Scale Separation Research Articles

A viscous vortex model for predicting the drag reduction of riblet surfaces

This paper introduces a viscous vortex model for predicting the optimal drag reduction of riblet surfaces, eliminating the need for expensive direct numerical simulations (DNSs) or experiments. The footprint of a typical quasi-streamwise vortex, in terms of the spanwise and wall-normal velocities, is extracted from smooth-wall DNS flow fields in close proximity to the surface. The extracted velocities are then averaged and used as boundary conditions in a Stokes-flow problem, wherein riblets with various cross-sectional shapes are embedded. Here, the same smooth-wall-based boundary conditions can be used for riblets, as we observe from the DNSs that the quasi-streamwise vortices remain unmodified apart from an offset. In particular, the position of these vortices remain unpinned above small riblets. The present approach is compared with the protrusion-height model of Luchini et al. (J. Fluid Mech., vol. 228, 1991, pp. 87–109), which is also based on a Stokes calculation, but represents the vortex with only a uniform spanwise velocity boundary condition. The key novelty of the present model is the introduction of a wall-normal velocity component into the boundary condition, thus inducing transpiration at the riblet crests, which becomes relevant as the riblet size increases. Consequently, the present model allows for the drag-reduction prediction of riblets up to the optimal size. The present approach does not rely on the scale separation formally required by homogenisation techniques, which are only applicable for vanishingly small riblets.

Effective double-poroelasticity derived via homogenization of two non-interacting solid phases percolated by a viscous fluid

This work carries out the derivation of the governing equations for a composite material that has the following microstructure. Our microstructure possesses an elastic matrix that has an incompressible Newtonian fluid flowing in the pores and then the latter is additionally reinforced by an elastic network that is fully surrounded by the fluid. We exploit the length scale separation that exists in the system between the microscale and the overall size of the material to apply the asymptotic homogenization technique. The resulting model comprises additional terms and equations to account for the discontinuity between the elastic phases, and reduces to more standard poroelastic formulations only when the two elastic phases are in contact. The coefficients of the novel model are to be computed by solving appropriate periodic cell differential problems. The coefficients encode the details of the geometry and stiffness of the microstructure. The model is applicable to a variety of scenarios, such as artificial constructs and biomaterials.

EMBED IN ENSEMBLE TO RIGOROUSLY AND ACCURATELY HOMOGENIZE QUASI-PERIODIC MULTI-SCALE HETEROGENEOUS MATERIAL

AbstractFor microscale heterogeneous partial differential equations (PDEs), this article further develops novel theory and methodology for their macroscale mathematical/asymptotic homogenization. This article specifically encompasses the case of quasi-periodic heterogeneity with finite scale separation: no scale separation limit is required. A key innovation herein is to analyse the ensemble of all phase-shifts of the heterogeneity. Dynamical systems theory then frames the homogenization as a slow manifold of the ensemble. Depending upon any perceived scale separation within the quasi-periodic heterogeneity, the homogenization may be done in either one step or two sequential steps: the results are equivalent. The theory not only assures us of the existence and emergence of an exact homogenization at finite scale separation, it also provides a practical systematic method to construct the homogenization to any specified order. For a class of heterogeneities, we show that the macroscale homogenization is potentially valid down to lengths which are just twice that of the microscale heterogeneity! This methodology complements existing well-established results by providing a new rigorous and flexible approach to homogenization that potentially also provides correct macroscale initial and boundary conditions, treatment of forcing and control, and analysis of uncertainty.

Metastable dynamics of Rydberg atomic system under electromagnetically induced transparency

