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Interactions between fluid flow and elastic structures are important in many naturally occurring and engineered systems. This review collects and organizes recent theoretical and experimental developments in understanding fluid-structure interactions at low Reynolds numbers. Particular attention is given to the motion of objects moving in close proximity to deformable soft materials and the ensuing interplay between fluid flow and elastic deformation. We discuss how this interplay can be understood in terms of forces and torques, and harnessed in applications such as microrheometry, tribology, and soft robotics. We then discuss the interaction of soft and wet objects close to contact, where intermolecular forces and surface roughness effects become important and are sources of complexity and opportunity.

The industrial significance of stability analysis for dual solutions and heat transfer sets the stage for this research. Focusing on Maxwell ternary nanofluid flow, the study aims to enhance thermal conductivity and stability by delving into viscous dissipation and velocity slip effects on a stretching/shrinking sheet. Employing a mathematical model, refined with nondimensional transformations and MATLAB's BVP4C solver, the research identifies dual solutions and examines the influence of key parameters on fluid dynamics and heat transfer. Results showcase a progressive improvement in convective heat transfer and skin friction from mono nanofluid (NF) to binary hybrid nanofluid (HNF), culminating with ternary hybrid nanofluid (THNF). These improvements are significantly associated with the suction/injection parameter (S), whereas the slip (σ) and elastic (K) parameters enhance thermal transfer but negatively affect skin friction efficiency at elevated levels. The robustness of the upper branch solutions underscores the reliability of these findings. Remarkably, at λ = − 1. 25 with a nanoparticle volume fraction of 0.04, ternary nanofluids achieve a 2.9% thermal efficiency leap over HNF, which itself surpasses NF by 0.46%. These findings hold potential for significant advancements in sectors such as electronics, manufacturing, energy, biomedical, environmental engineering, aerospace, and automotive, aiming at elevating thermal efficiency. [ABSTRACT FROM AUTHOR]

Measurements of densities (ρ), speeds of sound (u), and viscosities (η) for binary mixtures of N,N-dimethyl benzyl amine (DMBA) with 1-octanol (D1), 1-nonanol (D2), and 1-decanol (D3) were performed across temperatures from 303.15 K to 313.15 K under atmospheric pressure, covering all composition ranges. These experimental results were utilised to calculate the excess molar volume, excess isentropic compressibility, viscosity deviation, and the excess Gibbs free energy of activation for viscous flow. Calculations for partial molar properties and infinite dilution partial molar properties were also carried out for each binary mixture. The dominant intermolecular interactions within these mixtures were analysed using the PFP theory. Additionally, the Jouyban−Acree model was applied to predict the thermo physical properties such as density, speed of sound, and viscosity. The model’s accuracy was evaluated by comparing predicted values with experimental data through mean relative deviations (MRDs) and individual relative deviations (IRDs). [ABSTRACT FROM AUTHOR]

The shale formation, a common carbon-hydrogen reservoir, has numerous nanoscale pores that facilitate multiple gas transport mechanisms, including viscous flow, slip flow, Knudsen diffusion, and surface diffusion. Additionally, various action mechanisms involving effective stress, real gas effect, gas adsorption and desorption, and fracture-pore characteristics significantly influence gas transport. In this study, we conceptualize shale as a triple porosity medium comprising organic matrix, inorganic matrix, and microfractures. For each system, its hydraulic-mechanical coupled model with action mechanisms and gas transport mechanisms is derived based on fractal theory. After validating the model with Barnett and Marcellus data, the evolution of apparent permeability and gas pressure is studied, as well as the influences of pore fractal features, the real gas effect, and the number of hydraulic fractures on gas extraction. Simulation results indicate that, in comparison to organic matrix, inorganic pore fractal features exert a more noticeable effect on cumulative production. The real gas effect is critical in gas transport and reservoir reserve estimation; disregarding this effect results in a 17.4% underestimation of cumulative gas production by the 1600th day. Fracture interference attenuates the improvement in cumulative production gains from increased hydraulic fracture numbers. • A hydraulic-mechanical coupled triple porosity fractal model is established. • Inorganic matrix pore fractal features have a greater impact on gas transport than organic matrix. • Ignoring the real gas effect leads to an underestimation of gas productivity. • The hydraulic fracture interference significantly reduces gas productivity in the late stage of shale gas exploitation. [ABSTRACT FROM AUTHOR]

Diglycidyl ether of bisphenol A crosslinking with glutaric anhydride is used to form the conventional “covalent adaptive network”, polyether sulfone (PES) by coiling and aggregating on the adaptive network is used to significantly increase the uncured resin viscosity for improving the processability of epoxy resin, but inevitably affecting the curing reaction and dynamic transesterification reaction. This study investigates the crucial roles of PES in curing dynamics and stress relaxation behavior. The results indicate that although PES does not directly participate in the crosslinking reaction of polyester‐based epoxy vitrimers. Moreover, the isothermal curing studies reveal that the addition of PES can greatly bring forward the reaction rate peak from conversion α = 0.6 to α = 0.2, meaning that the curing mechanism transfers from chemical control to diffusion control. Dynamic property analysis shows that the addition of PES significantly accelerates stress relaxation, especially at lower temperatures, leading to low viscous flow activation energy Eτ and relatively insensitive stress relaxation behavior to temperature. Introducing PES into vitrimer resin greatly improves crosslinking density (2.31 × 10⁴ mol m−3), enhancing glass transition temperature (82.68 °C), tensile strength (68.66 MPa), and fracture toughness (6.25%). Additionally, the modified vitrimer resin exhibits satisfying shape memory performance and reprocessing capability. [ABSTRACT FROM AUTHOR]

Excess molar volume, excess isentropic compressibility, deviation in viscosity, and excess Gibbs free energy of activation for viscous flow for binary mixtures of N-Methyl benzyl amine (NMBA) with 2-Methyl-2-butanol (2M2B), 2-Methyl-1-butanol (2M1B), and 3-Methyl-1-butanol (3M1B) were determined from measured densities (ρ), viscosities (η) and speeds of sound (u) at 303.15 K to 313.15 K. Influence Structural disparities on excess properties is discussed concerning intermolecular forces. The Prigogine – Flory – Patterson (PFP) theory identifies predominant molecular interactions, and the Jouyban – Acree model correlates density, speed of sound, and viscosity with composition. Thermodynamic activation parameters were calculated using the Eyring equation to study viscous flow thermodynamics. FT-IR and 1H NMR spectra of equimolar binary mixtures were analysed to confirm experimental findings through absorption bands (cm−1) and chemical shifts. [ABSTRACT FROM AUTHOR]

