In this work, two-phase flow scalings are derived, which enable the quantification of grid-point and time-step requirements as functions of Reynolds ($\mathrm{Re}$), Weber ($\mathrm{We}$), and capillary ($\mathrm{Ca}$) numbers. The adequate grid resolution is determined in the inertia-dominated regime with the aid of high-fidelity simulations of stationary two-phase, i.e., interface-resolved, homogeneous isotropic turbulence by evaluating convergence of total interfacial area, size distribution, Sauter mean diameter (SMD), and curvature distribution. Although standards for direct numerical simulations (DNS) for single-phase turbulence flow exist, there is a lack of similar guidance in two-phase flows. Therefore, length scale ratios of the Kolmogorov-Hinze to the Kolmogorov scale of ${\eta }_{\mathrm{KH}}/\eta \sim {\mathrm{We}}_{\mathcal{L}}^{-3/5}{\mathrm{Re}}_{\mathcal{L}}^{3/4}$ in the inertia-dominated regime and the Kolmogorov-viscous to Kolmogorov scale of ${\eta }_{\mathrm{KV}}/\eta \sim {\mathrm{Ca}}_{\mathcal{L}}^{-1}{\mathrm{Re}}_{\mathcal{L}}^{3/4}$ for the viscous-dominated regime, are constructed. These scalings imply a computational cost increase like ${\mathrm{We}}_{\mathcal{L}}^{12/5}$ and ${\mathrm{Ca}}_{\mathcal{L}}^4$, in the inertia-dominated and viscous-dominated regimes, respectively. A dimensionless number, referred to as the ratio of interface scales ($\mathrm{Ris}$), defined as $\mathrm{Ris}:={\eta }_{\mathrm{KH}}/{\eta }_{\mathrm{KV}}={\mathrm{We}}_{\mathcal{L}}^{2/5}/{\mathrm{Re}}_{\mathcal{L}}$, is proposed to aid in the classification of the turbulence regimes in the presence of an interface. Convergence of the total interfacial area, size distribution, SMD, and curvature distribution are observed for grid resolutions of $k_{max}{\eta }_{\mathrm{KH}}\ge 60$ for second-order schemes in the inertia-dominated regime. Furthermore, it is observed that this lower bound is the minimum required to capture intermittent events responsible for the increase of instantaneous total interfacial area. This criterion will be a valuable tool for determining grid resolution and time-step requirements a priori for DNS of two-phase flows and for estimating the corresponding computational cost. This work provides guidelines and best practices for numerical simulations of two-phase flows, which will accelerate physics discovery and model development.

In three-dimensional turbulence, vortex stretching is the central mechanism enabling the transfer of kinetic energy toward smaller scales. If vortex stretching is absent in three-dimensional turbulence, energy is no longer conserved and enstrophy cascades to smaller scales. In this paper we propose a system that interpolates between these two cases by reducing the strength of vortex stretching in the Navier-Stokes equations. The resulting dynamics yield a cascade that is neither a pure energy cascade nor a pure enstrophy cascade. We refer to this process as a mesostrophy cascade. We formulate a consistent picture describing this cascade and the characteristic scales involved in the mesostrophy balance. We illustrate this picture via numerical integrations of the eddy-damped quasinormal Markovian model with reduced vortex stretching.

We present a systematic analysis of the statistics of the energy dissipation rate $\epsilon$ and the enstrophy $\mathrm{\Omega }$, obtained from direct numerical simulations (DNS) of forced, incompressible turbulence in a periodic box at Taylor-scale Reynolds numbers up to $R_{\lambda }\approx 1740$. Both quantities, quadratic in the velocity-gradient tensor, are closely associated with small-scale intermittency. This paper considers the spectra of $\varphi$, the second-order correlation functions of $\varphi$, and the second-order moments of local averages of $\varphi$, where $\varphi$ denotes $\epsilon , \mathrm{\Omega }$, or their fluctuating components. The DNS results at $R_{\lambda }\approx 1100$–1740 reveal a wave-number range where the spectra scale with an exponent about $-2/3$ for both quantities. In physical space, the correlations and local averages show two scaling ranges: one with exponent about 0.23 for the total fields ($\epsilon$ and $\mathrm{\Omega }$) and another with exponent about 0.43 for their fluctuating parts. These ranges are close but not identical, and in both the correlation functions and the local averages, the total-field values are not dominated by the fluctuating parts. Under these conditions, the scaling exponents of the total and fluctuating components are unlikely to coincide, as the total includes a nonscaling mean contribution that is not negligible relative to the fluctuations. The results suggest that even at $R_{\lambda }\approx 1740$, the Reynolds number remains insufficient to reach the asymptotic regime assumed in intermittency theories.