Open quantum system, coupled with an external bath is a key research field of quantum physics. Steady state is the state in which any initial state converges after a long time and is usually of the most interest. However, relatively speaking, the nonequilibrium dynamical processes of quantum many-body systems have been rarely studied. This is mainly due to the fact that quantum many-body systems generally have interactions, and the Hilbert space required for a complete description of their dynamical processes will grow exponentially with the number of particles increasing, and the computational difficulty will increase dramatically as well. Hence, it is a difficult problem to completely describe their dynamical processes completely. With the development of quantum technologies, the interest in the nonequilibrium dynamics of open quantum many-body systems is aroused. A common phenomenon is the metastable state, where the system initially relaxes into a long-lived state and then converges to the final stationary state for a longer time. In this paper, we establish a low-dimensional approximation to describe the metastability dynamics in Markovian open quantum system, based on the spectra of the Liouvillian super-operator. The separation of time scales implies a splitting in the spectrum, and this spectral division allows us to eliminate the fast decay modes by using the perturbation method, and then we establish the effective description in the low-lying eigenmodes subspace. Furthermore, we study the dynamics process of the Rydberg atomic system under electromagnetically induced transparency (EIT) conditions and find that the system can handle metastable dynamics if the atomic interactions are considered. We compare the effective dynamics in the subspace with the actual dynamics in the full space, and the results show that the effective dynamics works well on condition that the perturbation approximation holds. Our work provides a feasible idea and method for establishing an effective and simplified description of the dynamical process of open quantum many-body systems.

Multi-methods to investigate the baseflow: Insight from watershed scale spatiotemporal variety perspective

Baseflow is the stable part of streamflow meeting the ecological water requirement of the watershed in dry season. Baseflow separation plays a vital role in maintaining the biodiversity of watershed ecosystem. However, research systematically on spatiotemporal variety in watershed scale in baseflow separation is not well documented. In this study, we chose six hydrometric stations in the Yiluo River watershed and carried ten methods (in the group of HYSEP, UKIH and digital filter methods) to isolate the daily runoff data from 2002 to 2021. Two evaluation indicators (Nash-Sutcliffe efficiency coefficient and relative error) were applied to measure the accuracy of those methods. The results showed that the Yiluo River had the average annual baseflow of 10.73 × 108 m3 and average baseflow index (BFI) of 0.42. The UKIH and Eckhardt filtering method methods were fit for the Yiluo River watershed. Temporally, BFI in the wet season (average of 0.35) was smaller than the dry season (average of 0.49). As to the interannual scale, the baseflow in the wet year accounted for nearly a half (49 %) of whole twenty years. Spatially, the BFI of lower reaches (0.35 in Heishiguan) was higher than upper reaches (0.30 in Dongwan and 0.24 in Lushi) on the same river. Nearly half river runoff was from the groundwater recharge and suggests that the Yiluo River is a heavily “Groundwater-dependent River”. Those results of this study can enhance the understanding of spatiotemporal changes of baseflow separations in watershed scale and provide the important references to the international readers.

Efikasnost superkritične fluidne hromatografije u kreiranju ekološki prihvatljivih rešenja u farmaceutskoj analizi

Initially employed primarily at a preparative scale for enantiomer separation of chiral drug candidates, Supercritical Fluid Chromatography (SFC) is nowadays extensively used in the analytical mode. Recent advances in SFC separation science have emphasized its potential for modern and environmentally friendly pharmaceutical analysis. The aim of this review is to provide a deeper insight into the main fundamental and practical aspects of the SFC technique in order to familiarize readers with its versatile nature and efficiency in creating sustainable chromatographic solutions. All considerations are made primarily in the context of the most widely used mode of operation - achiral SFC. In addition, recent applications of this promising technique are presented at the end of the article to further promote its use in pharmaceutical analytical practice.

Electron transport chain-inspired coordination polymers for macroscopic spatiotemporal scales of charge separation and transport in photocatalysis.

Classic homogeneous photocatalysis is limited by the temporal transience and the spatial proximity of photoinduced charge separation and transport. The electron transfer chain (ETC) in cellular respiration can mediate unidirectional and long-range electron transfer to isolate the oxidation and reduction centres. Inspired by this, we modified electron-accepting (A) viologen with π-extending thiazolothiazole and electron-donating (D) phenyl carboxylate into a D-A-π-A-D-type ligand and assembled segregated dye stacking in coordination polymer Cd-TzBDP for breaking the spatiotemporal limitation of single-molecule photocatalysis. The offset characteristics of D-A segregated stacking not only allowed the photoinduced-2e- transfer from the D-type carboxylate terminal to the spatially adjacent A-type viologen motif within 1 ps but also permitted the following delocalization of e- and h+ along stacked columns. These advantages endowed Cd-TzBDP with long-lived photochromic visualization of intermittent aerobic photooxidation steps, which enabled the bioinspired ETC-mediated aerobic respiration of mitochondria, achieving the continuous photocatalytic α-C(sp3)-H functionalization of tertiary amines with pharmaceutical interest. Enlightened by ETC-mediated electron leak in hypoxia, the coordination polymer was further employed in a photocatalytic membrane reactor, which visually illustrated the photo-driven cross-membrane long-range transfers of multiple electrons and protons from the hypoxic compartment to normoxic one, benefiting the distal photooxidation and photoreduction with biomimetic compartment selectivity.

