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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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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 dynamics of heat and mass transfer, focusing on the impact of nonlinear convection and thermophoresis in the flow of viscous nanofluid towards a shrinking sheet embedded with a porous matrix. To facilitate understanding of the flow behavior, the study employs similarity variables to simplify the resulting nonlinear partial differential equations. Numerical analysis utilizing the collocation method with Legendre polynomials as basis functions reveals distinct distributions of velocity, temperature, and concentration. The results demonstrate that the dimensionless suction coefficient amplifies nanoparticle volume fraction and momentum along the stretching surface. In addition, an increase in internal frictional force leads to heightened injection of heat energy, accelerates the temperature field, and impedes nanoparticle diffusion due to heat absorption. Elevation of convection terms augments momentum, reduces energy dispersion, and enhances nanoparticle diffusion. Moreover, an increase in the dimensionless Eckert number (Ec) correlates with intensified energy and diminished diffusion concentration of the nanoparticle volume fraction [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]

We present a discrete filter for subgrid-scale model, coupled with the discretization corrected particle strength exchange method, for the simulation of three-dimensional viscous incompressible flow at high Reynolds flows. The majority of turbulence modeling techniques, particularly in complex geometries, face significant computational challenges due to the difficulties in implementing three-dimensional (3D) convolution operations for asymmetric boundary conditions or curved domain boundaries. In this contribution, Taylor expansion is used to define differential operators corresponding to the convolution filter, so that the transfer function remains very close to the unity of sizeable displacement in wave number, making the filter a good approximation to the convolution one. A discrete Gaussian filter, in both fourth and second-order forms, was evaluated with varying ratios of particle spacing to the cutoff length. The impact of the filter's order and the ratio's value is thoroughly examined and detailed in the study. Additionally, the Brinkman penalization technique is employed to impose boundary conditions implicitly, allowing for efficient and accurate flow simulations around complex geometries without the need for modifying the numerical method or computational domain. The incompressible flow is governed by the entropically damped artificial compressibility equations allowing explicit simulation of the incompressible Navier–Stokes equations. The effectiveness of the proposed methodology is validated through several benchmark problems, including isotropic turbulence decay, turbulent channel flow, and flow around four cylinders arranged in a square in-line configuration, which are representative but not exhaustive of the full range of engineering applications. These test cases demonstrate the method's accuracy in capturing the intricate flow structures characteristic of high Reynolds number flows (up to 15k), highlighting its applicability to turbulence modeling. [ABSTRACT FROM AUTHOR]

The dynamics of a single flexible flag behind a semi-circular cylinder are investigated using vortex interaction study and dynamic mode decomposition (DMD). The problem is numerically solved using the immersed boundary method. For Reynolds number 300, by the variation of the streamwise gap between flag and bluff body ( D x ), five regions, each exhibiting its unique pattern of flapping, from symmetric and periodic to chaotic, are identified by vortex interaction study. DMD and kernel-DMD are utilized for modal analysis and reconstruction of a viscous flow behind a semi-circular cylinder with a flexible flag located at a streamwise distance of D x = 1.8 for moderate Reynolds number (Re = 30–500) with emphasis on representing the dynamics of the system using as few DMD modes as is practically possible. Sampling rate sensitivity study shows that low sampling rate data induce an additional frequency in the decomposition, which actually make up for the high frequency content in the vicinity of the flag and single frequency system is decomposed as the quasiperiodic system. According to the modal analysis, the fundamental frequency mode conjugate pair has the same frequency as the flag's vertical flapping and lift. It accounts for vortex production and advection from the bluff and flag and lift phenomenon. The first harmonic mode contains information regarding vortex shedding from the bluff body edges and flag tip and drag as they share same frequencies. DMD reconstruction demonstrates that 97.65% of the Re 100 post-transient system can be reconstructed using 28 DMD modes, whereas 86.71% of the Re 300 post-transient system requires 25 DMD modes. For fully transient cases, poor performance is achieved when using the DMD. The kernel-DMD application to full transient cases yields a non-oscillatory "mean mode," a "shift mode," and stable harmonic modes that are also present in post-transient analysis. The shift mode is famous in the modal analysis community, and it accounts for the correction to the mean mode for the transient region. In addition, these modes, there are additional modes that represent the transient dynamics of the system. 50 DMD modes reconstruct 86.98% and 77.65% of the Re 100 and Re 300 full-transient system, respectively. [ABSTRACT FROM AUTHOR]

