Nanocapillaries are essential for a wide range of applications, from enhanced oil recovery to the study of fluid dynamics at the nanoscale. This study examines the dynamics of miscible flow in planar nanochannels under pressure-driven Poiseuille flow conditions. We conducted extensive molecular dynamics (MD) simulations to investigate the microscopic mechanisms governing solute displacement and dispersion within nanoscale confinement. As a representative case, we focused on ${\mathrm{CO}}_2$ dispersion in oil (n-decane) across various channel materials, estimating average velocity, slip lengths, and diffusion coefficients. Our findings reveal significant differences in slip lengths between various channel materials, with graphene exhibiting a slip length over an order of magnitude higher than others. We estimated the slip length of oil on graphene to be 4.5 nm, an order of magnitude smaller than that of water on graphene, whereas for ${\mathrm{MoS}}_2$ and silica, it was smaller than 1 nm. From MD simulations, we found that the diffusion coefficient increases nonlinearly with channel height and applied pressure, ranging from $\left[4\text{–}20\right]\times {10}^{-9}{\text{m}}^2/\text{s}$ for the studied conditions. Taylor analysis was used to qualitatively interpret these findings. This study enhances the understanding of the slippage dynamics and diffusion processes in nanoconfined space, particularly focusing on CO-oil systems. These findings provide insights that may be applicable to other solute-solvent systems, offering a new approach for extending theories to different two-phase flow and multiphase flow systems.

Data-driven reduced-order models of the dynamics of complex flows are important for tasks related to design, understanding, prediction, and control. Many flows obey symmetries, and the present work illustrates how these can be exploited to yield highly efficient low-dimensional data-driven models for chaotic flows. In particular, incorporating symmetries both guarantees that the reduced order model automatically respects them and dramatically increases the effective density of data sampling. Given data for the long-time dynamics of a system, and knowing the set of continuous and discrete symmetries it obeys, the first step in the methodology is to identify a “fundamental chart,” a region in the state space of the flow to which all other regions can be mapped by a symmetry operation, and a set of criteria indicating what mapping takes each point in state space into that chart. We then find a low-dimensional coordinate representation of the data in the fundamental chart with the use of an autoencoder architecture that also provides an estimate of the dimension of the invariant manifold where data lie. Finally, we learn dynamics on this manifold with the use of neural ordinary differential equations. We apply this method, denoted “symmetry charting” to simulation data from two-dimensional Kolmogorov flow in a chaotic bursting regime. This system has a continuous translation symmetry and discrete rotation and shift-reflect symmetries. With this framework we observe that less data is needed to learn accurate data-driven models, more robust estimates of the manifold dimension are obtained, equivariance of the NSE is satisfied, better short-time tracking with respect to the true data is observed, and long-time statistics are correctly captured.

Transient flows in poroelastic media arise in a broad range of applications, from geophysical flows to biological processes and industrial applications. The interplay of medium heterogeneity, poroelasticity, and transient forcing lead to complex flow and transport behaviors that manifest as a diverse set of Lagrangian coherent structures (LCSs). Previous studies have focused on how these structures govern dispersion of diffusive solutes, but the impact on solute mixing and transport has not been previously considered. We address this problem by examining how regular regions, Kolmogorov-Arnold-Moser (KAM) islands, stochastic layers, and other LCS types impact solute transport and mixing across a broad range of Péclet numbers. LCSs impart distinctly different mixing dynamics, with mixing metrics such as the dilution index ranging from algebraic to exponential growth with time. Transport structures such as KAM boundaries and hyperbolic manifolds form strong barriers to transport that govern transport of diffusive solutes at all Péclet numbers. These results show that mixing and transport are profoundly impacted by the complex advective dynamics inherent to transient poroelastic flows, and they can only be fully understood by resolving the governing LCS.

Physical systems are commonly described by a set of partial differential equations. In multidimensional, time-dependent systems (such as transient or chaotic ones), the behavior of these equations leads to the formation of distinct regions with different dynamics, which can be clustered accordingly. In this study, we propose a hybrid approach to flow clustering. It consists of characterizing each sample point of the system with equation-based features, i.e., features are budgets that represent the contribution of each term from the original governing equation to the local dynamics at each sample point. This was achieved by applying the a sparse regression algorithm pointwise to time evolution data. The method proceeds with equation-based clustering using the Girvan-Newman algorithm. This allows the detection of communities that share the same physical dynamics underlined by the active terms of the governing equation of desired fidelity. The algorithm is implemented in both Eulerian and Lagrangian frameworks. In the Lagrangian, i.e., dynamic approach, the clustering is performed on the trajectory of each point. Our results show that while the dynamics of the regions remain the same (with the same active terms in the regression process), the location of the clusters moves with time when applied to transient or turbulent data. The performance of the algorithm is first tested on a flow around a cylinder. The construction of the dynamic clusters in this test case clearly shows the evolution of the wake from the steady-state solution through the transient to the oscillatory solution. Dynamic clustering was then successfully tested on turbulent flow data. Two distinct and well-defined clusters were identified and their temporal evolution was reconstructed.