An overview of analytical techniques for heavy metal ion detection and removal from industrial sewage

Removal of heavy metal ions from wastewater is of paramount importance for a clean environment and human health. Various reported processes have addressed the removal of heavy metal ions from various wastewater sources. These processes can be divided into adsorption, membrane, chemical, electrical, and photo catalytic processes. This article provides a comprehensive and critical overview of these methods, discussing the media/sorbents used, removal efficiency, operating conditions, and advantages and disadvantages of each method. We also summarize the main results of previous studies reported in the literature. It should be noted that recent research has generally focused on adsorption techniques. The main obstacles to the adsorption process are the ability to simultaneously remove different types of ions, the long retention time of the adsorbent and cycle stability. Although chemical and membrane processes are practical, high levels of sludge formation and post-treatment requirements are key issues that must be addressed in chemical processes. Suppression of fouling and scaling can further improve membrane separation. However, pretreatment and regular cleaning of the membrane incurs additional costs. Electrical methods have also been reported to be efficient. However, in addition to overcoming the problem of massive sludge formation, industrial scale separation is required. Electrical and photo catalytic-based methods are not yet mature. Future research should focus on environmentally friendly, inexpensive, and sustainable materials and methods.

A review on recent advances of cellulose acetate membranes for gas separation.

This review thoroughly investigates the wide-ranging applications of cellulose-based materials, with a particular focus on their utility in gas separation processes. By focusing on cellulose acetate (CA), the review underscores its cost-effectiveness, robust mechanical attributes, and noteworthy CO2 solubility, positioning it as a frontrunner among polymeric gas separation membranes. The synthesis techniques for CA membranes are meticulously examined, and the discourse extends to polymeric blend membranes, underscoring their distinct advantages in gas separation applications. The exploration of advancements in CA-based mixed matrix membranes, particularly the incorporation of nanomaterials, sheds light on the significant versatility and potential improvements offered by composite materials. Fabrication techniques demonstrate exceptional gas separation performance, with selectivity values reaching up to 70.9 for CO2/CH4 and 84.1 for CO2/N2. CA/PEG (polyethylene glycol) and CA/MOF (metal-organic frameworks) demonstrated exceptional selectivity in composite membranes with favorable permeability, surpassing other composite CA membranes. Their selectivity with good permeability lies well above all the synthesised cellulose. As challenges in experimental scale separation emerge, the review seamlessly transitions to molecular simulations, emphasizing their crucial role in understanding molecular interactions and overcoming scalability issues. The significance of the review lies in addressing environmental concerns, optimizing membrane compositions, understanding molecular interactions, and bridging knowledge gaps, offering guidance for the sustainable evolution of CA-based materials in gas separation technologies.

Port-Hamiltonian Macroscopic Modelling based on the Homogenisation Method: case of an acoustic pipe with a porous wall

This paper addresses linear propagation in an acoustic pipe with a porous wall, a common scenario in wooden wind instruments. First, a scale separation technique is proposed for dissipative propagation within the wall: the material is modelled as a periodic assembly of identical microscopic cells, forming a network of channels filled with air. It is shown that the resulting PDE admits a port-Hamiltonian formulation, of which the state, flow, effort, Hamiltonian, and Differential connection operator are structured using powers of the scale parameter. The resulting macroscopic description, derived from the governing equations at the two lowest orders, manifests as a constrained port-Hamiltonian system involving a Lagrange multiplier. As an example, using an academic cell geometry, we determine the effective wavenumber and dissipation coefficient of a straight tube with a porous wall.