Reynolds-averaged Navier-Stokes (RANS) turbulence models rely on several simplifying assumptions that limit their accuracy, particularly in predicting separated flows. To address these limitations, significant efforts have focused on augmenting RANS models through field inversion and machine learning. In the present study, data assimilation and symbolic regression are used to formulate an analytical correction to the Spalart-Allmaras model, addressing local deficiencies in its production term. A key objective of this work is to develop a correction applicable to a wide range of flow configurations, improving predictions for separated flows without degrading the performance of the baseline model for wall-attached flows. To this end, symbolic regression is performed using assimilated data from two-dimensional separated-flow cases (converging-diverging channel, bump H42, and NASA wall-mounted hump) together with a reference case where the Spalart-Allmaras model remains accurate (flat plate). This methodology enforces the desired correction in separated flows while minimizing the impact on the model's accuracy for wall-attached flows. The symbolic correction accurately reproduces the assimilated quantities and its performance on unseen flows demonstrates that the resulting expression remains applicable across a broad range of flow configurations and Reynolds numbers (bump H38, square cylinder, and periodic hill). The correction is also assessed on three-dimensional cases, namely, the FAITH hill and the Ahmed body. While improvements are observed for some configurations, these tests also reveal limitations that warrant further investigation.

Dense non-Brownian suspensions undergo a viscous to inertial transition with increasing shear rate ($\dot{\gamma }$), from a regime of constant viscosity at low shear rates to a regime where the viscosity varies linearly with the shear rate. The shear rate associated with this transition has been shown to vary dramatically between different experimental systems. Using the discrete element method, we show that in the regime where frictional contacts are absent, the characteristic shear rate for the transition to an inertial state is sensitive to the volume fraction ($\varphi$) of the suspension and exhibits a critical behavior at the jamming volume fraction (${\varphi }_m$) for the system. By uncovering the presence of a microstructural length scale ($L_c$) that controls the emergence of inertial effects in the suspension, it is shown that the criticality emerges as a consequence of $L_c$ diverging at jamming. We further show that in contrast to the conventional Stokes number $St=\rho d^2\dot{\gamma }/{\eta }_f$, the definition of a modified Stokes number $S{t}_{\mathrm{cluster}}=\rho L_c^2\dot{\gamma }/{\eta }_f$ correctly quantifies the inertial effects within the suspension and leads to a collapse of the rheological data.

A detailed experimental campaign is conducted to assess the shear layer characteristics of an axisymmetric open cavity configuration exposed to a Mach 6 freestream flow. Experiments are carried out in a Ludwieg tunnel across varying Reynolds number cases $(23000\le {\text{Re}}_D\le 74000)$ based on the cavity depth $\left(D\right)$. The influence of associated geometrical parameters in the form of length-to-depth ratio $\left(\right[L/D]=[2,4,6\left]\right)$ and nondimensional excess height of the rear face with respect to the front face $\left(\right[\mathrm{\Delta }h/D]=[-0.5,-0.25,0,0.25,0.5\left]\right)$ is assessed. Thereby, a detailed interpretation of the shear layer evolution is made based on qualitative flow structures captured using schlieren imaging and planar laser Rayleigh scattering (PLRS), along with quantitative measures obtained through unsteady pressure probes. Regardless of the $[L/D]$, the state of the shear layer is observed to be laminar at lower ${\text{Re}}_D\mathrm{s}$, and when increased, reveals the presence of Kelvin-Helmholtz (K-H) vortices. Nevertheless, for the longest aspect-ratio case $\left(\right[L/D]=6.0)$, the shear layer transitions to turbulence in the extreme ${\text{Re}}_D$ cases owing to the availability of a longer length scale for K-H propagation. The spectral content obtained from the pressure response and the light intensity from the PLRS snapshots reveals an increase in the dominant frequency from the first Rossiter mode to higher-order modes for $[L/D]=6.0$. Apart from $[L/D]=6,[\mathrm{\Delta }h/D]=0$, the dominant frequency for all the cases considered herein matches the prediction of Rossiter modes and is found to be invariant of Reynolds number. While varying the $[\mathrm{\Delta }h/D]$, shifting of modes occurs as obtained using proper orthogonal decomposition analysis of PLRS snapshots. For the negative $[\mathrm{\Delta }h/D]$, the K-H mode is dominant (fifth and sixth Rossiter modes), whereas for the positive, the strong flapping mode (first Rossiter mode) prevails owing to significant pressure build-up inside the cavity recirculation region. For $[\mathrm{\Delta }h/D]=0$, both modes may coexist depending on ${\text{Re}}_D$. The azimuthal uniformity of the flow is also probed, indicating the dominance of the axisymmetric mode in the flapping scenario and much less correlated behavior in the case of K-H vortices in the shear layer.