When a slice of beet is placed on a plate with a thin layer of beet juice, one can observe a clear fringe around the beet, where the color is more translucent than the rest of the juice. The hypotheses in literature were inconsistent and limited, which motivated us to revisit this phenomenon. Using a motorized confocal displacement sensor, we measured the temporal evolution of the liquid surface profile across the fringe. Our findings suggest that a suction flow, induced by the capillary rise of the contact line, causes a dimple—a small concave depression—to form on the liquid surface. While surface tension and gravity tends to smooth out the dimple, viscous drag acts against them if the liquid film is sufficiently thin. Our scaling analysis correctly estimates the dependence of dimple lifetime on liquid properties and film thickness. We also capture the dimple formation dynamics by numerically solving the lubrication equation with the Young-Laplace equation. This work provides an interpretation for a common phenomenon.

This paper investigates the impact of bulk viscosity and relaxation model on the shock transition of diatomic gases using the nonlinear coupled constitutive relations (NCCR), which is an extended model to Navier-Stokes equations for simulating nonequilibrium compressible flows. To elucidate their roles in the mechanism of shock transition, a modified NCCR model including temperature-dependent bulk-shear-viscosity ratio and a thermal nonequilibrium NCCR model with rotational mode are developed from various physical perspectives. Subsequently, these models are employed to investigate the shock structure in nitrogen for Mach numbers up to 10. It is found that the shock profiles and shock thicknesses computed by proposed NCCR models are in close agreement with the experimental data and direct simulation Monte Carlo results across all Mach numbers, with an observation that introducing bulk viscosity or relaxation model improves the physical consistency of NCCR theory and thereby shock solutions in nonequilibrium flows. Moreover, the rationality of assuming a constant viscosity ratio in the original NCCR model for diatomic gases is validated. It is important to note that the relaxation model brings in a skewing of shock profiles towards downstream and strengthens the non-Newton-Fourier behavior and asymmetry in heat flux phase planes, whereas the bulk viscosity leads to a skewing of shock profiles towards upstream and enhances the non-Newton-Fourier behavior and asymmetry in stress phase planes. These findings highlight the distinct mechanisms through which the bulk viscosity and relaxation model improve the shock profiles, offering deeper insight into the physical mechanism inside the shock structures of diatomic gases.

Salts dissolved in water droplets are observed to remarkably retard the ice crystal growth during recalescence via high-speed imaging. This retardation effect can be 98.8% for a 1.00 mol/l magnesium chloride solution compared to pure water, and varies with both salt concentrations and types. The underlying mechanism is attributed to the reductions in water diffusivity and active crystal growth site caused by the presence of salts, which decreases the amount of unhydrated water. A modified Vogel-Fulcher-Tamman equation is thereby developed to quantify the reduction in diffusivity, accurately representing data for various salt types and concentrations. This equation is further integrated into the Wilson-Frenkel model, providing a modified equation that effectively captures the observed recalescence retardation in salty water.

We analyze the boundary-layer flow that develops in a quiescent fluid near the surface of a semi-infinite flat plate when a tangential stress is imposed at the boundary. This force induces motion confined to a layer that grows downstream of the leading edge. We find that a family of self-similar solutions exists for stress distributions that follow a power law with the streamwise coordinate. This family of solutions allows us to describe scenarios that involve increasing or decreasing stresses from an initial value. Beyond their academic relevance, the solutions to the governing equation are of interest in pumping devices that use magnetic or electric forces acting on a thin layer adjacent to the surface.