Biomimetic Interactive Symbiotic Strategies for Clothing Textiles in the Perspective of Non-Genetic Inheritance

Abstract This paper takes the application techniques of non-heritage paper-cutting elements on modern clothing fabrics as an example, analyzing and outlining the symbiotic trend of non-heritage elements and clothing design, i.e., personalization, ethnicity, and the unity of tradition and popularity. It is proposed to utilize the unique performance of bionic scale knitting structure fabrics in bionic technology, combined with the combination of non-heritage techniques, to innovate the clothing design process of non-heritage and to form a new way of bionic interaction and symbiosis between non-heritage and clothing textile. Simulate the performance of bionic scale knitting structure fabrics and explore the advantages of bionic technology in clothing textiles from the perspective of flexibility. Explore the market operation effect of clothing design works of non-heritage technology from the aspects of consumer demand, market evaluation, and market operation, respectively. From the load-displacement curve of the flexibility test, it can be obtained that when the loading value is 55N, the displacements of the bionic knitted structural fabric and the separate scale layer are all greater than 11mm, and the bionic scale knitted structural fabric possesses good bending deformability. The evaluation results of the enterprise experts show that the clothing works integrating the non-heritage elements have obvious market demand.

Insight into the effect of pressure on the CO2 capture capacity and kinetics by a biochar-ionic liquid composite

Agave bagasse fibers-derived biochar (BCw) impregnated with 1-butyl-3-methylimidazolium acetate ionic liquid (IL) exhibited a considerably CO2 capture capacity at atmospheric (1.47 mmol/g at 25 °C and 1 bar) and moderately high pressure (1.32 mmol/g at 25 °C and 8.5 bar) under dynamic and static systems, respectively. Biochar-IL composites improved the CO2 capture capacity, kinetics, and selectivity (CO2/N2) by 4–90% compared with than of the bulk adsorbents. By increasing the working manometric pressure from 1 to 8.5 bar in a static high-pressure system, the CO2 capture capacity and kinetics of impregnated-biochar improved 2 times. Additionally, the biochar-IL composites were regenerated under a pressure swing adsorption (PSA) arrangement, where more than 70% of the desorption was attributed to the depressurization of the system. The proposed CO2 sorption mechanism suggests gas-solid physisorption and gas-liquid chemisorption at low pressure. At moderately high pressure (≥ 1 bar), the textural properties of the adsorbent play an important role. Moreover, this study provided evidence that the CO2 capture is not only related to the textural properties of the biochar, but also to its surface chemistry. The biochar-IL composite materials reported herein could be an option for CO2 capture at low and moderate pressures, which could reduce operating costs if implemented at large scale for CO2 separation from flue gases under a PSA design.

Technoeconomic Assessment of Large-Scale Ethylene Production via the Electrochemical Reduction of CO2

In the last five years, several works have shown that CO2 may be electrochemically reduced to C2 products such as ethylene at current densities over 1 A cm-2 and Faradaic efficiencies over 70%. For the first time, these current densities and Faradaic efficiencies are comparable with commercial electrolytic processes. For reference, over 100 million metric tons per year of chlorine per is manufactured via the Chlor-alkali process at current densities near 0..4 A cm-2 and Faradaic efficiencies to Cl2 over 80%. While the current densities and Faradaic efficiencies for CO2 reduction are compelling; other metrics such as energy efficiency, selectivity, carbon efficiency, electrolyzer scaling, electrolyzer costs and post-electrolysis separation are not yet at the levels needed for commercialization.In this presentation, we consider the technoeconomics of ethylene production at large scales (25,000 to 150,000 metric tons per year). We investigate the impact of cell potential, Faradaic efficiencies, conversion level, process scaling and post-electrolysis separations on the cost of electrolytic ethylene production. Our results indicate that the “green” ethylene made using CO2 as a feedstock requires anywhere from approximately 1 to 10 times greater manufacturing costs than conventional cracking of ethane depending on factors such as electrical energy cost, electrolyzer costs and other parameters. In this case, we consider key technical and economic needs including: price premiums, tax incentives, CO2 emission taxes, and other factors that could enable electrolytic ethylene manufacturing at large scales within the next decade.