Electrophoresis is a widely used method for separating charged entities such as DNA, proteins, cells, and other biological and colloidal particles. In many instances, it is often combined with background flows to improve the separation efficiency. At the same time, most particles bear nonuniform surface charge profiles, and their kinetics can be quite fascinating when suspended in external flows, and yet they remain poorly explored so far. In this article, we thus devise a fairly general and exact reduced-order model based on a set of coupled ordinary differential equations to predict the trajectories of nonuniformly charged particles suspended in an arbitrary background flow and subject to an externally imposed electric field. While a fundamental approach can be built for this purpose, we establish that the reduced-order model is computationally efficient and has the added advantage of providing useful insights into the nonlinear physics of particle motion. Using this framework, we show that in general, the particle rotates, which makes its surface charge evolve over time with respect to a laboratory-fixed frame. This may result in a multitude of particle trajectories depending on the precise nature of the imposed flow, the variability of the particle's surface charge, its starting position and orientation within the flow field, and the relative strengths of the flow and electrophoretic propulsion. For instance, we show that under certain conditions, axisymmetric particles suspended in a Poiseuille flow tend to migrate towards the flow centerline, while nonaxisymmetric ones tend to settle at a distance from the same. We expect that our framework will enhance the fundamental understanding of electrophoretic motion and contribute towards more efficient separation of charged entities using electric fields.

The bursting of a laminar separation bubble subject to periodic forcing is studied experimentally on a NACA0018 airfoil at a chord Reynolds number of $7\times {10}^4$. Bursting of the bubble is initiated by a dynamic ramp increase in angle of attack past the static stall angle with a nondimensional pitch rate of 0.008. The initial and final effective angles of attack are $4.9^{\circ }$ and $7.2^{\circ }$. Periodic forcing is continuously applied to the boundary layer by a spanwise-uniform alternating current dielectric-barrier-discharge plasma actuator at the leading edge of the airfoil. The forcing frequency was chosen to match the unforced vortex shedding frequency of the separated shear layer at the initial angle of attack. Surface pressure and particle image velocimetry measurements were obtained during the airfoil motion to investigate the boundary layer development on the suction surface. In the unforced flow, bursting of the laminar separation bubble begins before the maximum angle of attack is reached. The results show that periodic forcing can either delay or prevent the onset of bursting past the end of the pitching motion. With increasing forcing amplitude, the laminar separation bubble may persist at the maximum angle of attack for on the order of 100 convective time units before bursting. Although periodic forcing can delay bursting, the dynamics of the bursting process are largely unchanged once the bursting process initiates, requiring a period of approximately 30 convective time units for the flow to settle to a massively separated state. The delay in the onset of bursting increases and becomes less deterministic as the forcing amplitude increases, until the forcing amplitude is sufficient to prevent bursting entirely.