In a review paper in this same volume, we present the state of the art on modeling of compressible viscous flows ranging from single‐phase to two‐phase systems. It focuses on mathematical properties related to weak stability because they are important for numerical resolution and on the homogenization process that leads from a microscopic description of two separate phases to an averaged two‐phase model. This review serves as the foundation for Parts I and II, which present averaged two‐phase models with phase exchange applicable to magma flow during volcanic eruptions. Part I establishes a two‐phase transient conduit flow model ensuring: (1) mass and volatile species conservation, (2) disequilibrium degassing considering both viscous relaxation and volatile diffusion, and (3) dissipation of total energy. The relaxation limit of this model is then used to obtain a drift‐flux system amenable to simplification. Here, in Part II, we summarize this model and propose a 1.5D simplification of it that alleviates three issues causing difficulties in its numerical implementation. We compare our model outputs to those of another steady‐state, equilibrium degassing, isothermal model under conditions typical of an effusive eruption at an andesitic volcano. Perfect equilibrium degassing is unreachable with a realistic water diffusion coefficient because conduit extremities always contain melt supersaturated with water. Such supersaturation has minor consequences on mass discharge rate. In contrast, releasing the isothermal assumption reduces significantly mass discharge rate by cooling due to gas expansion, which in turn increases liquid viscosity. We propose a simplified system using Darcy's law and omitting several processes such as shear heating and liquid inertia. This minimal system is not dissipative but approximates the steady‐state mass discharge rate of the full system within 10%. A regime diagram valid under a limited set of conditions indicates when this minimal system captures the ascent dynamics of effusive eruptions. Interestingly, the two novel aspects of the full model, diffusive degassing and heat balance, cannot be neglected. In some cases with high diffusion coefficients, a shallow region where porosity and velocities tend toward zero develops initially, possibly blocking an eventual steady state. This local porosity loss also occurs when a steady‐state solution is subjected to a change in shallow permeability. The resulting shallow porosity loss features many characteristics of a plug developing prior to a Vulcanian eruption. [ABSTRACT FROM AUTHOR]

We review the modeling and mathematical properties of compressible viscous flows, ranging from single‐phase systems to two‐phase systems, with a focus on the occurrence of oscillations and/or concentrations. We explain how establishing the existence of nonlinear weak stability ensures that no such instabilities occur in the solutions because of the system formulation. When oscillation/concentration are inherent to the nature of the physical situation modeled, we explain how the averaging procedure by homogenization helps to understand their effect on the averaged system. This review addresses systems of progressive complexity. We start by focusing on nonlinear weak stability—a crucial property for numerical simulations and well posedness—in single‐phase viscous systems. We then show how a two‐phase immiscible system may be rewritten as a single‐phase system. Conversely, we show then how to derive a two‐phase averaged system from a two‐phase immiscible system by homogenization. As in many homogenization problems, this is an example where physical oscillation/concentration occur. We then focus on two‐phase averaged viscous systems and present results on the nonlinear weak stability necessary for the convergence of numerical schemes. Finally, we review some singular limits frequently developed to obtain drift–flux systems. Additionally, the appendix provides a crash course on basic functional analysis tools for partial differential equation (PDE) and homogenization (averaging procedures) for readers unfamiliar with them. This review serves as the foundation for two subsequent papers (Part I and Part II in this same volume), which present averaged two‐phase models with phase exchange applicable to magma flow during volcanic eruptions. Part I introduces the physical processes occurring in a volcanic conduit and establishes a two‐phase transient conduit flow model ensuring: (1) mass and volatile species conservation, (2) disequilibrium degassing considering both viscous relaxation and volatile diffusion, and (3) dissipation of total energy. The relaxation limit of this model is then used to obtain a drift–flux system amenable to simplification. Part II revisits the model introduced in Part I and proposes a 1.5D simplification that addresses issues in its numerical implementation. Model outputs are compared to those of another well‐established model under conditions typical of an effusive eruption at an andesitic volcano. [ABSTRACT FROM AUTHOR]

Eukaryotic cell rheology has important consequences for vital processes such as adhesion, migration, and differentiation. Experiments indicate that cell cytoplasm can exhibit both elastic and viscous characteristics in different regimes, while the transport of fluid (cytosol) through the cross-linked filamentous scaffold (cytoskeleton) is reminiscent of mass transfer by diffusion through a porous medium. To gain insights into this complex rheological behaviour, we construct a computational model for the cell cytoplasm as a poroviscoelastic material formulated on the principles of nonlinear continuum mechanics, where we model the cytoplasm as a porous viscoelastic scaffold with an embedded viscous fluid flowing between the pores to model the cytosol. Baseline simulations (neglecting the viscosity of the cytosol) indicate that the system exhibits seven different regimes across the parameter space spanned by the viscoelastic relaxation timescale of the cytoskeleton and the poroelastic diffusion timescale; these regimes agree qualitatively with experimental measurements. Furthermore, the theoretical model also allows us to elucidate the additional role of pore fluid viscosity, which enters the system as a distinct viscous timescale. We show that increasing this viscous timescale hinders the passage of the pore fluid (reducing the poroelastic diffusion) and makes the cytoplasm rheology increasingly incompressible, shifting the phase boundaries between the regimes. [ABSTRACT FROM AUTHOR]

We present LinStab2D, an easy-to-use linear stability analysis MATLAB tool capable of handling complex domains, performing temporal and spatial linear stability, and resolvent analysis. We present the theoretical foundations of the code, including the linear stability and resolvent analysis frameworks, finite differences discretization schemes, and the Floquet ansatz. These concepts are explored in five different examples, highlighting and illustrating the different code capabilities, including mesh masking, mapping, imposition of boundary constraints, and the analysis of periodic flows using Cartesian or axisymmetric coordinates. These examples were constructed to be a departure point for studying other flows. [ABSTRACT FROM AUTHOR]

We consider the Cahn–Hilliard/Navier–Stokes system with non–degenerate mobility in the space–periodic case, describing the flow of two viscous immiscible and incompressible Newtonian fluids with matched densities. We identify sufficient conditions on the velocity field for weak solutions to satisfy an energy identity, improving previous results on the literature. [ABSTRACT FROM AUTHOR]

We study surface gravity waves for viscous fluid flows governed by Darcy's law. The free boundary is acted upon by an external pressure posited to be in traveling wave form with a periodic profile. It has been proven that for any given speed, small external pressures generate small periodic traveling waves that are asymptotically stable. In this work, we construct a class of slowly traveling waves that are of arbitrary size and asymptotically stable. Our results are valid in all dimensions and for both the finite and infinite depth cases. [ABSTRACT FROM AUTHOR]

A three-dimensional model of polydisperse reactive sedimentation is developed by means of a multilayer shallow water approach. The model consists of a variety of solid particles of different sizes and densities, and substrates diluted in water, which produce biochemical reactions while the sedimentation process occurs. Based on the Masliyah–Lockett–Bassoon settling velocity, compressibility of the sediment and viscosity of the mixture, the system of governing equations is composed by non-homogeneous transport equations, coupled to a momentum equation describing the mass-average velocity. Besides, the free-surface depicted by the total height of the fluid column is incorporated and fully determined through the multilayer approach. A finite volume numerical scheme on Cartesian grids is proposed to approximate the model equations. Numerical simulations of the denitrification process exemplify the performance of the numerical scheme and model under different scenarios and bottom topographies. • Polydisperse reactive sedimentation. • Multilayer shallow water approach. • Denitrification and eutrophication processes. [ABSTRACT FROM AUTHOR]

Fluid resonance in the narrow gap formed by a two-box system under irregular wave actions is investigated by employing a viscous numerical wave flume based on the OpenFOAM package. The accuracy of the numerical model is validated by comparing it with previous experimental data and numerical results in the literature. It can be observed that the viscous fluid flow model can work well in predicting the free surface amplitudes around the resonant frequency, while the potential flow model overpredicts the resonant amplitude. Numerical simulations suggested that the periods of wave responses in the narrow gap are always around the resonant period with small standard deviations. This can be explained by the spectral analysis that the wave energy in the narrow gap is concentrated at the resonant frequency. The normalized wave amplitudes calculated from the samplings of the large free surface amplitudes are always smaller than the samplings of the small free surface amplitudes. With the increase of the peak enhancement factor, the normalized significant wave heights under irregular wave actions increase and decrease around resonant and nonresonant frequencies, respectively. Compared to the results under regular wave actions, smaller and larger wave amplitudes appeared in the results of irregular wave actions around the resonant and nonresonant frequency ranges, respectively. The decreased normalized wave amplitudes with the increase of incident irregular wave amplitudes can be observed at all the frequency ranges. [ABSTRACT FROM AUTHOR]