Mixing and dispersion in random porous materials are complex processes governed by the interplay of local velocity fields and pore morphology randomness. For purely advective transport in Newtonian fluid flow within porous media at macro scale, a linear relationship is established between the dispersion coefficient and average interstitial velocity, characterized by a coefficient known as dispersivity. Previous studies highlight that dispersivity remains constant and is solely dependent on the properties of the porous medium. However, whether dispersivity is constant when considering non-Newtonian fluids, which exhibit spatially variable viscosity, is questionable. For example, for a shear-thinning fluid, viscosity decreases as the shear rate increases. In non-Newtonian shear-thinning fluids, viscosity varies across pore spaces, influenced by local shear rates, making pore size distribution and fluid pathway connectivity critical factors that impact solute transport dynamics. In this study, we present experimental insights into solute transport for both non-Newtonian and Newtonian fluid flows within porous media using glass micromodels and optical microscopy. Xanthan gum solution, representing a shear-thinning fluid, and water, as a Newtonian control, were used to evaluate the differences in transport behavior. Results indicate an enhanced dispersion effect for shear-thinning fluids in porous media. While dispersivity remains constant in Newtonian fluid flow, our experiments reveal a nonmonotonic relationship between dispersivity and injection rate for shear-thinning fluids. Unlike in Newtonian fluids, dispersivity in non-Newtonian fluids is influenced not only by the properties of the porous medium but also by the fluid's rheology. We propose a mathematical model to account for this variability, offering a framework that aligns with our experimental findings and provides insights into the mechanisms governing solute transport in non-Newtonian fluid flow within porous media.

The flow and passive scalar fields in a time-space developing turbulent spot within a Poiseuille flow are analyzed using direct numerical simulations realized in a large computational domain. The turbulent core of the spot is populated by the quasistreamwise vortices as in the buffer layer of the fully developed wall turbulence. There is a massive clustering of the outer-layer vortices in the immediate vicinity of the spot periphery near the centerline. These long coherent chains are induced by the wave area. They provoke large-scale-motions (LSM) as a detailed spectral density analysis of the fluctuating flow and scalar fields reveals. The outer spectral core is dense and there is a clear scale separation with respect to the inner core. A bridge between the outer and inner spectral cores set up near the wall. The size and location of the large-scale spectral core are independent of the wall normal distance. An adequately modified existing model, based on the long and short term dispersion of the structures, describes relatively well the bounds of the outer spectral core. By their very nature, there is a restrictive similarity between the effect of the LSM in a turbulent spot and that of the passive attached Townsend eddies in a fully developed turbulent flow.

The effect of substrate topography on the settlement of coral larvae in moderate wave-driven oscillatory flow is investigated using computational fluid dynamics coupled to a 2D agent-based simulation of individual larvae. Substrate topography modifies the boundary layer flow by generating vortices within roughness features that can be ejected into the bulk flow, directly influencing larval transport and settlement. In agreement with recent experimental findings, millimeter-scale ridged topographies were found to increase settlement compared to sub-mm feature heights. At this length scale, features with ridge spacing-to-height ratios of 10 to 20—representing gaps of more than 30 coral larval body lengths—resulted in the highest settlement rates. These optimal topographies produce a high averaged vertical velocity variance in the bulk flow, indicating that vertical larval movement to benthic surfaces is dominated by passive transport driven by recirculatory flow structures. Indeed, larval settlement was found to be positively correlated with mean vertical velocity variance, and settlement results with substrates comprising complex multiscale roughness were quantitatively similar to those with a simple rectangular model. Our findings reveal how substrates can be designed with surface features to promote larval settlement in natural flow conditions above shallow coral reefs independent of biological cues and substrate material composition.

The momentum dispersion model of flows in porous media has been validated and successfully applied by Rao and Jin [J. Fluid Mech. 937, A17 (2022)]. However, the modeling of heat-fluid-solid coupling in turbulent forced convection requires further development. This research identifies two primary scaling laws for the heat transfer coefficient $h$ between the fluid and solid: $h\sim {\mathrm{Re}}_p^{\beta }$ with $\beta =2$ for the Darcy regime and $\beta =0.5$ for the Forchheimer regime, both taking into account the Prandtl number. The transition between the two scaling regimes occurs around $\mathrm{Re}{}_p=1$. To effectively connect these two regimes, a bridge function is employed. The influence of thermal dispersion on energy transport is approximated using a Laplacian term, analogous to the momentum dispersion model. A Taylor expansion is utilized to calculate the effective thermal diffusivity in relation to the local Reynolds number $\mathrm{Re}{}_d$. The first two leading-order terms of the series are adopted. The corresponding model coefficients are determined by fitting direct numerical simulation (DNS) results. The effective thermal diffusivity approaches molecular diffusivity as porosity approaches 1, while it tends toward infinity as porosity approaches zero. The macroscopic energy equation is applied in conjunction with our previous macroscopic momentum equation and has been validated across four typical scenarios. The results indicate that the proposed coupled macroscopic models maintain a high level of accuracy across a wide range of Darcy numbers, Reynolds numbers, porosities, and Prandtl numbers. The coupled macroscopic equations, though calibrated with statistically stationary DNS data, can predict not only statistically stationary temperature distributions but also overall temperature evolutions successfully, which is addressed in this research.