In multiphase flows, kinetic and interfacial energies coexist, and their mutual conversion can potentially influence the overall energy balance. However, in statistically steady flows, these energy reservoirs remain constant, making such conversions undetectable. For them to be observed, a degree of unsteadiness must be introduced, here provided by the deliberate use of a fluctuating time-periodic input of kinetic energy into the system. The main focus of the present work is on the dynamical cycle connecting energy injection, conversion, and dissipation, which we explore using direct numerical simulations of multiphase homogeneous isotropic turbulence, subjected to periodic forcing. The database includes various Reynolds and Weber numbers and volume fractions in the dense regime. To interpret and replicate the observed dynamics, we reformulate the Ka-Pi-bara model of Bos [J. Turbul. 27, 157 (2026)] (an extension of the $k\text{−}\epsilon$ model) in terms of total energy (the sum of kinetic and surface energy), which we further enhance by adding equations for the surface energy and its destruction. This model accurately captures a key feature of turbulence: nonequilibrium effects, seen as the phase lag between kinetic energy and its rate of dissipation, which are also found to operate in multiphase flows. Linearizing the model highlights the various relevant timescales of the system and provides predictions of how different observables are coupled and respond to the energy input.

The pinch-off of bubbles in viscoelastic liquids is a fundamental process that has received little attention compared to viscoelastic drop pinch-off. While these processes exhibit qualitative similarities, the dynamics of the pinch-off process are significantly different. When a drop of a dilute polymer solution pinches off, a thread is known to develop that prevents breakup due to the diverging polymer stresses. Conversely, our experiments reveal that this thread is absent for bubble pinch-off in dilute polymer solutions. We show that a thread becomes apparent only for high polymer concentrations, where the pinch-off dynamics become very sensitive to the size of the needle from which the bubble detaches. The experiments are complemented by numerical simulations and analytical modeling using the Oldroyd-B model, which capture the dilute regime. The model shows that polymer stresses are still singular during bubble pinch-off, but the divergence is much weaker as compared to drop pinch-off. This explains why, in contrast to droplets, viscoelastic bubble threads do not appear for dilute suspensions but require large polymer concentrations.

We report on singular jets in a free-falling liquid tin droplet following nanosecond laser-pulse impact. Following impact, the droplet (with diameter $D_0=50$ or $70\mu \mathrm{m}$) undergoes rapid radial expansion and subsequent retraction, resulting in the formation of an axisymmetric jet. Using numerical simulations in tandem with our experiments, we reveal that a delicate interplay between radial flow and the curvature of the retracting droplet governs jet formation. The resulting dynamics is characterized using the impact Weber number, $\mathrm{We}$ (in the experiments $2\lesssim \mathrm{We}\lesssim 16$), and a pressure width, W (typically $1\lesssim W\lesssim 2$), which describes the angular distribution over the droplet surface of the instantaneous pressure impulse exerted by the transient laser-produced plasma. For values $\mathrm{We}<10$, the droplet presents a pronounced curvature during the retraction, leading to the formation of a cavity. The collapse of such a cavity leads to a singular jet that greatly enhances the jetting velocity up to ten times the impact propulsion velocity, an effect that narrowly peaks around $\mathrm{We}\sim 6–8$, reminiscent of singular jets in droplet-solid impact. We identify a further sensitivity of the jet velocity enhancement on the pressure width W and capture the dynamics in a phase diagram connecting the various deformation morphologies with jet velocity.

We report a striking bouncing phenomenon exhibited by pairs of $\simeq 100\mu \mathrm{m}$ biopolymer microcapsules subjected to a low-frequency AC electric field. The bouncing occurs at twice the applied frequency, suggesting that its origin lies in polarization-induced charge transfer during capsule-capsule contact. This interpretation is supported by the observation that, once the field is removed, the capsules spontaneously attract each other with a force consistent with Coulombic interaction between oppositely charged objects. A minimal toy model incorporating electrophoretic driving and Coulombic attraction captures semiquantitatively the observed dynamics. These findings provide direct experimental evidence of charge transfer in microcapsule suspensions and offer insights into the anomalous gel-like properties of these non-Brownian systems at low volume fractions.

