Papers

The Rayleigh-Plateau instability predicts that infinitesimal perturbations of a liquid jet grow only for kR < 1, with kR = 1 marking the classical stability boundary. Here, we show that femtosecond-laser-induced cavitation generates a localized, impulsive recoil perturbation on a flowing liquid jet, enabling a two-dimensional map of jet breakup across the (kR, epsilon/R) plane. The perturbation's spacing (wavelength) and strength (amplitude) are set independently by the laser repetition rate and pulse energy, respectively. At low amplitudes, tuning the repetition rate recovers the classical Rayleigh-Plateau dispersion relation and its kR = 1 cutoff, while increasing the wavelength enables controlled generation of monodisperse droplet trains, bidisperse droplet populations, and ultimately isolated single droplets. Along the amplitude axis, low pulse energies produce a seed that amplifies only the imposed wavenumber, whereas above a critical energy Ec, the seed broadens to excite many wavenumbers simultaneously. At still higher amplitudes, we demonstrate deterministic breakup for kR > 1, extending to kR = 1.9, with laser-synchronized droplet production rates up to 0.2 MHz. These results establish localized femtosecond-laser-induced cavitation as a route to controlled Rayleigh-Plateau breakup both within and beyond the classical linear-stability boundary.

This paper presents a cell-centred unstructured finite-volume method for time-harmonic two-phase acoustics. A volume-fraction representation supplies density and acoustic compressibility. Face fractions average available neighbouring planar interface cuts independently of velocity direction, retaining the established one-field face-density closure. Cartesian complex-coordinate stretching provides perfectly matched layers (PMLs). Real-imaginary splitting yields a real-valued block system, discretized with corrected non-orthogonal fluxes and consistent boundary contributions. Verification covers homogeneous waves, layered gas-liquid transmission with PML truncation, baffled-piston radiation with Kirchhoff far-field reconstruction, and resolved rigid-sphere radiation forces. Homogeneous-wave pressure converges at approximately second order on orthogonal meshes and on meshes with non-orthogonal interiors and orthogonal boundary cells. Reconstructed velocity converges at approximately second order on orthogonal meshes and with an observed order of about 1.7 on the latter mesh family. Under aligned refinement, the layered case's relative whole-domain complex-pressure $L_2$ error decreases to $2.657\times10^{-4}$. The resolved-sphere force differs from the Gorkov prediction by at most 1.5% over the tested Rayleigh size range. The results quantify the accuracy and current limitations of the heterogeneous Helmholtz-PML formulation.

The total collision energy (TCE) approach originally developed for taking into account gas-phase chemistry in the direct simulation Monte Carlo method is applied to surface chemistry modeling. In the proposed surface TCE (sTCE) model probability of the impact process as a function of the translational energy of the molecule is found analytically from the finite-rate Arrhenius data. This probability function lacks some mathematical drawbacks typical of previous models. Effects of surface temperature, incident angle and internal energy can be taken into account in the sTCE model. Additionally the model is generalized to the specified reaction efficiency formulation.

The influence of rear-face inclination on turbulence around a surface-mounted protrusion depends on the separated flow approaching its trailing edge. This dependence is examined experimentally using stereoscopic particle image velocimetry over twelve trapezoidal protrusions with upper-surface length-to-height ratios $L/h=1,2,3,4$ and rear-face angles of $30^\circ$, $45^\circ$, and $90^\circ$. Measurements were conducted at a height-based Reynolds number of approximately $5\times10^4$, with an incoming boundary-layer thickness comparable to the protrusion height. For $L/h=1$ and 2, a connected reverse-flow region extends over the upper surface into the wake. For $L/h=3$ and 4, upper-surface reattachment separates the two regions. Length governs this change in topology and the variation in turbulence levels at common spatial locations, whereas rear-face inclination has its strongest influence close to the surface. From $L/h=2$ onward, shallower faces have higher near-face turbulent kinetic energy, while vertical faces have lower energy but a larger spanwise fraction. A decomposition of the in-plane deviatoric production separates the effects of Reynolds-stress and mean-strain magnitudes from those of their relative principal-axis orientation. At the inclined faces, this contribution changes from negative to positive between $L/h=1$ and 2, before upper-surface reattachment occurs. Its subsequent increase with length is driven mainly by increasing tensor magnitudes, with the largest contribution at $L/h=4$ and $30^\circ$, where strong production remains close to the rear face. These results show that local turbulence production depends jointly on the flow state approaching the trailing edge and the position of the energetic shear layer relative to the rear surface.