Steady solutocapillary convection and instability near the air–liquid interface are studied. First, under the assumption of the conically similar viscous flow, an exact axisymmetric solution of the steady solutocapillary convection near the air–liquid interface is determined due to a constant mass flux. It is shown that the constant mass flux and the radial surface tension cause the divergent motion at the interface and the Marangoni convection beneath the interface. Then, the linear stability of the steady solutocapillary convection in response to the azimuthal disturbance is analyzed. At a given Peclet number (or Schmidt number), the steady basic flow loses its stability when the Reynolds number is beyond its critical value. It is found that for the fixed Schmidt number, the critical Reynolds number increases monotonously as the harmonic wave number of the azimuthal disturbance increases. However, for the fixed Peclet number, a nonlinear relationship between the critical Reynolds number and the harmonic wave number of the azimuthal disturbance is found. The structures of iso-concentration lines and velocity fields in the three-dimensional flow system depend on the disturbance harmonic wave number, which is dominated by both the radial and the azimuthal surface tensions. This study provides a profound understanding of the soluble surfactant-driven instability of a divergent flow near the air–liquid interface, which is of great significance for practical applications in the micro-fluidics related to chemistry and biology. [ABSTRACT FROM AUTHOR]

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]

To retard the mutual contact of W grains to inhibit their growth, in this study, CeO2·2H2O was first coated on the surface of pure W (undoped) particles by a weight percentage of 4% using a wet chemical method to prepare CeO2·2H2O-doped W-based (doped) powders, with W particles as the core and CeO2·2H2O as the shell (W–CeO2·2H2O core–shell structure), without hydrogen reduction treatment. The undoped and doped powders were subsequently sintered using a spark plasma sintering (SPS) apparatus to fabricate bulk materials. The macroscopic migration of the CeO2 shell in the core–shell W–CeO2 system via viscous flow during the initial sintering stage was studied through simulations and experiments. The results showed that a core–shell structure with W particles as the core and CeO2·2H2O as the shell was successfully prepared. The doped powder contained approximately 3.97% CeO2, consistent with the designed content of 4%. The shell materials migrated among the selected four sintered powders, filling the pores and contributing to the improvement in the relative density of the sintered bulk. [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]

Glacier‐Like Forms (GLFs) are a subset of ice‐rich landforms known as Viscous Flow Features that populate Mars' mid‐latitudes. GLFs are morphologically similar to terrestrial valley glaciers and are thought to result from the redistribution of water ice from the Martian poles during periods of high obliquity throughout the Amazonian period. Their ages, formation, and evolutionary processes are poorly constrained. We selected the 100 largest GLFs from the most recent GLF population data set, and by analyzing their superimposing crater morphologies and populations, we calculated their Crater Retention Ages (CRAs) and identified any relationships between CRAs, crater morphologies, and GLF geometries. We also organized the crater morphologies into states of degradation based on the understood erosional sequences. 3,630 craters were mapped, which we classified into 15 different crater morphologies. We calculated 98 CRAs, ranging from ∼2.88 Ma to ∼3.5 Ga. On average, GLFs in the southern hemisphere have younger CRAs, higher average slopes, smaller crater populations, and show less variability in crater morphological development than in the northern hemisphere. GLFs with higher mean slopes display less crater morphology variety, suggesting that shallow GLFs experience less reworking than steeper GLFs. We propose that these regional and hemispheric differences are due to a combination of favorable topography and climate conditions, both during and between high obliquity periods. We present several scenarios for the GLFs observed in this study and suggest that the glacial and erosional processes that affect GLF evolution are likely locale‐dependent. Plain Language Summary: Glacier‐Like Forms (GLFs) are ice‐rich landforms located in the mid‐latitudes of Mars and are similar in appearance to valley glaciers found on Earth. They are thought to be a result of the redistribution of water ice from the Martian poles during periods when Mars' axis tilts to a higher angle, exposing the poles to more heat from the sun. We selected the 100 largest glaciers to estimate the age of their surfaces via impact crater counting, to identify impact crater morphologies, and to compare this data to existing data on GLF geometrics. We mapped 3,630 craters, identified 15 different impact crater morphologies, and determined the surface ages of 98 glaciers, which ranged from 2.88 million years to 3.5 billion years old. Our analysis shows that glaciers with lower than average slopes have impact craters with a wider range of morphologies than glaciers with higher average surface slopes. Overall we find that glaciers in the southern hemisphere of Mars have young surface ages, and fewer and less developed craters compared with the northern hemisphere. We suggest different regional processes are occurring across Mars, with some areas favoring resurfacing processes more than others, and that glacier surface evolution is specific to the local environment. Key Points: The surface ages, crater morphologies, and metrics of the 100 largest Glacier‐Like Forms (GLFs) on Mars were explored to determine any trendsSurface ages range from 3430 to 2.88 Ma with 15 different crater morphologies. Slope exerts a substantial control on crater morphology developmentResurfacing processes occurring in certain regions of Mars have a greater effect on GLF surfaces than in others [ABSTRACT FROM AUTHOR]