A direct numerical simulation of a turbulent plane Couette flow over a two-dimensional (2D) rod-roughened wall is conducted to examine the effect of surface roughness on this type of flow. The turbulent Couette flow is driven by imposing a constant velocity on the top wall, with transverse 2D rods periodically arranged in the streamwise direction on only the stationary bottom wall. The roughness height ($k$) and width ($w$) employed are $0.2h$ ($h$ is the channel-half height) and the streamwise spacing between the roughness elements ($p$) is set to $p/k=10$. A comparison of the root-mean-square of the streamwise velocity fluctuations (${u^{\prime }}_{\mathrm{rms}}$) and mean Reynolds shear stress ($\langle u^{\prime }{v}^{\prime }\rangle$) between smooth- and rough-wall Couette flows (hereafter, SCF and RCF) shows that the turbulence activity in the outer layer for the RCF decreases compared to that of the SCF due to the abatement of the large-scale negative $u^{\prime }$ component, indicating that the wall-similarity hypothesis between the SCF and RCF in the outer layer is not established. The weakening of the large-scale negative $u^{\prime }$ component in the outer layer results from the reduced streamwise coherence of the large-scale $u^{\prime }$ structure in the outer layer with the decreased energy. In addition, linear estimates for conditional structures demonstrate that the reduced coherence of the large-scale $u^{\prime }$ structure with less energy in the outer layer for the RCF is found to occur due to the suppressed development of a hairpin packet resulting from the weakened roll-cell motions with less influence on the near-wall region.

We explore the energy spectra and associated fluxes of turbulent two-dimensional quantum droplets subjected to a rotating paddling potential which is removed after a few oscillation periods. A systematic analysis on the impact of the characteristics (height and velocity) of the rotating potential and the droplet atom number reveals the emergence of different dynamical response regimes. These are classified by utilizing the second-order sign correlation function and the ratio of incompressible versus compressible kinetic energies. They involve vortex configurations ranging from vortex dipoles to vortex clusters and randomly distributed vortex-antivortex pairs. The incompressible kinetic energy spectrum features Kolmogorov ($k^{-5/3}$) and Vinen-like ($k^{-1}$) scaling in the infrared regime, while a $k^{-3}$ decay in the ultraviolet captures the presence of vortices. The compressible spectrum shows $k^{-3/2}$ scaling within the infrared and $k$ power law in the case of enhanced sound-wave emission suggesting thermalization. Significant distortions are observed in the droplet periphery in the presence of a harmonic trap. A direct energy cascade (from large to small length scales) is mainly identified through the flux. Our findings offer insights into the turbulent response of exotic phases of matter, featuring quantum fluctuations, and may inspire investigations aiming to unravel self-similar nonequilibrium dynamics.

Unsteady loads induced by gusts are a significant concern affecting flight safety. This study concentrates on gust load alleviation, exploring the strategy and mechanism of dynamic airfoils in alleviating gust-induced load. Based on classical aerodynamic theory, this paper proposes three distinct airfoil motion strategies aimed at alleviating gust-induced loads. Experimental analyses employing a two-dimensional NACA 0012 airfoil subjected to periodic vertical gusts with various prescribed motions are undertaken to assess the efficacy of the proposed load alleviation strategy. It is found that compared to static airfoil configurations, dynamic motions devised according to Theodorsen-Sears theory yield substantial gust load reduction, with lift fluctuations reduced by up to 90%. The dynamic airfoil alleviates gust-induced disturbances around the airfoil, thereby maintaining flow attachment on the airfoil surface or inducing minor-scale flow separation. Quantitative assessments establish a relationship between flow field momentum changes and lift fluctuations, suggesting that even in scenarios where precise aerodynamic force measurements are unavailable, the efficacy of load alleviation can be deduced through an analysis of flow field momentum. Furthermore, dynamic airfoil configurations notably dampen fluctuations at the stagnation point along the airfoil's leading edge. Consequently, in practical flight scenarios, an effective control of stagnation point stability holds promise for effective gust load alleviation.

Continuum mechanics principles are applied to standard balance equations assuming constitutive equations carried out to first derivatives of density, temperature, and velocity. Using the principles of isotropy, frame invariance, and equipresence, we obtain constitutive equations for the Helmholtz free energy, entropy, entropy flux, extra entropy flux, and Cauchy stress tensor that satisfy the Clausius-Duhem inequality. The equation for the Cauchy stress tensor contains a term that is missing in the well-known Navier-Stokes-Fourier equations. The additional term, when applied to an ideal gas, appears to be due to the local time relaxation of molecular vibrational energy and leads to a new definition of the bulk viscosity. We also obtain additional terms in the entropy that are due to the relative time rate of change of the local volume.