Understanding the effective diffusion coefficient (D) is crucial for describing atomic transport during crystal nucleation in supercooled liquids and glasses. However, pinpointing the key structural units driving crystallization in intricate, multicomponent glass-formers remains a challenge. This study presents a novel analysis of lithium diborate (Li₂O·2 B₂O₃ - LB₂) crystallization in supercooled and glassy states by using available viscosity and crystallization data for samples of the same batch. An original key feature is that the nucleation rates were measured using a single-stage rather than the traditional double-stage heat treatment. We compared three proxies for D : D η obtained from viscosity, D U derived from crystal growth rates, and D τ estimated from nucleation time-lags. Our analysis revealed that at deep supercoolings, below the glass transition temperature, D U and D τ yield similar steady-state nucleation rate estimates, which significantly exceed those predicted by using D η (the most frequently used diffusion proxy). This result suggests that the atomic jumps governing crystal nucleation may be comparable to those in crystal growth, but distinct from those associated with cooperative rearrangements controlling viscous flow. Additionally, the estimated kinetic spinodal temperature (T k s) is above the Kauzmann temperature T k , implying that crystal nucleation precedes relaxation to the supercooled liquid state, circumventing the entropy paradox and corroborating recent MD simulations for other substances. These findings are valuable for refining theoretical models of crystal nucleation and highlight the complexities of the glassy state. [ABSTRACT FROM AUTHOR]

This article investigates the laminar flow of power-law fluids through two porous square cylinders in a side-by-side configuration. The effects of power-law index (n), Darcy number (Da), and gap ratio (g/W) are examined within ranges of g/W = 0.5–5, n = 0.4–0.8, and Da = 10−6–10−2, respectively. Two flow conditions are considered: first, for a creeping flow (unseparated flow) at Re = 1 where Darcy's law is applicable; second, for a viscous dominant flow at Re = 100, where Darcy–Forchheimer-extended model is exercised. Flow patterns behind the porous cylinders are analyzed using streamlines, velocity profiles, pressure distribution curves, and vorticity structural parameters (Г). In low permeability levels, the flow exhibits an irregular nonperiodic vortex shedding characterized by a single large vortex street far off the downstream for g/W = 0.5. However, synchronized wake patterns were observed in either antiphase or in-phase modes for higher gap ratios. Leading-edge separation with two-side recirculation induces quasi-periodicity in the flow for all g/W. It was found that increasing the permeability can prevent the leading edge separation. Additionally, a transition from antiphase to in-phase mode occurs when the permeability is altered while maintaining constant flow-time. The presence of a jet-like flow between cylinders significantly impacts unsteady wake patterns. The impact of g/W, power-law index, and permeability on drag is also examined. A jump in some flow parameters was observed at higher Re for the midrange Darcy number, but no such increase was noted for the high shear-thinning behavior. These findings provide a potential approach for improving the design of fluidic systems involving porous cylinders. [ABSTRACT FROM AUTHOR]

The work was conducted to analyze convective heat transfer theory concerning the MHD effect on a flat and vertical plane. Thus, it is assumed that the plane has an unlimited surface area. In this work, we have tried to investigate the speed, temperature, and concentration by examining the impact ability of the studied space from changes in the mass concentration of nanoparticles and course, other dimensionless parameters such as Soret number, magnetic parameter, and Grashof. We attempted to analyze the idea of the treatise using the Caputo‐Fabrizio‐fractional derivative model, which is worth mentioning. One of the interesting results of this work is that with the increase of volume fraction of nanofluids from 0.01 to 0.04 wt%, we see that the thermal distribution increases significantly. The temperature profile has decreased by almost 7% as a result of increasing the dimensionless Prandtl number from 4 to 7. A 19% increase in velocity values is caused by increased fractional parameter effects from 1 to 3. [ABSTRACT FROM AUTHOR]

A comprehensive study on the thermodynamic and transport properties of binary mixtures composed of active amyl alcohol (AAA) and haloalkane’s was conducted within a temperature range of 303.15 K to 313.15 K. Experimental data on densities (ρ), viscosities (η), and speeds of sound (u) were employed to calculate excess molar volume (VE), isentropic compressibility (KsE), viscosity deviation (Δη), and excess Gibbs free energy for viscous flow (∆G*E). The impact of dipole moment on these excess properties was investigated to gain insights into the prevailing intermolecular interactions within the mixtures. The Prigogine – Flory – Patterson (PFP) theory is applied to identify the predominant molecular interaction. The accuracy of the Jouyban–Acree model in correlating densities (ρ), viscosities (η), and speeds of sound (u) with composition were evaluated, demonstrating satisfactory agreement with experimental data. [ABSTRACT FROM AUTHOR]

Capillarity-driven transport in nanoporous solids is widespread in nature and crucial for modern liquid-infused engineering materials. During imbibition, curved menisci driven by high negative Laplace pressures exert an enormous contractile load on the porous matrix. Due to the challenge of simultaneously monitoring imbibition and deformation with high spatial resolution, the resulting coupling of solid elasticity to liquid capillarity has remained largely unexplored. Here, we study water imbibition in mesoporous silica using optical imaging, gravimetry, and high-resolution dilatometry. In contrast to an expected Laplace pressure-induced contraction, we find a squareroot-of-time expansion and an additional abrupt length increase when the menisci reach the top surface. The final expansion is absent when we stop the imbibition front inside the porous medium in a dynamic imbibition-evaporation equilibrium, as is typical for transpiration-driven hydraulic transport in plants, especially in trees. These peculiar deformation behaviors are validated by single-nanopore molecular dynamics simulations and described by a continuum model that highlights the importance of expansive surface stresses at the pore walls (Bangham effect) and the buildup or release of contractile Laplace pressures as menisci collectively advance, arrest, or disappear. Our model suggests that these observations apply to any imbibition process in nanopores, regardless of the liquid/solid combination, and that the Laplace contribution upon imbibition is precisely half that of vapor sorption, due to the linear pressure drop associated with viscous flow. Thus, simple deformation measurements can be used to quantify surface stresses and Laplace pressures or transport in a wide variety of natural and artificial porous media. [ABSTRACT FROM AUTHOR]

Herein, the influence of P2O5 on the break temperature and phase composition of slag from the double slag converter steelmaking process is investigated comprehensively. The composition and micromorphology of crystallized phase are analyzed by X‐Ray diffractometer and scanning electron microscope equipped with energy dispersive spectrometer. The results reveal that the break temperature of slag increases owing to an increase of P2O5 content. When the P2O5 content is 2%, the break temperature is 1198 °C, and it increases to 1209 °C for the slag with 4% P2O5. With the increase of P2O5 content from 2% to 8%, the activation energy for viscous flow shows an upward trend. The crystallized phase at the same temperature with different P2O5 contents remains nearly unchanged, but the diffraction peak intensity is different. When the P2O5 content remains constant, a decrease in temperature results in significant changes in the micromorphology of crystallized phases. The present results improve the knowledge about the P‐rich slag, and are also significant in optimizing the double slag converter steelmaking process. [ABSTRACT FROM AUTHOR]