We develop a conservative micro-continuum-cellular automaton method for simulating multispecies biofilm dynamics in complex flows. The proposed method couples the Darcy-Brinkman-Stokes equations, reactive transport, suspended bacteria, and biofilm dynamics with a two-stage cellular automaton algorithm for biofilm redistribution and interface evolution. While treating biofilms as evolving porous media, we ensure conservative redistribution of multispecies biomass across partially occupied cells. Donor and recipient cell volumes are explicitly accounted for to conserve biomass and preserve species composition on non-uniform meshes. The proposed method is assessed against diffusion-dominated benchmark cases, including single-species fingering and multispecies stratification, and is further evaluated through a mesh-convergence study for flow and growth over a rectangular bump. The framework is then applied to counter-diffusional biofilms in a membrane-aerated biofilm reactor as a canonical example. The results demonstrate that the framework captures the expected biofilm morphology and stratification in systems involving coupled flow, substrate transport, and biofilm dynamics. The proposed method provides a flexible computational approach for simulating multispecies biofilm dynamics in complex flows and geometries.

SIREN (Ship Inviscid Resistance and Elevation eNgine) is a Rankine-source panel solver for the steady wave resistance of a ship, in the tradition of Dawson's method. The free-surface condition is linearised about a base flow, and the linearisation is iterated. In the present formulation the base flow is the solution of a Neumann problem on the actual boundary: sources on the entire hull, wet and dry, and on the free surface panels, with impermeability imposed on both, so that the free surface acts as a rigid lid at the position it currently occupies. This replaces the classical double-body flow, whose image about z=0 is meaningful only for a flat surface and a hull cut at z=0, and it removes the need for desingularised free-surface panels. In the non-linear iteration the free-surface panels are moved rigidly in the vertical to the relaxed wave elevation at their centroid, the hull panels are marked wet or dry against the moved surface, and the base flow is recomputed on the moved geometry; impermeability applies to the whole hull regardless of this marking, which is used only to select which panels enter the force integral, and under-relaxation is confined to the passes where the non-linear correction accumulates without being reset. The radiation condition is imposed by a one-row upstream shift of the collocation points, and the wave resistance is obtained by pressure integration and, independently, by transverse wave-cut analysis.

In this communication, we discuss results obtained with the numerical in-house PHP simulation code CASCO (French abbreviation for Advanced PHP simulation code). The aim is to study the impact of bubble generation (boiling) on the established oscillation of a PHP with a high turn number (10-turn water-copper tubular PHP with independently heated turns in the evaporator region). We vary the nucleation barrier value, i.e. the local superheating $\Delta$Tnucl at which the nucleation occurs and the heat load Pe; other simulation parameters are kept constant. The PHP heat transfer performance is evaluated with the PHP thermal resistance Rth for both horizontal and vertical favorable PHP orientation. Since the bubble generation plays a positive role for the PHP functioning, one expects that the function Rth($\Delta$Tnucl) monotonously increases. This is true for high $\Delta$Tnucl. For small $\Delta$Tnucl, the Rth($\Delta$Tnucl) function is decreasing, thus a minimum occurs. It appears because of a transition between the regimes of stable PHP functioning. The regimes strongly differ by the average penetration of liquid plugs into the evaporator. For horizontal PHP, these regimes correspond to the intermittent and continuous oscillations. The regimes are discussed and the regime map in the coordinates Pe -$\Delta$Tnucl is obtained.

Gas bubbles impose large penalties in water electrolysis at industrially relevant rates. Capillary-fed electrolyzers greatly mitigate them by wicking electrolyte to electrodes and venting gas from the backside, but only below a threshold current density. We show that the separator pore size sets this threshold through two opposing effects: smaller pores raise the supersaturation required for nucleation but reduce the permeability for electrolyte replenishment. A coupled electrochemical-transport model, anchored to a single measured onset, quantifies both mechanisms across 0.1-8 $\mu$m pores. Experimentally, reducing pore size from 8 to 1.2 ${\mu}$m raises the bubble onset limit from 0.18 to 1.73 A cm$^{-2}$ and lowers cell voltage by 0.11 V at 1 A cm$^{-2}$, primarily by suppressing bubble-induced overpotential. At 0.45 ${\mu}$m and below, the replenishment limit takes over and the cells dry out before bubbles form. Our findings establish the bubble-free operation limit as designable rather than purely empirical.