This work investigates the influence of classically coherent structures on wall-shear stress and energy dissipation in turbulent channel flow, utilizing direct numerical simulations (DNS) data and explainable deep learning (XDL). Sweeps, defined as regions of low streamwise velocity moving toward the wall, are found to be the most influential structures for both energy dissipation and drag. Moreover, the volume of these key structures falls within a narrow range, making it easier to identify the most significant ones. Consequently, this work paves the way for the development of novel, highly efficient turbulence-control strategies for the reduction of drag.

This study examines the dynamics of roll waves that spontaneously arise in muddy debris flows, where phase separation is not observed. To this end, a set of bulk mass and momentum balance equations is derived from the depth-averaged model proposed by Meng et al. [J. Fluid Mech. 943, A19 (2022)]. The derived equations are shown to be well-posed, with the threshold Froude number for flow instability slightly exceeding the classical $2/3(1-\mathrm{\Gamma })$, which corresponds to dry granular flows on rough planes. A high-resolution shock-capturing scheme is employed to resolve the evolution of debris roll waves, which emerge from initially steady, uniform flows subjected to sinusoidal perturbations. These waves grow under the influence of inertial forces and eventually saturate into steady, traveling waveforms. A traveling-wave solution is subsequently constructed, accurately capturing the steady traveling waves observed in the simulations. This theoretical framework is further applied to natural debris roll waves observed in the Illgraben torrent, Switzerland. Simulated time series of the flow depth and wave speeds, based on the $\mu \left(I\right)$-dependent basal granular friction law, exhibit excellent agreement with field measurements. Numerical results also reveal that large-amplitude waves, which carry significant mass flux, are dynamically unstable and tend to fragment into multiple smaller-amplitude waves. These smaller waves are overtaken and merged by trailing waves with larger amplitudes and faster propagation speeds, a phenomenon consistent with field observations.

Density-driven segregation, extensively studied in a simple rotating drum, is enriched with a wide range of underlying physics. Diverse symmetrical segregation patterns formed by mixing two types of dry mono-sized grains have been revealed due to variations in heavy and light grain densities ${\rho }_{\text{h}}$ and ${\rho }_{\text{l}}$ and rotating speeds $\omega$. We engender experimentally a nearly complete segregation, not occurring in dry conditions of the same ${\rho }_{\text{h}}$, ${\rho }_{\text{l}}$, and $\omega$, in submerged states. Furthermore, based on the experiment-validated simulations, using coupled computational fluid dynamics and the discrete element method, it is found the mixing index can be well predicted over a wide parameter space in the effective density ratio, $\mathcal{D}=({\rho }_{\text{h}}-{\rho }_{\text{f}})/({\rho }_{\text{l}}-{\rho }_{\text{f}})$ with ${\rho }_{\text{f}}$ being the fluid density. Specifically, with increasing $\mathcal{D}$ well-mixed states transit to fully segregated states with a rising number of vortices and more severe asymmetrical patterns. When the global Reynolds number ${\text{Re}}_{\text{g}}$ is enlarged, the vortex area of heavy particles shrinks for lower $\mathcal{D}$, while the area of light particles gradually saturates; meanwhile, for higher $\mathcal{D}$ a new vortex with a continuously expanded area can be encountered in the light particle zone. These results improve our understanding of segregation transitions, especially in submerged granular systems, and shed new light on various science and engineering practices.

Gravity-driven collapses such as landslides, avalanches, and mudslides have garnered increasing attention, and understanding their complex dynamics is a key concern for risk assessment. In this paper, we design a laboratory experiment to investigate the dry granular column collapse from a rough slope to a horizontal plane. Here, we mainly focus on the effects of the slope characteristics on the dynamic behaviors and final geometry of the grains. In the experiment, we capture the dynamic granular motion using a computer vision-based recognition method. It is found that particles form deposits at both the top and bottom of the slope. The granular collapse process that occurs on the top is similar to the collapse on a horizontal plane. The particles entering the slope accumulate kinetic energy and spread along the slope and horizontal plane to form a granular flow. The dynamic flow behaviors observed in this experiment and the final deposit properties are found closely related to the properties of the slope and the initial granular column configurations. In addition, we present scaling arguments for the runout distance, final height, and characteristic time and attempt to elucidate their underlying physics. The modified scaling laws, which consider the effect of aspect ratio, prove to be applicable in this scenario.