This article discusses the thermal radiation significance on the 2-D laminar MHD boundary layer flow of a nanofluid, as well as the heat transfer associated with the viscous flow across a nonlinear stretching surface. The flow is produced by a nonlinearly enlarging sheet with varying temperatures in the existence of suction, radiation, and viscous dissipation. By applying suitable similarity conversions, the resultant governed PDEs are transformed to a set of nonlinear ODE's, and then, they are solved by applying the Keller–Box approach numerically. The impact of several flow pertinent factors on heat, species concentration, and velocity fields are exposed graphically and numerically. Numerical calculations for friction factor, mass, and heat transmission rates are discussed in table form. Prior results were examined under constraining circumstances and found to be adequate. It is discovered that when the velocity slip factor is enhanced, the fluid velocity distribution declines whereas the heat and concentration gradients increase. The principal results indicate that the porosity parameter effectively decreases the velocity distribution. [ABSTRACT FROM AUTHOR]

Multiple flow mechanisms that coexist in nanoscale porous media are responsible for deviations from the linear Klinkenberg equation. The use of mathematical models in the literature has obvious limitations in evaluating this flow phenomenon because the viscosity/diffusion coefficients of nanoscale porous media are more accurate only in the limited Knudsen number region. By introducing, the concept of an effective molecular mean free path, this paper proposes single models of viscosity/diffusion for the full Knudsen number range to replace the combination model in the literature. On this basis, a new apparent permeability model is developed with multiple coexisting mechanisms for the full Knudsen number range, and the effectiveness of the proposed model is verified by using published data. The discontinuous problem of the combination model of the viscosity/diffusion coefficient in the literature for the full Knudsen number range is solved using the new viscosity and diffusion coefficient models. The new apparent permeability model accurately predicts the absolute permeability and explains the phenomenon of deviation from the linear Klinkenberg equation. This paper further discusses the influence of different mechanisms on the permeability. The rarefaction effect weakens the diffusion ability in porous media but increases the contribution of Darcy flow to permeability. The viscous flow increment, absolute permeability and slippage effect were the most important flow mechanisms in nanopores. Article Highlights: We present the equation of the gas viscosity/diffusion coefficient in nanopores for the full Knudsen number range. We present a new apparent permeability model with multiple coexisting mechanisms for the full Knudsen number range. Our model predicts the absolute permeability of nanoscale porous media. [ABSTRACT FROM AUTHOR]

The featured problem explores the impact of cross-diffusion on the two-dimensional electrically conducting flow of a viscous liquid over a nonlinearly stretching sheet through a permeable medium. An inclusion of radiative heat energizes the heat transport phenomenon whereas the solutal transfer enriches by the conjunction of the chemical reaction. To justify the behavior of electromagnetic radiation, the Rosseland approximation is used by considering nonlinear thermal radiation. Further, the convective boundary conditions also affect the flow properties. The approachable transformations are employed to get a suitable non-dimensional form of the governing equations for the formulated problem. Due to the complex nature of the distorted equations, the system of equations is solved using an in-built code bvp5c predefined in MATLAB. The computation is carried out for the involvement of the suitable values of contributing parameters on the flow characteristics and along with the simulations of the rate coefficients. Further, the assigned particular parameters present an outcome that validates with a good correlation. Finally, the important outcomes are — enhanced suction due to the permeability of the surface augments the fluid velocity whereas the trend is reversed in the case of injection. The augmentation in the fluid temperature is exhibited for the radiating heat but the reacting species attenuates the fluid concentration. [ABSTRACT FROM AUTHOR]

Due to the intrinsic brittleness of ceramics, it is challenging to shape and plastically deform them. In this study, we plastically deformed ZrO 2 -SiO 2 dual-phase nanocrystalline ceramics (DPNCs) by an oscillatory pressure-assisted hot forging method, termed as "dynamic hot forging" (DHF). Under the synergistic effects of oscillatory pressure (60 ± 5 MPa, 2 Hz) and heat (1250 °C), significant dimensional changes of the DPNCs occurred after DHF. The as-sintered DPNCs consisted of tetragonal ZrO 2 nanocrystallites (NCs) embedded in an amorphous SiO 2 matrix. The forging process did not significantly alter the phase composition of the DPNCs, but obvious coarsening of ZrO 2 NCs occurred during DHF. Microstructural observations showed that the DPNCs deformed predominately through the viscous flow of amorphous SiO 2 at high temperature. No microcracks were observed although the DPNCs experienced large deformation. The morphology of ZrO 2 NCs did not significantly changed, i.e., they maintained a near-spherical morphology before and after forging. However, a large number of lattice defects in ZrO 2 NCs were formed due to forging, including edge dislocations, subgrain boundary, nanotwins, and stacking faults. The formation of lattice defects did not cause significant effect on the microhardness of the DPNCs. The results of this study suggest that DHF process is a promising technique to plastically deform and shape ceramics with crystalline-amorphous dual-phase microstructure. [ABSTRACT FROM AUTHOR]

The acceleration self-starting performance of hypersonic inlets is of critical importance for the stable operation of scramjet engines. The occurrence of soft unstart during the transition from hard unstart to start is an important flow state that has yet to be fully elucidated. The stability mechanism and corresponding self-starting characteristics of soft unstart remain poorly understood, and there is a pressing need for detailed modeling research in this area. This paper presents a rapid prediction model for the self-starting Mach number of two-dimensional hypersonic inlets with soft critical unstart mode, fully considering the influence of various geometric parameters and Reynolds number in the internal contraction section, and achieving a quantitative analysis of the two-dimensional soft unstart critical flow field. Given the incoming flow conditions and the inlet geometry, the prediction model is capable of accurately representing the actual viscous unstart flow field. It can fully map the unstart separation bubble and its surrounding critical wave structures, and calculate the minimum pressure rise required to maintain the current scale of the main separation bubble and the pressure rise exerted on the unstart separation bubble by the current actual flow field structure. Comparing the relative magnitude of these two pressures determines whether the inlet can transition from soft unstart to start. The proposed prediction model was validated using results from unsteady numerical simulations. The predicted results align well with the simulation results and are significantly better than previous prediction methods. [ABSTRACT FROM AUTHOR]

Particulate Taylor–Couette flow of a particle-laden viscous fluid between two coaxial rotating cylinders is studied using a novel hydrodynamic model. With the volume fraction of particles as the dimensionless small parameter, explicit leading-order solutions are derived for the general case of dispersed particles heavier or lighter than the carrier fluid. It is shown that, unlike the classical azimuthal velocity field of a clear fluid without particles, dispersed particles generally have a radial velocity toward the outer or inner cylinder depending on the angular velocities and radii of the two cylinders and whether the particles are heavier or lighter than the carrier fluid, in qualitative agreement with some known results reported in literature on heavier or lighter particles, respectively. In some cases, such as the flow driven by rotating inner cylinder with a wider gap between the two cylinders and a moderate value of Stokes number of particles, our results predict the existence of a circular ring between two cylinders, which attracts or repels heavier or lighter particles that could have relevant physical implications. Beyond existing literature on the Taylor–Couette flow with neutrally buoyant particles, these results could offer new insight and useful explicit solutions to the Taylor–Couette flow with particles heavier or lighter than the carrier fluid. [ABSTRACT FROM AUTHOR]

