method for the analytical solution of the incompressible Stokes flow equations is presented, incorporating concepts from variational calculus into a series expansion framework. The proposed approach employs the Implicit POTential (IPOT) method to achieve velocity-pressure coupling, allowing for an explicit expression of the pressure term through a series of pressure variations. The analytical solution is derived using the separation of variables method, combined with Fourier series expansions to describe the velocity and pressure fields. The method is applied to the two-dimensional lid-driven cavity flow, which is a fundamental benchmark problem in fluid mechanics. The resulting equations are implemented computationally, in order to obtain velocity field distributions. A convergence study is conducted to evaluate the rate of convergence with increasing Fourier mode truncation parameters. A comparison with numerical solutions that are obtained from the OpenFOAM simulation platform is also presented, to assess the efficiency of the analytical approach. The findings demonstrate the effectiveness of the method in providing accurate solutions, while they highlight the key factors influencing its convergence behavior.
This study investigates the role of Fe-and Mn-as a B-site transition metal cation in neodymium-based perovskite Nd1-xSrxBO3 (B = Mn, Fe) for two-step thermochemical splitting of CO2. Sr substitution (x = 0, 0.2, 0.4, 0.6, 0.8) was employed to tune the redox thermodynamics of Nd-based perovskites in Nd1-xSrxBO3 (B = Mn, Fe). Ferrites (Nd1-xSrxFeO3) exhibited the largest first-cycle O2 release (92-913 & micro;mol/g) but give low thermal oxidation CO yield (40-60 & micro;mol/g) with only partial recovery in the second cycle. In ferrites, XPS confirmed a reduced, vacancy-rich, carbonate-covered surface after cycling. Manganites show smaller O2 release yet efficient re-oxidation at mid-Sr with high % re-oxidation yield; their Mn 2p and O 1 s spectra change modestly and return toward the as-calcined state. DFT maps oxygen-vacancy formation energies that are lower for ferrites and higher for manganites at the same Sr-doping level; the ferrite landscape is also smoother, which supports fast vacancy percolation. XRD/Rietveld indicates oxygen-deficient starting references for several ferrites (%Sr = 40, 60, 80) and, together with the yields, points to a partial perovskite-brownmillerite excursion that is not fully reversed in CO2. The results identify a mechanism split: Fe-based compositions are anion-centered and prone to deep but only partly reversible reduction; Mn-based compositions are cation-centered and deliver balanced depth and reversibility.
Retailers traditionally deploy demand response (DR) mainly to reduce procurement costs in energy markets, overlooking the potential to leverage flexible loads in reserve or flexibility markets. This paper proposes a two-stage, data-driven framework that enables retailers to stack revenues from energy and reserve markets through the aggregation of flexible demands. The first stage employs inverse optimization (IO) to infer flexible load parameters from historical price and consumption data, while the second stage formulates a bilevel model capturing the strategic interaction between the retailer and the system operator. The bilevel problem is reformulated as a Mathematical Program with Equilibrium Constraints (MPEC) and McCormick envelopes. Applied to the Chilean electricity market, results show that multi-market DR participation increases retailer profits fourfold and reduces system reserve procurement costs by 8.91% during the actives hours of the demand response procurement, underscoring DR’s role in enhancing flexibility and delivering system-wide savings.
Recent experiments by Daneshi & Frigaard (J. Fluid Mech., vol. 957, 2023, p. A16) examined the response of an initially spherical, stationary bubble in an elastic yield-stress material to stepwise ambient-pressure variations under two protocols. In the first protocol, pressure decreases and the bubble swells, elongates, and mobilises. In the second protocol, pressure decreases then increases; the bubble stays stationary, but its volume shows hysteresis between the two phases. This hysteresis was attributed to elastic non-recoverable strain. In the present study, we numerically investigate these two protocols, accounting for elasticity, residual stresses and nonlinear viscoelastic deformation before yielding, using the Saramito-Herschel-Bulkley model. In the first protocol, assuming constant bubble mass yields clear deviations from experiments in (a) the bubble radius evolution, (b) the pressure-volume product at different pressures and (c) the bubble mobilisation. These deviations are resolved by including mass transfer of gas from the surrounding material, which increases bubble mass. This is caused by the pressure reduction, which decreases the gas concentration at the bubble interface below the ambient value, generating a mass influx. In the second protocol, we demonstrate that hysteresis can be predicted only when mass transfer is included. Finally, we propose a simplified model to predict the bubble dynamics during either pressure protocol, which can also be used to extract the mass-transfer properties of gas-fluid systems in yield stress materials.
Brackish aquaponics is expected to be a promising approach to sustainable food production, integrating saline water resources with simultaneous co-cultivation of fish and halophytes. The present study investigated the effects of three feeding ratios (FR1.5: 1.5%, FR3: 3%, and FR6: 6% b.w/d) on the growth performance of European sea bass (Dicentrarchus labrax) and glasswort (Salicornia europaea) co-cultured in three autonomous one-loop recirculation aquaponic systems (180 L each) at 20 ppt salinity over 78 days. Each system comprised three fish-rearing tanks connected to a two-stage sump filter and a nutrient film technique (NFT) hydroponic subsystem. Sea bass fed at FR3 achieved significantly higher weight gain, specific growth rate, and feed conversion efficiency than FR1.5. At FR6, feed consumption nearly doubled compared to FR3 (3.79 vs. 1.91 g), yet the feed conversion ratio increased from 0.79 to 1.65, and protein efficiency ratio declined from 3.80 to 1.91, indicating overfeeding effects. Regarding glasswort, FR6 produced significantly higher chlorophyll a content and plant biomass, whereas FR1.5 showed superior ammonia removal efficiency. Overall, FR3 provided the best balance between fish growth, plant yield, and water quality maintenance. These findings highlight the critical role of feeding management in brackish aquaponics in order to optimize nutrient coupling between fish and halophyte production.