Recent advances have linked mixing in porous media to the deformation of infinitesimal fluid elements. However, these Lagrangian frameworks generally neglect or simplify interactions with solid surfaces. We consider transport of thin solute blobs (strips or sheets) near single generic obstacles, in particular along separation lines (separatrices) which connect to stagnation points at solid boundaries. In this case, we demonstrate that the coupling between flow and diffusion is analytically tractable. We provide a complete theory for scalar mixing near upstream stagnation points, which we validate by numerical simulations. We identify a mixing time scale $t_B \sim Pe^{1/3}$, where $Pe$ is the Péclet number, which controls whether scalar decay is driven by fluid stretching or by interaction with the solid boundary. Asymptotically, for times $t < t_B$, we find that the maximum concentration $c_{\rm max}$ decays as $t^{-5/2}$ and that the width $\sigma$ grows like $t^{1/2}$. For $t > t_B$, we find exponential decay of $c_{\rm max}$ and constant width $\sigma \sim s_B \sim Pe^{-1/3}$, where $s_B$ is a mixing length scale distinct from that which appears in shear flows. The asymptotic scalings of $c_{\rm max}(t)$ and $\sigma(t)$, and their dependence on $Pe$, are universal to no-slip stagnation points and qualitatively different from stagnation points in open flows.

Here, I give a brief history of the theory, with twists and turns, and list possible predictions for the spectra of the direct cascade of gravity waves on the water. The description of long waves is straightforward within the weak-turbulence theory developed by Zakharov and his school. As the energy cascade proceeds to shorter scales, the mean surface steepness grows, and wave-breaking events appear with increasing frequency. Considering surface cusps, Phillips suggested a wavenumber spectrum (with a wrong magnitude, as I argue here) and a frequency spectrum whose whole form is incorrect. The right form for the frequency spectral slope due to breaking waves was suggested by Kuznetsov. Here we estimate the magnitude and argue that the frequency spectrum is expected to continue unchanged through the whole cascade. The transition from weak to strong turbulence in the wavenumber and spatio-temporal spectra is due to spectrally nonlocal interactions and happens earlier (at larger scales) than the dimensional estimate suggests. As a result, the magnitude of the strong-turbulence spectrum is not universal but depends on the pumping for a sufficiently long weak-turbulence cascade. The reason for nonlocality is likely that breaking of shorter waves is determined by the magnitude of the longest wave on whose crest they are running.

We report measurements of the surface tension of aqueous sodium dodecyl sulfate solutions at sixteen concentrations from 0.17 to 43$\,$mM, spanning 0.02 to 5 times the room-temperature critical micelle concentration (cmc), and at temperatures from 26 to 83$\,$$^\circ{\rm C}$, using the Wilhelmy plate method. At the lowest concentration the surface tension decreases with temperature, as it does for pure water. Above about 0.4$\,$mM, however, it increases: the temperature coefficient changes sign at a concentration of 0.3 to 0.8$\,$mM, roughly a tenth of the cmc, and reaches $+0.53\,\rm mN\,m^{-1}\,K^{-1}$ near 3$\,$mM, three times the magnitude of that of pure water and of the opposite sign. Above the cmc the surface tension is nearly independent of temperature, saturating at $35.2\pm0.3\,\rm mN\,m^{-1}$. The behavior cannot be attributed to the temperature dependence of the cmc, which is an order of magnitude too weak. It is instead consistent with a surfactant layer that thins as the temperature rises. The results imply that the sign and magnitude of thermocapillary stresses in SDS solutions can be selected through the concentration.

Machine-learning surrogates accelerate physical simulation, but lower prediction error need not coincide with lower error in physically relevant flow statistics. We examine this question for flow around a NACA4418 airfoil using paired computational-fluid-dynamics simulations and experimental particle-image-velocimetry measurements. A mean-preserving input intervention removes velocity fluctuations from selected regions of observed flow histories. Across four neural operators, removing fluctuations from the most energetic 10% of valid observed cells changes forecasts more than equal-area random removal. Because the masks are not matched for removed fluctuation energy, this contrast measures sensitivity, not independent evidence of physical importance. Separately, a CNO has lower velocity-field error but substantially higher two-component fluctuation-energy error than the reference on both analysis subsets. An output attenuation stress test also demonstrates disagreement between benchmark errors and domain-summed fluctuation energy. These single-benchmark results motivate reporting complementary physical diagnostics alongside aggregate prediction scores; they do not establish counterfactual physical correctness.