In this study, the hydrodynamic forces and power absorption performance of an autonomous underwater vehicle (AUV)-based two-body wave energy converter (2BWEC) are investigated. A theoretical model is developed within the framework of linear potential flow to solve for added mass, radiation damping, and wave excitation force using the matched eigenfunction expansion method (MEEM). A computational fluid dynamics (CFD) model is employed to account for vortex-shedding effects of the floater and inner cylinder with a damping plate under various excitation conditions. Empirical formulas for supplementary added mass and drag coefficients caused by flow separation are proposed based on curve-fitting the differences between CFD results and MEEM calculations. These formulas are integrated into motion equations to enhance accuracy in evaluating the power absorption of the 2BWEC. It has been found that in the context of viscous flow, both the added mass and damping coefficients are increased, particularly for the inner cylinder with a damping plate. In addition, the viscous hydrodynamic coefficients exhibit strong dependence on the Keulegan–Carpenter number, while showing insensitivity to changes in the frequency parameter β. The supplementary (viscous) added mass provides additional inertia for the AUV with a limited mass itself, which is advantageous for the power absorption of the AUV-based 2BWEC. Conversely, the presence of viscous damping from the damping plate impedes wave energy capture. [ABSTRACT FROM AUTHOR]

Understanding the mechanisms by which fish sense vortical perturbations is crucial for both biological insights and technological advancements. We investigate the hydrodynamics of a solid plate moving vertically through the reverse Kármán vortex street generated by a horizontally moving flexible flapping plate in a viscous flow. The impacts of the horizontal distance between the two plates (D) and the moving speed of the solid plate ( v y ) are considered. The horizontal distance determines the vortical environments, i.e., whether the solid plate impinges through the vortex cores or the gaps. Different vortical environments exhibit varying vortex-induced velocities, resulting in distinct force and pressure patterns on the solid plate. The evolution of these sensed forces and pressures is mapped along the path of the solid plate, suggesting a potential mechanism by which fish detect the position and properties of surrounding vortices. Furthermore, it is found that increasing speed can amplify the sensed force and pressure signals by thinning boundary layers and strengthening friction force. Nevertheless, the established mapping relationships remain applicable across varying velocities, and a scaling relation has been derived to normalize this amplification effect on the vertical force. These findings enhance our understanding of fish sensory mechanisms and could inspire innovative designs and control strategies for underwater vehicles. [ABSTRACT FROM AUTHOR]

Oceanic plates are doubly curved spherical shells, which influences how they respond to loading during subduction. Here we study a viscous fluid model for gravity‐driven subduction of a shell comprising a spherical plate and an attached slab. The shell is 100–1,000 times more viscous than the upper mantle. We use the boundary‐element method to solve for the flow. Solutions of an axisymmetric model show that the effect of sphericity on the flexure of shells is greater for smaller shells that are more nearly flat (the "sphericity paradox"). Both axisymmetric and three‐dimensional models predict that the deviatoric membrane stress in the slab should be dominated by the longitudinal normal stress (hoop stress), which is typically about twice as large as the downdip stress and of opposite sign. Our models also predict that concave‐landward slabs can exhibit both compressive and tensile hoop stress depending on the depth, whereas the hoop stress in convex slabs is always compressive. We test these two predictions against slab shape and earthquake focal mechanism data from the Mariana subduction zone, assuming that the deviatoric stress in our flow models corresponds to that implied by centroid moment tensors. The magnitude of the hoop stress exceeds that of the downdip stress for about half the earthquakes surveyed, partially verifying our first prediction. Our second prediction is supported by the near‐absence of earthquakes under tensile hoop stress in the portion of the slab having convex geometry. Plain Language Summary: Tectonic plates on earth are doubly curved spherical shells, which influences how they respond to applied forces during subduction. We use axisymmetric and three‐dimensional viscous flow models to study the dynamics of spherical shells sinking under gravity into the mantle below. We find the surprising result that the effect of spherical geometry on the bending of shells is greater for smaller shells that are more nearly flat, which we call the "sphericity paradox." We also find that the stress in the subducted portions of plates ("slabs") is dominated by the longitudinal normal stress (hoop stress), which is about twice as large as the more familiar downdip stress. Earthquake focal mechanisms from the Mariana subduction zone in the Pacific ocean confirm our prediction that no deep earthquakes should occur under tensile hoop stress in portions of slabs having convex landward geometry. Key Points: The dynamical effect of plate sphericity on subduction is greater for smaller plates (the "sphericity paradox")The state of stress in the central portions of subducted slabs is dominated by the longitudinal normal (hoop) stressMariana slab earthquakes confirm our prediction that convex slab geometry and tensile hoop stress never occur together [ABSTRACT FROM AUTHOR]

In this study, a numerical framework based on the material point method is presented for the simulation of material extrusion (MEX)-based 3-D printing processes. The melt flow during material extrusion is assumed to be viscous flow including phase changes. To apply the free surface boundary conditions, the framework utilizes the level set method to track the free surface and the ghost fluid method for the application of the boundary conditions. For validation, three representative problems are first investigated to show the versatility of the model. Then, the numerical framework is adapted for the simulation of material extrusion (MEX) based 3-D printing processes. An in-depth parametric study is presented to show how printing parameters affect the overall extruded printing material. [ABSTRACT FROM AUTHOR]

Phase transformations play a key role in numerous coupled natural processes, and they are important for many industrial applications. However, the kinetics of phase transformations in coupled chemo-mechanical systems undergoing large mechanical deformations still needs to be better quantified. Here, we study the phase transformation kinetics of a two-phase binary mixture using the diffuse interface approach. We couple a Cahn–Hilliard type model with a mechanical model for a compressible viscous flow. The bulk compressibility is a nonlinear function of the pressure, and the shear viscosity is a nonlinear function of the concentration. The mechanical coupling is achieved by employing a pressure-dependent mechanical mixing term in the equation for the Gibbs energy. We derive a dimensionless system of equations which we solve numerically with a pseudo-transient method using conservative finite differences for discretization. We perform numerical simulations in 1D and 2D model setups considering far-field simple shear and pure shear. For a chemo-mechanically coupled system, we show that the velocity of the phase boundary is a linear function of the degree of metastability and, hence, confirm the hypothesis of "normal growth." A stronger mechanical coupling and a larger volumetric effect of the chemical reaction result in lower phase boundary velocities. The 2D results show a significant impact of the mechanical coupling and the far-field deformation on the orientation and kinetics of the phase transformations. Under far-field simple shear and pure shear in 2D, the phase transformations generate string-like patterns. The orientation of these patterns is controlled by the applied far-field deformation and orientations differ by 45 degrees between simple shear and pure shear. [ABSTRACT FROM AUTHOR]

Excess molar volume, excess isentropic compressibility, deviation in viscosity and excess Gibbs free energy for activation of viscous flow for binary mixtures of allyl alcohol (AA) with 2-methyl-2-butanol (2M2B), 2-methyl-1-butanol (2M1B) and 3-methyl-2-butanol (3M1B) components in different compositions were determined from the measured values of densities (ρ), viscosities (η) and speeds of sound (u) of pure components and their mixtures at various temperatures ranging from 303.15 K to 313.15 K. The excess properties have been discussed in terms of disruption of H-bonding and dipole–dipole interaction between the components of the mixtures. The Jouyban–Acree model results are discussed in terms of mean relative deviation (MRD) and individual relative deviation (IRD) between calculated and experimental parameters as an accuracy criterion and obtained a good agreement. The thermodynamic functions of activation of viscous flow have been estimated and tested. FTIR studies further confirm the experimental findings. [ABSTRACT FROM AUTHOR]