Slow drying of a thin porous medium containing a colloidal dispersion is studied from numerical simulations developed within the framework of the continuum approach to porous media. The modeling considers two effects, referred to as the edge and breakthrough effects, affecting the saturation profiles during slow drying in thin systems. These effects result in different saturations compared to the bulk saturation in the vicinity of the porous medium limiting surfaces, lower near the top surface exposed to evaporation, and larger near the solid wall at the porous medium bottom. The impact of both effects on the colloid distribution over the thickness during drying is studied, and comparisons are performed with the standard case not considering these effects. Simulations indicate markedly more uniform colloid spatial distributions as the result of both effects compared to the predictions of the standard model. This holds in the presence of colloid adsorption phenomena on the pore wall and when adsorption is neglected.

Analyzing particle-vortex interactions in quantum turbulence is essential to interpreting the results from particle-laden experiments and revealing characteristics of thermal counterflow dynamics of superfluid He II. In this experimental investigation, the trapping and de-trapping of particles on quantum vortex lines were extracted from two-dimensional Lagrangian particle trajectories, and their processes were analyzed using particle kinetic energy. Comparison between trapping and de-trapping processes reveals that the two processes are governed by distinct physical mechanisms, with de-trapping associated with a greater loss of particle kinetic energy than trapping. In addition, time-lag-invariant patterns in ensemble averages of particle kinetic energy and kinetic energy increment suggest that these processes may exhibit self-similar features across short time lags.

We report a physics-informed neural framework for reconstructing unsteady fluid-structure interactions (FSI) from sparse, single-phase observations of the flow. Our approach combines a modal surface model with coordinate neural representations of the fluid and solid states, constrained by the fluid's governing equations and interface conditions. Using only off-body Lagrangian particle tracks and a moving-wall boundary condition, the method infers both flow fields and structural motion. It does not require a constitutive model for the solid or measurements of surface position, although including these can improve performance. We demonstrate the approach numerically on two canonical FSI benchmarks: vortex-induced oscillations of a two-dimensional (2D) flapping plate and pulse-wave propagation in a 3D flexible pipe. We also demonstrate it on flow around a swimming fish. In all cases, the framework achieves accurate reconstructions of flow states and structural deformations despite acute data sparsity near the moving interface. A key result is that reconstructions remain robust to overparameterization. This work extends physics-informed neural networks to coupled fluid-structure dynamics learned from single-phase observations, and it provides a pathway toward quantitative FSI analysis when flow measurements are sparse and structural measurements are asynchronous or unavailable.

Vortex lattices—highly ordered arrays of vortices—are known to arise in quantum systems such as type II superconductors and Bose-Einstein condensates. More recently, similar arrangements have been reported in classical rotating fluids. However, the mechanisms governing their formation, stability, and eventual breakdown remain poorly understood. We explore the dynamical stability of vortex lattices in three-dimensional rotating flows. To that end we construct controlled initial conditions consisting of vortex lattices superimposed on turbulent backgrounds. We then characterize their evolution across different Rossby numbers and domain geometries. By introducing an Ekman drag we are able to reach a steady state where vortex lattices persist with near constant amplitude up until spontaneous breakup of the lattice, or an equivalent of “melting,” occurs. We examine an ensemble of runs in order to determine the mean lifetime of the lattice as a function of the system parameters. Our results reveal that the stability of the lattices is a memory-less random process whose mean lifetime depends sensitively on the system parameters that if finely tuned can lead to very long-lived lattice states. These metastable states exhibit statistical properties reminiscent of critical systems and can offer insight into long-lived vortex patterns observed in planetary atmospheres.

In homogeneous and isotropic turbulence, measurements of the longitudinal velocity derivative, ${\partial }_1{u}_1$, make it possible to estimate a surrogate of the rate of energy dissipation per unit mass, $\epsilon$: ${\epsilon }_s=15\nu {\left({\partial }_1{u}_1\right)}^2$, where $\nu$ is the fluid viscosity, in the sense that the averages of $\epsilon$ and ${\epsilon }_s$ are equal. We show here that the $n\text{th}$ moments of the fluctuations $\epsilon$ and ${\epsilon }_s$, for $n>2$, are not exactly proportional to each other, and that the expression for the moment $\langle {\epsilon }_s^n\rangle$ for $n\ge 3$ involves in addition to a term proportional to $\langle {\epsilon }^n\rangle$, other contributions involving the invariant of the strain tensor, $\mathbf{S}$: $\mathrm{tr}\left({\mathbf{S}}^3\right)$. The contribution of this term depends on the distribution of the dimensionless ratio $\mathcal{R}\equiv \mathrm{tr}\left({\mathbf{S}}^3\right)/\mathrm{tr}{\left({\mathbf{S}}^2\right)}^{3/2}$. We find, however, that the relation obtained by assuming that $\mathcal{R}$ is uniformly distributed in the interval $-1/\sqrt{6}\le \mathcal{R}\le 1/\sqrt{6}$, which is obtained when the matrix $\mathbf{S}$ has a Gaussian distribution, differs by no more than a few percent from the exact distribution.