Dynamic approaches to minimize the classical curvature-elasticity free energy for a fluid lipid membrane, are extended towards a Surface Beris–Edwards–Helfrich model. This extension explicitly treats the liquid crystal structure of the membrane, which results from the lipid molecules, that are, on average, oriented normal to the surface. Locally varying liquid crystal order leads to local variations in bending rigidities and surface viscosity and thus influences the shape evolution. This provides a multiscale coupling between the local membrane mechanics on the level of the lipids and the mesoscopic length and time scales of biological functions. The model is derived using the Lagrange–d'Alembert principle. We provide a numerical algorithm to solve the equations in the one-constant approximation and demonstrate the impact on the emerging equilibrium shapes, which not only depend on the specified conserved surface area and enclosed volume, as for the classical curvature-elasticity free energy, but also the elastic parameter. Exploring the dynamic evolution shows a tight coupling of tangential flow, shape evolution and liquid crystalline order. We further point to extensions towards lipid phase separation and asymmetric lipid bilayers.

Titan, a unique body in the solar system, resembles a life-size Miller-Urey experiment where pockets of liquid water might interact with abundant organic matter. Its young surface (less than a billion years) shows signs of material exchange with the interior, and an isotopic signature is detected in the atmosphere. Cryovolcanism and meteor impacts represent potential high energy mechanism for these exchanges. Although cryolava or impact melt properties are largely unknown, Titan's internal structure makes a significant water content in these fluids highly probable. The temperature of these fluid mixtures at the onset of the flows is above 0~$^\circ$C. The primary objective of this work is to investigate the dynamical and thermal properties of potential Titanian flows, while ensuring their spatial extents remain broadly consistent with the few available observations. We also aim to assess whether their evolution could enable the hydrolysis of encountered organic material. On Earth, in the context of lava flow risk assessment, numerical techniques based on cellular automata have been developed for many years. This approach allows simulating the flow of Bingham fluids over distance scales of several tens of kilometers. In the context of Titan's surface, and within the explored parameter space, flows with a spatial extent of several tens of kilometers can be produced with our model. The resulting flow thickness is about a meter. The flow extent is primarily controlled by the total erupted volume and the terrain topology. As expected, the rheology and thermo-physical properties of the erupted fluid have significant influence on the flow's extent and the cooling rate of the cryolava. We predict hydrolysis reactions between an aqueous cryolava and the organic matter likely ubiquitous on Titan's surface. Our model code is publicly available.

Beyond a critical Toner–Tu drive, bacterial turbulence exhibits universal statistics, including a parameter-independent energy spectrum $E(k)\sim k^{-3/2}$. We show that the same universal state can be reached not only by increasing activity, but also by strengthening nonlinear advection, weakening nonlinear saturation, or tuning the Swift–Hohenberg instability. Motivated by the competition between these processes, we identify the independent dimensionless groups governing the dynamics and construct a Reynolds-like control parameter from them. A single critical value, calibrated from the known activity-controlled transition, predicts the onset of universality along the other parameter routes and collapses them onto a common threshold. These results identify a dynamical organizing parameter for the onset of universal active turbulence and provide a Reynolds-like measure for the Toner–Tu–Swift–Hohenberg universality class.

The distinct dynamical roles of vorticity amplification (VA) and vortex tilting (VT) in three-dimensional homogeneous isotropic turbulence are investigated using direct numerical simulations of a modified Navier–Stokes system. By selectively suppressing VA while retaining VT, we demonstrate that gradient amplification by VA is strictly required to sustain the classical forward energy cascade. Progressively suppressing VA weakens small-scale velocity gradients, heavily depletes extreme fluctuations, and entirely eliminates the classical energy dissipative anomaly, causing the normalized energy dissipation to decay as $Re_\lambda^{-1}$. In the limit of complete VA suppression, enstrophy emerges as the relevant inviscid invariant. Scale-by-scale budget analyses confirm that the dynamics transition to a purely forward enstrophy cascade, characterized by an anomalous enstrophy dissipation and a robust $E(k) \sim k^{-3}$ intermediate energy spectrum. We verify that these asymptotic scaling limits—including a $Re_\lambda^{-1/2}$ finite-Reynolds-number correction for the enstrophy anomalous dissipation—are universal properties of the VA-suppressed dynamics, independent of whether the large-scale forcing is helical or non-helical. Remarkably, despite the smoothing of the velocity field and the elimination of the energy dissipative anomaly, anomalous structural scaling and a broad multifractal spectrum persist. These results reveal a fundamental mechanistic separation: while VA is responsible for amplifying intense localized fluctuations, geometric reorganization by VT alone is mechanically sufficient to sustain multifractal intermittency.