The current investigation focuses on examining viscous corrections for viscous potential flow (VCVPF) analysis concerning the Rayleigh–Taylor instability occurring at the interface of a Rivlin–Ericksen (R–E) viscoelastic fluid and a viscous fluid during the transfer of heat and mass between phases. The R–E model is a fundamental framework in the study of viscoelastic fluids, providing insights into their complex rheological behavior. It characterizes the material's response to both deformation and flow, offering valuable predictions for various industrial and biological applications. Within the framework of viscous potential flow (VPF) theory, viscosity is exclusively accounted for in the normal stress balance equation, disregarding the influence of shearing stress entirely. This study introduces a viscous pressure term into the normal stress balance equation alongside the irrotational pressure, presuming that this addition will improve the discontinuity of tangential stresses at the fluid interface. Through derivation of a dispersion relationship and subsequent theoretical and numerical stability analyses, the stability of the interface is investigated across various physical parameters. Multiple plots are generated using the dispersion relation, and a comparative analysis between VPF and VCVPF is conducted to establish improved stability criteria. The investigation highlights that the combined impact of heat/mass transport and shearing stress serves to delay the instability of the interface. [ABSTRACT FROM AUTHOR]

This paper introduces a novel platform that integrates three preconditioning matrices based on conservative variables: the Turkel, Choi–Merkle and Onur matrices. The platform aims to compare these matrices in terms of accuracy and robustness by investigating their performance in solving three distinct and challenging high-gradient laminar flow problems: (i) Bi-Plane NACA0012 airfoil, (ii) lid-driven flow in a square cavity and (iii) flow in a planar T-junction. These problems serve as new and challenging test cases to accurately determine the abilities of the preconditioning matrices. The preconditioning matrices are applied to evaluate the numerical solutions, and their performance in complex flow fields is assessed in terms of accuracy and efficiency. By solving these flow problems, the effectiveness of the preconditioning matrices is thoroughly analyzed. By integrating these preconditioning matrices into a single platform, this paper significantly contributes to the field. The approach enables a direct and meaningful comparison of the performance of the Turkel, Choi–Merkle and Onur matrices in solving these new and challenging laminar flow problems. While all three matrices demonstrate comparable accuracy in predicting flow characteristics like pressure coefficients, Turkel's method shows superior convergence acceleration across the almost test cases due to alpha parameter and modifications of the momentum equations. In the external flow case, Turkel converges 22–53% faster than the other matrices by adjusting momentum terms with an alpha parameter. For the internal lid-driven cavity case, Turkel again accelerates convergence up to 38% over Choi–Merkle as Reynolds and Mach numbers increase. However, Onur's method stalls at high Reynolds/Mach numbers. At low values of Reynolds and Mach numbers, Onur reduces computational cost by 17%. Finally, for the T-junction case, Turkel and Choi–Merkle perform almost identically, decreasing CPU time by 55% vs Onur, which lacks convergence robustness. While the preconditioning matrices have similar accuracy, Turkel offers the best convergence improvement by accounting for momentum effects. Onur works well at low Reynolds/Mach numbers but shows limitations at higher values. The selection of the optimal preconditioning matrix should be based on whether momentum or viscosity dominates in the flow field, as well as the intensity of the viscosity gradient rate. [ABSTRACT FROM AUTHOR]

The influence of oblique currents in narrow and shallow channels causes the fluid flow around ships to become complex. To analyze the hydrodynamic characteristics of a ship in such channels, it is essential to examine the influence of oblique currents on the ship's hydrodynamic characteristics. In this study, current direction, ship speed, current speed, and water depth were identified as determinants affecting the hydrodynamic characteristics of a ship. Numerical simulations were conducted on a large oil tanker to investigate the effects of these factors on the ship's hydrodynamic characteristics. The viscous fluid flow was modeled using the unsteady Reynolds-averaged Navier–Stokes (URANS) equations in conjunction with the k-ε turbulence model. The URANS equations were discretized using the finite volume method. The numerical results indicate substantial differences in the hydrodynamic characteristics of ships under oblique current conditions compared to still-water conditions. At a current direction of β = −45°, the direction of the sway force is consistent with that of still water's sway force, which is an attractive force. The yaw moment at β = −45° changes from a bow-out moment under still-water conditions to a bow-in moment. Conversely, at a current direction of β = 45°, the sway force shifts from an attractive force under still-water conditions to a repulsive force. The yaw moment acts as a bow-out moment, which is consistent with that observed in still-water conditions. Furthermore, the influence of hydrodynamic characteristics on a ship varies significantly with changes in ship speed, current speed, and water depth. To ensure the safe navigation of ships, it is essential to develop and apply comprehensive strategies and countermeasures that account for practical conditions. [ABSTRACT FROM AUTHOR]

This article presents research into the feasibility of applying a nonlinear damper of a new conceptual structure. The key component of the damper is a circular membrane with slits that can move in a cylinder filled with viscous fluid. When an external load is applied to the damper, the membrane deforms, opening the slits. The flow of viscous fluid through the slits generates a damping force. The phenomenological model of the damper is based on the notion that the slit membrane moves according to the fundamental axisymmetric vibration mode of a circular membrane. The slit membrane blocks the entire radius of the pipe in the state of equilibrium when all slits are closed. As the membrane moves, the opening area of the slits varies depending on its deformation. This gives a nonlinear damping characteristic. The damping constant depends on the input displacement and velocity, which is the reason for the nonlinearity of the damping characteristic. From the phenomenological model, the nonlinear characteristic of the drag force is obtained. The performance of the damper is simulated using a mass–spring–damper system. Two cases of harmonic excitation and impulse excitation are analyzed. The results show that, using the slit membrane damper, the suppression of dynamic loads is more effective compared to a conventional linear damper. [ABSTRACT FROM AUTHOR]

This paper studies the instability of a non-ideal pipe system conveying fluid. Unlike ideal modeling, three types of possible non-ideal factors have been considered in the present analysis. The pipe has a crack and is subjected to boundary relaxation, and the fluid in the pipe is viscous. It is an interesting instability problem of a fluid-structure system with multiple forms of imperfections. It gains motivation from our previous study and aims at further essential results for comprehensively understanding the nature of such a problem. In order to incorporate multiple imperfections, a new data-driven approach is developed to model the non-ideal pipe-fluid system. Then the influences of the support stiffness, fluid–solid mass ratio, crack, and fluid viscosity on the pipe instability are systematically discussed. Results show that the pipe exhibits flutter-divergence conversion at low mass ratios and flutter-mode transition at high mass ratios. Due to the two types of instability transitions, the critical flow speed could experience multiple sudden jumps as the support stiffness changes. With the imperfections of crack and viscous flow, the pipe's instability behavior tends to be more complicated, but the inducing mechanisms for the sudden changes are straightforward. They are instability-type conversion, instability-mode transition, and laminar-turbulent flow transition. [ABSTRACT FROM AUTHOR]

Nanostructured amorphous composites are novel materials comprising nano-sized crystal phases embedded in an amorphous matrix, but often necessitating ultra-high-pressure molding for preparation. In this study, nanostructured amorphous ZrO 2 –Y 2 O 3 composite ceramics were rapidly prepared for the first time using flash viscous flow sintering without the application of pressure. The relative density of the ZY ceramics increased with increasing current density, and ZY composite ceramics with relative density of 86%–97 % were prepared by FS in a short time of 60 s under 700 V/cm with 0.16–0.56 A/cm2. Furthermore, the sintering activities in FS were compared between partially amorphous powder and crystalline powder. The ceramics prepared by flash sintering of partially amorphous powder show a much higher relative density than that from crystalline powder, suggesting that partially amorphous powder achieves easier densification than crystalline powder in flash sintering under given current density and power dissipation. This phenomenon was attributable to the differing sintering mechanisms between the two materials, i.e., solid-state sintering for crystalline powder and viscous flow sintering for partially amorphous powder. [ABSTRACT FROM AUTHOR]