The muphyII code: Multiphysics plasma simulation on large HPC systems

Collisionless astrophysical and space plasmas cover regions that typically display a separation of scales that exceeds any code's capabilities. To help address this problem, the muphyII code utilizes a hierarchy of models with different inherent scales, unified in an adaptive framework that allows stand-alone use of models as well as a model-based dynamic and adaptive domain decomposition. This requires ensuring excellent conservation properties, careful treatment of inner-domain model boundaries for interface coupling, and robust time-stepping algorithms, especially with the use of electron subcycling. This multi-physics approach is implemented in the muphyII code, tested on different scenarios of space plasma magnetic reconnection, and evaluated against space probe data and higher-fidelity simulation results from literature. Adaptive model refinement is highlighted in particular, and a hybrid model with kinetic ions, pressure-tensor fluid electrons, and Maxwell fields is appraised.

Experimental scalings of scrape-off layer particle flux width by outboard divertor Langmuir probes for deuterium and helium plasmas on EAST

The scrape-off layer (SOL) power width (λq ) is an important parameter for predicting the heat load on divertor targets for future magnetically confined devices. Currently, the underlying physics for λq scaling is not fully understood. This paper extends the previous SOL particle flux width (λjs, λq ≈ λjs is assumed, js is the measured ion current density used as a proxy for particle flux) scaling measured by the inboard divertor Langmuir probes (Div-LPs) in deuterium plasmas (Liu et al 2019 Plasma Phys. Control. Fusion 61 045001) to the λjs scalings measured by the outboard Div-LPs in both deuterium and helium plasmas on EAST. A systematic method has been used to correct the upper-outer Div-LP measurements to reduce the measurement uncertainty of λjs . About 520 discharges are selected for the construction of six databases (H-mode, L-mode, and Ohmic for deuterium and helium plasmas) to scale λjs . Since the published λq scalings do not fit EAST λjs well in the databases, four separate λjs scalings are proposed using statistical method to minimize the scaling parameters. It is found that λjs has a robust scaling dependence on the plasma line-averaged density ( nˉe ) for both deuterium and helium plasmas and a strong positive scaling dependence on the divertor leg length (L div,leg). The scaling exponent of the stored energy agrees well with the previous λq /λjs scalings for deuterium plasmas. The near unity scaling exponents of edge safety factor and L div,leg reveal the importance of parallel connection length in determining λjs . The positive scaling dependence of λjs on nˉe and the 2 ∼ 4 times larger scaling amplitude compared with the published λq scalings probably indicate the turbulence broadening of λjs on EAST. The comparison of λjs for deuterium and helium plasmas using the constructed databases shows no significant difference. Statistical comparison of the normalized λjs with different ELM types suggests that the grassy-ELM λjs is slightly larger than the inter large-ELM (type-I ELM) λjs for both deuterium and helium plasmas.

Locating saddle points using gradient extremals on manifolds adaptively revealed as point clouds.

Steady states are invaluable in the study of dynamical systems. High-dimensional dynamical systems, due to separation of time scales, often evolve toward a lower dimensional manifold M. We introduce an approach to locate saddle points (and other fixed points) that utilizes gradient extremals on such a priori unknown (Riemannian) manifolds, defined by adaptively sampled point clouds, with local coordinates discovered on-the-fly through manifold learning. The technique, which efficiently biases the dynamical system along a curve (as opposed to exhaustively exploring the state space), requires knowledge of a single minimum and the ability to sample around an arbitrary point. We demonstrate the effectiveness of the technique on the Müller-Brown potential mapped onto an unknown surface (namely, a sphere). Previous work employed a similar algorithmic framework to find saddle points using Newton trajectories and gentlest ascent dynamics; we, therefore, also offer a brief comparison with these methods.