The interaction of vortical structures with boundaries has been extensively studied in Newtonian fluids, where conditions such as no-slip walls, free surfaces, or contaminated surfaces dictate whether vortices rebound, dissipate, or generate secondary structures. In this work, we investigate a related but fundamentally different problem: the interaction of a vortex pair with a finite, nonuniform layer of polymeric fluid. Numerical simulations employing the finitely extensible nonlinear elastic-Peterlin model are used to examine the effects of polymer concentration, relaxation time, polymer layer thickness, and maximum polymer extension on the evolution of kinetic energy and enstrophy. The results show that, while the polymeric fluid dissipates vortical motion, vortex-polymer layer interactions can also generate new coherent structures. In particular, the formation of secondary and tertiary vortices coincides with transient increases in kinetic energy, a behavior absent in the Newtonian case. Unlike classical vortex-boundary interactions, where the primary vortex survives, we find that under certain conditions it completely dissipates upon interaction with the polymer layer. These findings emphasize that fluids with nonuniform polymer concentrations act not only as dissipative agents but also as sources of vorticity, extending the traditional view of polymer-induced drag reduction and providing insights into vortex-polymer interactions.

We investigate the effective rheology of a train of elongated bubbles of negligible viscosity flowing in capillary tubes. Building upon the classical Bretherton theory for a single bubble, we extend the analysis to a train of bubbles in a single capillary tube and finally to an array of parallel, noninteracting capillary tubes, i.e., a capillary bundle. Our goal is to characterize the nonlinear pressure drop-flow rate relation of this simplified two-phase system by incorporating the thin-film hydrodynamics at small capillary numbers. We model the structural heterogeneity of the bundle by assuming that the tube radii follow a truncated power-law distribution and examine deviations of the system from the Darcy law in terms of both its statistical properties and the parameters characterizing the bubble train (i.e., the tube slenderness ratio, the volume fraction, and the number of bubbles). The main result is that two-phase flow alters the effective rheology, leading to deviations from Darcy-type behavior across the entire parameter space investigated. Specifically, for a limited number of bubbles, the flow exhibits a smooth transition from the Bretherton regime, where the pressure drop scales with the flow rate to the power of $2/3$, to weaker sublinear regimes with exponents between $2/3$ and unity. Interestingly, increasing the number of bubbles or narrowing the pore-size distribution leads to only minor deviations from the Bretherton regime. The resulting pressure drop-flow rate exponents are qualitatively similar to those reported in the literature for immiscible two-phase flow in porous media, despite the inherent simplicity of the capillary bundle model.

Cone-and-plate (CP) viscometry is now widely employed to quantify slip lengths on superhydrophobic surfaces owing to its sensitivity at the micrometer scale; however, the presence of wall slip disrupts its intrinsic flow homogeneity. In this study, we present a combined theoretical and numerical investigation on how different slip boundary formulations affect flow homogeneity and its consequences for non-Newtonian fluid flows. Semianalytical solutions are derived under both constant slip-length and constant wall-stress boundary conditions. Numerical simulations are performed to examine the spatial structure of velocity, shear rate, and apparent viscosity in non-Newtonian fluids. The results demonstrate that a fixed slip length induces pronounced spatial variations in shear rate and radial dependence of viscosity for Carreau fluids, whereas a stress-controlled slip condition restores a nearly uniform shear field despite the presence of slip. The drag reduction and effective slip length for shear-thinning Carreau fluids are shown to depend explicitly on the imposed shear rate, with maximum slip enhancement occurring in the intermediate shear-thinning regime. These findings clarify the fundamental limitations of conventional slip interpretations in CP rheometric systems and provide a physically consistent framework for a homogenous flow field.