The mixing-plane method plays a pivotal role in steady simulations of multiple turbomachinery components. With advances in computational power, a whole-engine gas turbine simulation is no longer an elusive approach. However, whole-engine simulations require simultaneous coupling of the compressor, turbine and combustor. A key challenge is that the working fluid after the combustor can no longer be treated as a perfect gas, since the combustion introduces composition variations and combustion products. Conventional mixing-plane methods based on a fixed-composition gas cannot guarantee a thermodynamically consistent mixed-out state. To overcome the difficulty, this paper extends the classic mixing-plane approach to handle compressible reacting flows. The nonlinearity in the thermodynamic closure is addressed using a novel nested algorithm combining an outer pressure-root search with an inner enthalpy inversion. Physical state checks and power-law pressure sampling are incorporated to improve numerical robustness at low normal velocities where the pressure root approaches its upper physical bound. The performance of the method is demonstrated in three configurations: a quasi-1D interface test elucidating the thermodynamic stiffness of the proposed mixing-plane formulation for different fuel types and flow conditions; the Darmstadt transonic compressor case that verifies the proposed method reduces to the classic mixing-plane formulation when the mixture fraction reduces to zero; and a whole-engine simulation of the KJ66 micro-turbojet is used to demonstrate the performance of the method for multiphysics turbomachinery simulations. Good agreement with experimental data is observed, and the maximum relative mass-flow error across the mixing planes remains below 0.11%, demonstrating conservative and thermodynamically consistent interface coupling for compressible reacting turbomachinery flows.

The interaction between flame dynamics & hydrodynamic instabilities plays a fundamental role in determining the stability of swirl-stabilized combustors. In the present study, we investigate the hypothesis that spatial overlap between flame & wavemaker region is a necessary prerequisite for combustion stability in flows characterized by a wavemaker region. To test the hypothesis, a low-momentum secondary methane injection was introduced through circumferential holes located on the centerbody of a swirl-stabilized burner. The injection velocity was maintained below 5% of bulk flow velocity to minimize momentum-induced modifications of flow field while selectively redistributing heat release. In addition, an equivalent amount of fuel was diverted from primary fuel supply to secondary injection ports, known as fuel-staging, to isolate the effects of flame relocation from those of the total fuel flow rate. The introduction of secondary injection produced a transition of the flame from M-shaped to V-shaped structure, while fuel-staging yielded a similar flame response, demonstrating that observed behavior results primarily from redistribution of heat release. Linear stability analysis revealed that wavemaker region remains near inlet of the combustion chamber. Moreover, flame root transitions from a lifted M-flame to attached V-flame and consistently stabilizes at radial position corresponding to the identified wavemaker region. The coincidence of flame attachment & wavemaker location under stable operating conditions provides strong experimental evidence that flame stabilization is governed by their spatial overlap rather than by a modification of the underlying hydrodynamic instability. The proposed framework provides new insight into the coupling between flame stabilization & hydrodynamic instability & offers practical guidance for the design of stable, low-emission combustion systems.

Explicit lattice Boltzmann simulations of slow transient flows are constrained by the acoustic time step. Dual-time stepping can remove this restriction, but slow inner convergence has limited reported wall-clock gains to roughly four- to tenfold, without a mechanism that strengthens under refinement. We present the macroscopic-shadow-corrected lattice Boltzmann method (MSC-LBM), which applies defect correction to the unsplit kinetic residual. At each Fourier wavenumber, a Stokes-like system is solved exactly for the conserved residual moments while preserving the second-order backward-differentiation formula (BDF2) fixed point and temporal accuracy. Along the two-relaxation-time axis $\Lambda=1/4$, $\omega^+=\omega^-=1$ makes one collision eliminate all non-hydrodynamic perturbations; $\eta(\nu)=|6\nu-1|/(6\nu+1)$ vanishes at $\nu=1/6$, leaving hydrodynamic slow modes whose long-wave shadow is inverted by the corrector. In completed timing campaigns, MSC-LBM achieves 27.95- and 52.71-fold wall-clock speedups at $N=256$, $\mathrm{Re}=1$ under matched-accuracy and $1\%$ gates. The matched speedup rises monotonically to 122.02 at $N=1024$, with gains persisting across $\mathrm{Re}=10^{-4}$–$100$. The three-dimensional D3Q19 extension reaches 27.85 and 8.84 under the same gates at $N=128$, $\mathrm{Re}=1$. A bounce-back-consistent kinetic coarse solver with adaptive relinearisation extends MSC-LBM to fully enclosed cavities, yielding setup-excluding physical-march speedups of 26.86 at $\mathrm{Re}=10$ and 3.84 at $\mathrm{Re}=100$ for $N=128$. An exact per-wavenumber symbol inverse establishes the attainable off-design contraction envelope. The contraction, parameter-sweep, and timing results jointly delimit the demonstrated operating regime: low-to-moderate-Reynolds-number transients for which acoustic stepping need not dictate computational cost.