This paper aims to find an exact solution for the von Kármán swirling viscous fluid flow caused by the infinite radius rotating disk with uniform suction. The swirling flow occurred at infinity or far from the rotating disk, and two conditions were considered. The first condition is when the direction of swirling flow at infinity is the same as the direction of angular velocity that the rotating disk has. The second condition is when the direction of the rotating disk and that of the swirling flow are opposites. When there are no swirling flow at infinity and no suction on the surface of the rotating disk, the pressure distribution is just a function of distance above the disk. The similarity transformation converts the governing equations from partial differential equations into ordinary differential equations and then is solved analytically with the HAN method. In this study, three cases were considered. The first case is a swirling flow at infinity that has the opposite and same direction of the rotating disk when there is no suction on the disk's surface. The second case is no swirling flow at infinity, but the suction occurs on the rotating disk's surface. The third one is both suction on the rotating disk and swirling flow. In the first case, it was observed that when the angular velocity of the fluid at a distance away from the disk is insignificant compared to the angular velocity of the disk, the skin friction coefficient reaches the maximum value and vice versa when the angular velocity of the fluid increases at a distance away from the disk, the value of skin friction coefficient decreases. In the second case, it was observed that the more the surface suction increases, the more the skin friction coefficient increases. Hence, the skin friction coefficient on a porous disk on which suction occurs is higher than on a normal non-porous disk. The results demonstrate that when parameters such as s = a = 0, the pressure will be a distance function above the disk if we put r = 0 . [ABSTRACT FROM AUTHOR]

Shape‐morphing structures capable of significantly altering shape and volume play a crucial role in diverse applications, ranging from soft robotics to minimally invasive surgery, deployable structures, and space exploration. This article presents an approach to achieve simple and controllable morphing onto multiple stable complex 3D surfaces—a long sought after goal in the field. The method is based on interconnected multistable straw‐like deformable tubes, constrained by rigid links that can be assembled and connected in many different ways. By leveraging the director‐field theory, the links and their assembly process are modeled and designed to reach a variety of desired final operational shapes from a single base‐structure. The use of viscous‐fluid actuation enables precise control and predictable shape‐morphing while facilitating a wide range of configurations through inflation and deflation sequences, all with a single input. [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]

Steady viscous flow past a circular cylinder with velocity slip boundary condition is numerically solved. The Navier–Stokes equations are solved using the vorticity-stream function formulation for two-dimensional incompressible flows. A time-accurate solver is developed which can be used for accurate solution of time-dependent flows. However, only steady results for Reynolds numbers up to 40 are presented in this paper. Most of the emphasis is dedicated to the validation of the solver and the results, something which is more or less missing in previous studies of slip flows. There has been a controversy regarding the computation of the drag coefficient and its various contributions in the past. As reviewed in the text, some papers did not present the formulation of the drag coefficient and only presented the results, some papers used the no-slip formulae and some papers presented formulae for the slip case but did not validate them. Due to this controversy, we derived formulae for the various contributions to the drag coefficient and validated them by comparison to existing data, especially using an analytical solution of Oseen's equation for creeping flow around a cylinder with slip condition. At the end, some results are presneted including wall vorticity and slip velocity distribution, streamlines, vorticity contours and various contributions to the drag coefficient. [ABSTRACT FROM AUTHOR]

In this work, the physiochemical properties of the drug, isoproterenol hydrochloride, were analyzed in the presence of β-cyclodextrin in an aqueous medium to gain a better understanding of the prevailing interactions among solute–solvent systems with the help of viscosity and conductivity studies. From viscosity measurements, the viscosity B -coefficient along with its transfer parameter was calculated using the Jones–Dole equation. In addition to this, the activation parameters such as Δ μ 1 o # , Δ μ 2 o # , Δ S 2 o # , and Δ H 2 o # were evaluated and discussed to gain a better understanding of the mechanism of viscous flow in terms of transition state theory. Along with this, conductivity studies were performed to investigate the thermodynamics of the ternary system in terms of changes in Gibbs free energy. Also, the delayed critical aggregate concentration of the ternary system supports favourable interaction between the studied drug and β-cyclodextrin molecules. [ABSTRACT FROM AUTHOR]

We investigate the crack-healing mechanism of 4H silicon carbide (4H-SiC) and reveal the effect of dopants on the crack-healing behavior of 4H-SiC. Vickers indentation tests and thermal annealing are utilized to generate cracks and heal cracks in 4H-SiC, respectively. High-temperature thermal annealing in the air atmosphere is found to be capable of effectively healing indentation-induced cracks and releasing indentation-induced stress in undoped 4H-SiC by the formation and viscous flow of glass phase SiO2. Nitrogen (N) doping is found to assist the atomic diffusion of 4H-SiC. The crack healing of N-doped 4H-SiC is realized by the synergy of host solid diffusion and the padding of glassy SiO2. In contrast, vanadium (V) doping hinders the viscous flow of SiO2 and results in the incomplete healing of cracks in V-doped 4H-SiC. Although the generation of cracks lowers the bending strength of 4H-SiC, the healing of cracks by the padding of glassy SiO2 is found to effectively recover the bending strength of indented 4H-SiC samples. Our work opens a pathway to design thermal processing technologies to heal the cracks and enhance the mechanical properties of 4H-SiC wafers. [ABSTRACT FROM AUTHOR]