Asymptotic behavior of a class of multiple time scales stochastic kinetic equations

We consider a class of stochastic kinetic equations, depending on two time scale separation parameters ɛ and δ: the evolution equation contains singular terms with respect to ɛ, and is driven by a fast ergodic process which evolves at the time scale t/δ2. We prove that when (ɛ,δ)→(0,0) the spatial density converges to the solution of a linear diffusion PDE. This result is a mixture of diffusion approximation in the PDE sense (with respect to the parameter ɛ) and of averaging in the probabilistic sense (with respect to the parameter δ). The proof employs stopping times arguments and a suitable new perturbed test functions approach which is adapted to consider the general regime ɛ≠δ.

Restrictions of Pfaffian systems for Feynman integrals

This work studies limits of Pfaffian systems, a class of first-order PDEs appearing in the Feynman integral calculus. Such limits appear naturally in the context of scattering amplitudes when there is a separation of scale in a given set of kinematic variables. We model these limits, which are often singular, via restrictions of D\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{D} $$\\end{document}-modules. We thereby develop two different restriction algorithms: one based on gauge transformations, and another relying on the Macaulay matrix. These algorithms output Pfaffian systems containing fewer variables and of smaller rank. We show that it is also possible to retain logarithmic corrections in the limiting variable. The algorithms are showcased in many examples involving Feynman integrals and hypergeometric functions coming from GKZ systems. This work serves as a continuation of [1].

Anisotropic molecular diffusion in confinement II: A model for structurally complex particles applied to transport in thin ionic liquid films

HypothesisDiffusion in confinement is an important fundamental problem with significant implications for applications of supported liquid phases. However, resolving the spatially dependent diffusion coefficient, parallel and perpendicular to interfaces, has been a standing issue and for objects of nanometric size, which structurally fluctuate on a similar time scale as they diffuse, no methodology has been established so far. We hypothesise that the complex, coupled dynamics can be captured and analysed by using a model built on the 2-dimensional Smoluchowski equation and systematic coarse-graining. Methods and simulationsFor large, flexible species, a universal approach is offered that does not make any assumptions about the separation of time scales between translation and other degrees of freedom. The method is validated on Molecular Dynamics simulations of bulk systems of a family of ionic liquids with increasing cation sizes where internal degrees of freedom have little to major effects. FindingsAfter validation on bulk liquids, where we provide an interpretation of two diffusion constants for each species found experimentally, we clearly demonstrate the anisotropic nature of diffusion coefficients at interfaces. Spatial variations in the diffusivities relate to interface-induced structuring of the ionic liquids. Notably, the length scales in strongly confined ionic liquids vary consistently but differently at the solid–liquid and liquid–vapour interfaces.

Regenerable planting of multifunctional amine: Regeneration-enhanced antifouling/antiscaling properties and performance of thin film composite nanofiltration membrane

The problems of poly(piperazineamide)-based thin film composite (TFC) nanofiltration (NF) membrane are the fouling, scaling and poor separation performance of uncharged organics and heavy metal ions. Permanent surface modification lowers the fouling/scaling problems. However, these problems persist as the separation progresses. We address these issues by the on-demand regenerable planting of polyethyleneimine (PEI) into the polyamide (PA) layer of TFC NF membrane. The regenerable planting is based on the electrostatic interaction among the protonated amine groups of low molecular weight PEI and ionized carboxylic acid groups situated at the relatively inner sites (low dielectric constant) of the PA network. The incorporated PEI chains are stable at the pH range of 3–9. The PEI incorporated membrane exhibits significantly enhanced antifouling/antiscaling property, rejection of heavy metal ions (98–99%) and bisphenol A (BPA, 95%) without much negatively affecting the bivalent anion rejection (Na2SO4, 97.5%) and water permeance (11 L m−2 h−1 bar−1) as compared to the pristine and commercial membranes (55–82%, 50–76% and 98–99% rejections of heavy metal ions, BPA and Na2SO4). Advantageously, PEI chains are removable at pH ≤ 2 or pH ≥ 9.5 without affecting the main PA layer. The multiple removal and re-generation of the membrane have been achieved. The flux recovery of the membrane after antifouling/antiscaling tests significantly improved upon intentional removal and reincorporation of PEI. Inherent properties of the modified membrane channels couple with the on-demand regenerable ability show immense promises of the membrane in the separation applications.