Slender flexible structures such as mooring lines, aquaculture netting, and aquatic vegetation are too thin to be resolved economically by a body-fitted mesh, yet they exchange momentum with the flow in both directions. This paper presents a finite volume actuator-line formulation for the fluid–structure interaction of such structures, in which a geometrically exact Simo–Reissner beam, discretised by cell-centred finite volumes, is coupled two-way to an incompressible finite volume flow solver through conservative, parallel-consistent transfer operators. The fluid velocity is sampled upstream of each beam control volume, a quasi-steady Morison-type drag closure evaluates the line force, and the equal and opposite reaction is projected into the fluid momentum equation through a normalised Gaussian kernel that conserves force. The two subsystems share a discretisation, time loop, and domain decomposition, so no external structural code is required, and the OpenFOAM implementation is released publicly. The accuracy of the drag-only closure and the conditions over which it holds are quantified against two channel benchmarks and a wave-flume experiment, with all drag coefficients fixed in advance. In a steady confined channel flow the tip deflection of a wall-mounted cantilever falls within the range of published continuum solutions. For a flexible leaflet in sinusoidal channel flow the peak tip excursion departs from the reference at the longer forcing period. The leaflet then moves further relative to the surrounding fluid, so added-mass and history forces, which the closure omits, become important. In the wave flume the simulated stem reproduces the measured mode shape, intra-wave asymmetry, and base force, and recovers 71–83% of the oscillation range. A quasi-static reconstruction test places the remaining shortfall in omitted fluid inertia rather than in the structural model.

We develop a sharp-interface method for freely moving solid particles undergoing pure or binary melting. A Level-Set representation preserves the particle geometry during long-distance translation and rotation, while an embedded-boundary formulation imposes hydrodynamic, thermal and solutal conditions sharply on a Eulerian Cartesian mesh. Liquid temperature and solutal concentration are advanced with a conservative moving-cut-cell discretization, whereas the solid temperature is transported through a geometry-consistent conservative tracer. Hydrodynamic loads, rigid-body motion and phase change are coupled iteratively within each physical time step. The method is validated progressively for rigid-body motion, prescribed-motion pure and binary melting, and fully coupled melting with free particle motion. It reproduces established reference solutions and captures wake-induced rotation of a melting sphere and the simultaneous translation, rotation and thermosolutal melting of a three-dimensional oblate ellipsoid. As a final application, simulations of a floating ice disc reveal how thermoconvective instability, geometric confinement and melting jointly determine its spontaneous motion, with phase change feeding back on the instability through the evolving particle geometry. Additional tests establish the importance of long-time geometrical fidelity, local scalar conservation and geometry-consistent solid-temperature transport. The resulting framework provides a sharp and conservative approach for strongly coupled moving-body phase-change problems.

Computing effective hydraulic properties of porous materials with a dynamically changing pore morphology presents a complex and critical challenge in both theoretical and applied sciences. This paper presents a tool to effectively compute the intrinsic permeability k(x,t) for domains with both temporally and spatially varying pore structures, by utilizing a sample of snapshots of microfluidic experiments with calcium carbonate precipitation. To compute large domains at reasonable cost, a pseudo-3D Stokes solver with an additional viscous drag term is employed. In order to simulate the intricate domains with highly heterogeneous pore space, we derive vertically averaged governing equations including a vertically averaged drag term from scratch and without limiting assumptions. For exemplary precipitates (semi-spheres) of varying sizes within a rectangular channel with fixed solid boundaries, results are compared across multiple modeling approaches, each employing different drag force formulations. In addition, the performance of the derived models is examined for segments of an EICP experiment in terms of accuracy (comparison with 3D solvers) and computational efficiency. Finally, an entire experimental domain is used to demonstrate the capabilities offered by the solver thanks to its efficiency as well as accuracy and the permeability tensor k is computed and compared with experimental results. In all these applications, the vertically averaged drag term proves to be the optimal solution in terms of speed and accuracy, thus allowing for an efficient analysis of the non-uniformity of local fluid flow fluctuations resulting from alterations in the pore space.