In this paper, we consider a singular limit problem for a diffuse interface model for two immiscible compressible viscous fluids. Via a relative entropy method, we obtain a convergence result for the low Mach number limit to a corresponding system for incompressible fluids in the case of well‐prepared initial data and same densities in the limit. [ABSTRACT FROM AUTHOR]

Pure boron carbide (B4C) ceramics are sintered by hot oscillating pressing at temperatures of 1700–1900 °C for different soaking times. The densification mechanism, grain growth kinetics, and mechanical properties obtained under these sintering conditions are systematically investigated. It is found that the fully densified B4C ceramic is obtained at 1900 °C within 120 min, possessing an excellent combination of hardness (≈38.5 GPa) and fracture toughness (4.8 MPa m1/2). The densification mechanisms during sintering are as follows: viscous flow at the initial stage (relative density D ranged from 55% to 65%) under 1700 °C; lattice diffusion/grain boundary diffusion at the sintering stage (62% < D$\textrm{ } D$ < 75%) of 1800 and 1850 °C; grain boundary sliding by dislocation motion at the late stage (65% < D$\textrm{ } D$ < 82%) of 1700 °C and the sintering stage (75% < D < 90%) at 1800–1900 °C; and dislocation gliding and stacking faults at the final stage (90% < D < 95%) occurring at 1850–1900 °C. The dislocation motion exhibits a critical impact on the densification process of the hot oscillating–pressed B4C ceramic. The grain growth kinetics at 1900 °C is controlled by grain boundary diffusion. [ABSTRACT FROM AUTHOR]

The duality between deformations of elastic bodies and noninertial flows in viscous liquids has been a guiding principle in decades of research. However, this duality is broken when a spheroidal or other doubly curved liquid film is suddenly forced out of mechanical equilibrium, as occurs, e.g., when the pressure inside a liquid bubble drops rapidly due to rupture or controlled evacuation. In such cases, the film may evolve through a noninertial yet geometrically nonlinear surface dynamics, which has remained largely unexplored. We reveal the driver of such dynamics as temporal variations in the curvature of the evolving surface. Focusing on the prototypical example of a floating bubble that undergoes rapid depressurization, we show that the bubble surface evolves via a topological instability and a subsequent front propagation, whereby a small planar zone that includes a singular flow structure, analogous to a disclination in elastic systems, nucleates spontaneously and expands in the spherically shaped film. This flow pattern brings about hoop compression and triggers another, symmetrybreaking instability to the formation of radial wrinkles that invade the flattening film. Our analysis reveals the dynamics as a nonequilibrium branch of "jellium" physics, whereby a rate-of-change of surface curvature in a viscous film is akin to charge in an electrostatic medium that comprises polarizable and conducting domains. We explain key features underlying recent experiments and highlight a qualitative inconsistency between the prediction of linear stability analysis and the observed "wavelength" of surface wrinkles. [ABSTRACT FROM AUTHOR]

This work is devoted to a numerical analysis of the sensitivity of the spatial stability characteristics of boundary layers to uncertainties of the main flow. It is proposed to use structured pseudospectra for this purpose. It is shown that the obtained estimates are much more accurate than estimates based on an unstructured pseudospectrum. The presentation is based on an example of the flow of a viscous incompressible fluid over a slightly concave surface with flow parameters favorable for the development of the Görtler vortices and Tollmien–Schlichting waves. [ABSTRACT FROM AUTHOR]

Despite significant progress in studying subduction earthquake cycles, the vertical deformation is still not well understood. Here, we use a generic viscoelastic earthquake‐cycle model that has recently been validated by horizontal observations to explore the dynamics of vertical earthquake‐cycle deformation. Conditioned on two dimensionless parameters (i.e., the ratio of earthquake recurrence interval T to mantle Maxwell relaxation time tM (T/tM) and the ratio of downdip seismogenic depth D to elastic upper‐plate thickness Hc (D/Hc)), the modeled viscoelastic deformation exhibits significant spatiotemporal deviations from the simple time‐independent elastic solution. Caution thus should be exercised in interpreting fault kinematics with vertical observations if ignoring Earth's viscoelasticity. By systematically exploring these two parameters, we further investigate three metrics that characterize the predicted vertical deformation: the coastal pivot line (CPL), the uplift zone (UZ) landward above the downdip seismogenic extent, and the secondary subsidence zone (SSZ) in the back‐arc region. We find that these metrics can all be time‐dependent, subject to D/Hc and T/tM. The CPL location and the UZ width are mainly controlled by D/Hc and T/tM, respectively. The presence of the SSZ is prevalent during the interseismic phase due to viscous mantle flow driven by ongoing plate convergence. Contemporary vertical deformation in Nankai and Cascadia is largely consistent with the model predictions and features differences mainly related to contrasting D/Hc values in the two margins. These findings suggest that vertical crustal deformation bears fruitful information about subduction‐zone dynamics and is potentially useful for inversions of key subduction‐zone parameters, deserving properly designed monitoring. Plain Language Summary: The community studying subduction earthquake deformation usually focuses on the horizontal component due to its strong signals and low observation errors. However, over the past decade, it has increasingly been realized that the vertical deformation is often more diagnostic of megathrust faulting and rheological structure. Additionally, communities studying glacial isostatic adjustment, sea‐level rise, surface and mantle processes and beyond are recently working hard to refine their models by teasing out the earthquake component, which is thought to contaminate their vertical observations. To address these demands, we use computer models validated by the horizontal observations to simulate the vertical movement of the land during the period between great subduction zone earthquakes. We find that the earthquake and subsequent fault locking can cause vertical movement of the surface—subsidence near the coast, uplift landward and subsidence again in the far field. These three features can vary in deformation rates and location/area depending on how deep the fault is locked, how weak the mantle is, and how much time has elapsed since the earthquake. Therefore, previous vertical observations and newly deployed instruments designed to detect key signals are essential for understanding earthquakes, tsunamis and the dynamics of the subduction system. Key Points: On earthquake (EQ)‐cycle time scale, coastal pivot line (CPL), uplift zone (UZ) and secondary subsidence zone (SSZ) are key vertical featuresLocation of the CPL is indicative to downdip seismogenic extent and may migrate landward or seaward depending mainly on the mantle rheologyThe SSZ, as observed in Nankai and Cascadia, is due to interseismic viscous mantle flow and are affected by EQ elapsed and recurrence time [ABSTRACT FROM AUTHOR]