We study the effect of pitch and yaw on the bifurcations of the laminar flow past an Ahmed body, a bluff body of width-to-height ratio $W/H=1.2$ and length-to-height ratio $L/H=3$. When perfectly aligned with incoming flow, its wake first undergoes pitchfork bifurcations leading to a static vertical or horizontal deflection, and becomes oscillatory via a secondary Hopf bifurcation at larger Reynolds number $Re$. As commonly observed for imperfect pitchfork bifurcations, any small misalignment preselects one of the steady states, referred to as the "primary" branch, at low $Re$. At larger $Re$, a disconnected "secondary" branch is born via a saddle-node bifurcation. Here, we investigate the effect of misalignment using three-dimensional computations. We first focus on pure pitch and pure yaw with linear stability analysis. In both cases, the secondary branch becomes unstable as soon as the incidence exceeds a small value. In the pure yaw case, the primary branch becomes unstable via a horizontal Hopf bifurcation, destabilised by yaw. In the pure pitch case, the primary branch sees the crossover of vertical Hopf and horizontal pitchfork bifurcations, destabilised and stabilised by pitch, respectively. This motivates use of DNS to study this nonlinear competition, already observed for aligned Ahmed bodies in ground proximity. We then study the effect of simultaneous yaw and pitch with a weakly nonlinear analysis. The competition between the two stationary modes gives rise to rich bifurcation diagrams, allowing us to predict the number of stable solutions and phase space trajectories between different states

Physics-informed computational methods usually optimize parameters within a functional representation whose structure is fixed in advance. This work proposes a Physics-Informed Method of Group Data Handling (PI-GMDH), in which representations of coupled physical fields are progressively constructed during solution. Candidate functional directions are evaluated through the first variation of the complete physical and observational objective, introduced in packages, and followed by block-coordinate damped Gauss-Newton coefficient optimization. The framework is demonstrated with tensor-product Chebyshev functions on the incompressible Navier-Stokes equations using a two-dimensional time-dependent Taylor-Green benchmark. Under the tested configuration, adaptive PI-GMDH reached validation and held-out test losses of 5.299e-19 and 5.296e-19 with 204, 201, and 175 active functions for u, v, and p. Complete degree-by-degree and all-terms PI-GMDH variants, together with selected PINN and KAN reference configurations, are used to examine the effect of structural construction policy. The results show that, for this controlled synthetic benchmark, selective progressive construction can provide a favorable combination of accuracy, representation size, and wall-clock time. The comparison is illustrative rather than a claim of universal superiority over alternative physics-informed approaches.

We explore the effect of wing sweep on the interaction between leading-edge separation and tip vortex for a finite wing with sweep angles $\Lambda=0^\circ$ to $45^\circ$, semi-aspect-ratio $sAR=2$, angle of attack $14^\circ$, and chord-based Reynolds numbers $Re=600$, $1000$, $2500$, $5000$, and $10000$. Through this parametric study, we seek to bridge the knowledge gap between existing studies on separated flows over swept finite wings at low Reynolds numbers ($Re\approx 10^2$) and the behavior of turbulent flows at higher Reynolds numbers ($Re\approx10^4$). The flow structure significantly varies over this range of parameters, altering the lift characteristics. Specifically, increasing $\Lambda$ at $Re\leq5000$ reduces the lift, while increasing $\Lambda$ at $Re>5000$ enhances the lift. The flow modifications that lead to this effect with increasing Reynolds number are analyzed in terms of the streamwise vorticity, revealing three key effects: (i) a change in the sign of streamwise vorticity with increasing sweep angle, due to the higher spanwise velocity component, (ii) the progressive weakening and eventual disappearance of the tip vortex, when increasing the wing sweep, is accompanied by the emergence of a dominant inboard vortical structure near the root, and (iii) at higher Reynolds numbers and sweep angles, this inboard vortical structure merges with the main wake, intensifying the shear-layer roll-up and giving rise to a leading-edge vortex with an extended reattached region over the wing. These findings reveal how the flow characteristics vary with Reynolds number, transitioning from regimes where swept wings offer limited benefit to regimes where they significantly enhance the aerodynamic performance. This study contributes to a deeper understanding of swept-wing wake dynamics, which is crucial for modern air vehicle design.

Evaluating the drag coefficient Cd for a sphere moving in a fluid at finite Reynolds number Re has become a classical research subject in fluid dynamics, with publications appearing continuously by numerous authors over the years due to the unavailability of closed-form mathematical solutions. To date, mathematical formulas for calculating Cd as a function of Re can only be obtained by correlation curve fitting to experimental data. The consequence is the coexistence of various formulas with different mathematical fitting functions and an increasing number of fitting parameters. The present study focuses on examining the accuracy of Klyachko's 1934 formula for Cd with two common fractions as fitting parameters, which could enable closed form integration of a simplified equation governing rectilinear motion of aerosol spheres. The computed values of root-mean-square relative error from recently developed formulas show reasonable accuracy of the Klyachko formula for Re less than 1000 and its extension to Re less than 3e5 as a piecewise continuous function, with the possibility of significant improvement through a slight modification. Hence, a few demonstrative examples are presented using the extended Klyachko formula in the study of rectilinear acceleration, the calculation of the terminal velocity of aerosol spheres, and so forth, to shed fresh light on how this classical problem can be studied.