The geometrical prediction of multiple hydraulic fractures fed from a single fluid source is a major challenge due to transient stress interference among fractures and nonlinear coupling between rock deformation and fluid flow. Here we find that the evolution of multiple hydraulic fractures under isotropic stresses is controlled by a dimensionless toughness, which measures the ratio of the energy dissipated in rock fracturing to that dissipated in viscous fluid flow. The existence of a relation between the dimensionless toughness and the dimensionless length of the arrested fractures is demonstrated by using a bifurcation analysis. The numerical results show that the fractures tend to grow simultaneously in the viscosity‐dominated regime, and the scaling remains effective when the number of fractures varies. This study provides a quantitative and efficient tool for predicting the fracture pattern in engineered and natural fracture systems. Plain Language Summary: The formation of multiple fluid‐driven fractures fed from a single fluid source is ubiquitous in geological features such as sub‐parallel dyke swarms and hydraulic fractures in reservoirs. Due to the stress interference exerted by neighboring fractures, the growth of multiple fractures is not uniform, which finally leads to a complex fracture system. However, the geometrical prediction of such fracture system is a major challenge, and a general understanding in the evolution of the fracture system is lacking. In this study, we investigate the controlling factors in the propagation of multiple hydraulic fractures by using theoretical and numerical techniques. A relation is found between the fracture pattern and a dimensionless number that accounts for the energy dissipation between rock fracturing and fluid flow. Numerical results show that the scaling remains effective when the number of fractures varies under isotropic stresses, and the fractures tend to grow simultaneously when the energy is mainly dissipated in fluid flow, while the uniform fracture growth is suppressed when the energy is mainly dissipated in rock fracturing. This work provides insights into the mechanics controlling the evolution of multiple hydraulic fractures and offers an efficient method in predicting the fracture geometry in engineering applications. Key Points: A quantitative relation is found between a dimensionless number and the pattern of multiple plane‐strain hydraulic fracturesA uniform fracture growth is favored when energy is mostly dissipated in fluid flow instead of rock fracturingThe scaling remains effective for different number of hydraulic fractures under isotropic stresses [ABSTRACT FROM AUTHOR]

The basic objective of this article is to highlight the impact of Joule heating, thermal radiation, and viscous dissipation on heat transfer rate and friction drag in the flow of viscous nanofluid subject to the curved stretching sheet. Moreover, the effects of magnetic field and two-heating process termed as prescribed surface temperature and prescribed heat flux is considered on the surface. The nanofluid is addressed as a mixture of alumina ( $ Al_2O_3 $ A l 2 O 3 ) nanoparticle and ethylene glycol ( $ C_2H_6O_2 $ C 2 H 6 O 2 ) base fluid. Initially, certain dimensionless variables have been addressed to modify the governing partial differential equation (PDEs) and the associated boundary condition into non-dimensional ordinary differential equations (ODEs) coupled with boundary conditions. Subsequently, the resulting equations are solved numerically by implementing bvp4c package in MATLAB. Multiple graphical results for heat transfer rate, friction drag, velocity, and temperature are obtained under the influence of several flow parameters like radiation parameter, Eckert number, curvature parameter, stretching parameter, Hartmann number, and volume fraction of nanoparticles. Moreover, several interesting results for the flat surface ( $ K \to \infty $ K → ∞), with prescribed heat flux and surface temperature have been determined. The current radiative and dissipative flow coupled with the Joule heating process have countless applications in various industrial and engineering techniques. [ABSTRACT FROM AUTHOR]

The flow as well as the chemically reactive solute transfer problem in a viscous fluid over an exponentially stretching sheet are analytically investigated in this work. The nonlinear differential equations associated to the motion equations are approximately solved by means of the modified Optimal Homotopy Asymptotic Method (OHAM). The dual approximate analytical solutions are obtained. By comparison with the corresponding numerical solutions a good agreement is performed and show that this procedure is effective, accurate and easy to use in applications. [ABSTRACT FROM AUTHOR]

This document is a correction notice for an article titled "On the two-dimensional Boussinesq equations with temperature-dependent thermal and viscosity diffusions in general Sobolev spaces." The authors make several corrections to the original article, including removing certain results and estimates, correcting the proof of the uniqueness result, and providing corrected proofs for the three endpoint regularity cases. The corrected proofs are provided using the same notations and equation numbering as in the original article. The document concludes by stating that the original article can be found online. The article discusses the uniqueness result of the two-dimensional Boussinesq equations with temperature-dependent thermal and viscosity diffusions in general Sobolev spaces. The authors mention that the uniqueness result is not expected below a certain regularity assumption. The article is available under the Creative Commons Attribution 4.0 International License. The publisher remains neutral regarding jurisdictional claims and institutional affiliations. The article is authored by Zihui He and Xian Liao from the Institute of Analysis at the Karlsruhe Institute of Technology in Germany. [Extracted from the article]

This study investigates the boundary layer flow problem arising in the viscous fluid flow of a slightly rarefied gas-free stream over a moving plate embedded in a porous medium. Previous works were mainly focused on numerically, and some properties of the solutions were discussed from numerical results. But, numerical solutions are only sometimes guaranteed the solution's existence. In this work, we have adopted the famous topological shooting argument to prove the existence result of the solution. We have shown that the solution may be convex or concave depending on the parameter values. Also, for these reasons, there arise some difficulties. However, we have rectified all the challenges and proved that unique solutions exist for all the particular governing parameter values. Nevertheless, we found an exact solution for some specific parameter values. Furthermore, the Haar wavelet collocation method is used to address the numerical results of the nonlinear boundary value problem. We first validate the obtained results with the existing numerical outcomes. The impacts of permeability and slip parameters on the velocity profiles and shear stress are elucidated through tables and figures, and probable arguments are explained in detail. [ABSTRACT FROM AUTHOR]

Coalbed methane (CBM) content is a crucial parameter for CBM exploitation and disaster prevention, with accurate gas loss calculation being essential for improving measurement precision. To investigate the physical response to gas loss and quantify the impact and interrelation of various factors, this study developed a comprehensive model incorporating the effects of gas diffusion, temperature, and pressure effects on porosity and coal deformation. By utilizing the OpenFOAM platform and C++ for numerical solution development and establishing an experimental system for gas loss measurement, the model's reliability was confirmed. The new model demonstrates an 8.56% average error, representing a significant improvement over traditional methods, with error reductions of 26.59% and 18.31% compared to the square root of time and power function methods, respectively. The hierarchy of gas loss is determined to be gas flow > gas-coal deformation coupling > gas-temperature coupling > gas-coal deformation-temperature coupling. Average diffusion contributions are identified as 41.43% from surface diffusion, 30.71% from Knudsen diffusion, and 27.86% from viscous flow. The factors affecting gas loss, in decreasing order of impact, are adsorption equilibrium pressure, temperature, porosity, moisture, and adsorption constants. These findings provide theoretical support for enhancing gas content measurement accuracy and techniques, significantly benefiting CBM extraction and mine safety. [ABSTRACT FROM AUTHOR]

We investigate the effectiveness and universality of the turbulence control strategy for wall-bounded shear flows proposed by Chagelishvili et al. The basis of this strategy is the continuous seeding of the flow viscous sub-layer with spanwise asymmetric and specially designed velocity perturbations. This seed velocity field, amplifying due to the shear flow non-normality, breaks the flow spanwise reflection symmetry, specifically leading to the generation of a secondary nonuniform spanwise mean flow, which significantly reduces the flow turbulence. For now, this strategy is realized by a weak near-wall volume forcing, which, though theoretical/hypothetical, initiates the needed seed velocity field in the flow. To confirm the practical significance of this control strategy, we evaluated its effectiveness in the plane Couette flow at various Reynolds numbers, and with the forcing locations at different distances from the wall. The universality of the discussed turbulence control strategy is shown through the direct numerical simulations. The simulations with the near-wall volume forcing having specially designed, fixed configuration and amplitude result in the reduction of turbulence kinetic energy production by 30%–40% across a wider range of Reynolds numbers, R e τ = 52 , 92 , 128 , and 270 , and the forcing various wall-normal localizations in plus units, y peak + = 0.16 , 0.28 , 0.38 , 0.81 , 2.56 , and 2.76. [ABSTRACT FROM AUTHOR]