We explore new methods for inducing the movement of water droplets on elastomeric substrates, such as polydimethylsiloxane (PDMS). Our approach builds upon the well-known phenomenon that water droplets move easily across these substrates when swelled w,ith silicone oil. While designing shallow open channels and traps on a PDMS film offers a simple way to control a droplet's trajectory by tilting the substrate in two orthogonal directions, this method is poorly suited for manipulating multiple droplets simultaneously. To address this limitation, we introduce two new methods. The first method utilizes a plano-concave PDMS platform with a radius of curvature significantly larger than the size of the droplet and its translation distance. When the system's configuration is altered, this curved substrate consistently guides the droplet along a curved geodesic. The second method incorporates diode-like gates on the PDMS. These gates are created on either flat or plano-concave PDMS films by embedding thin, rigid plates into the elastomer prior to crosslinking, followed by swelling in silicone oil. This process generates sigmoidal steps that restrict droplet motion to a single direction. Finally, we demonstrate how combining these two strategies enables various forms of directed motion for both single and multiple droplets.

Active nematics are non-equilibrium fluids composed of rod-like self-propelled units that collectively generate large-scale coherent flows. Here, we focus on a canonical experimental system: an active nematic fluid in $2D$ driven by ATP, composed of densely packed, extended microtubule (MT) bundles cross-linked by kinesin motors. An intriguing feature of this system is the creation and annihilation of topological defects with topological charge $\pm1/2$, due to the fracturing of the material. Experiments confirm that the positive ($+1/2$) defects serve as "virtual stirring rods" that move around each other in a complex braiding pattern. This collective braiding motion of positive defects stretches and folds the fluid itself, i.e., produces macroscale chaotic advection. The degree of self-mixing due to the chaotic advection can be measured using topological entropy and the Lyapunov exponent. Our goal is to determine whether continuum models of MT-based active nematic fluid can reproduce these measurements. To this end, we use two continuum models: the traditional Beris-Edwards (BE) model and the more recently developed Beris-Edwards model with enhanced nematic locking (BENL). The difference between the two models is the adoption of the "nematic locking principle", which states that an individual MT bundle cannot rotate independently of its neighbors due to steric interactions among elongated dense MT bundles. This principle holds in the BENL model except in small localized areas of the material domain where the material fractures, specifically near the creation and annihilation of topological defects. We employ several numerical methods to estimate measures of chaotic advection using both models. Our study shows that the BENL model more accurately reproduces experimental measures of self-mixing driven by chaotic advection in MT-based active nematic fluids.

The Rheological Universal Differential Equation (RUDE) framework embeds neural networks within a frame-indifferent tensorial constitutive backbone and so enables data-driven discovery of complex material rheological behavior. However, the flexibility that makes the RUDE framework attractive also makes it difficult to deploy: the learned neural network correction can make the constitutive equation numerically stiff during training, distribute corrections across non-unique combinations of tensor-basis terms, and extrapolate poorly with increasing nonlinearity, especially for industrially relevant materials with broad relaxation spectra. We develop a stability- and reliability-focused multi-mode RUDE framework that addresses three key challenges: thermodynamic admissibility, out-of-distribution prediction, and interpretability. Logarithmic compression of the input invariants and a split-network architecture improve numerical conditioning during training, while a differentiable projection layer enforces the Clausius–Duhem inequality at every time step. We illustrate the framework with both synthetic (a multi-mode Giesekus model) and experimental data on an entangled silicone polymer melt. Both models were trained on LAOS; they remain stable and accurate under unseen flow conditions, including steady shear, transient stress growth, and extensional flows, for which the unconstrained models may diverge numerically. To aid in interpretation of the contributions of each learned correction to the rheological behavior, we introduce the rheome, a compact way of representing the dominant weighted tensor-basis contributions to the overall rheological behavior. These improvements to the RUDE framework lead to stable and interpretable trained models, paving the way for implementation in computational fluid dynamics simulations and for guiding the rational design of soft material processing operations.

We investigate the dynamics of spherical lipid vesicles subjected to an osmotic shock using continuum simulations of a permeable, area-incompressible fluid membrane with bending elasticity and surface viscosity. The dynamics are governed by a single dimensionless parameter $\varGamma$, which measures the relative strength of osmotic pressure and bending forces. Osmotic forcing drives a three-stage evolution comprising rapid buckling and collapse, smoothing of the resulting wrinkles and ridges, and slow folding into an invaginated morphology resembling the precursor to experimentally observed vesicle-in-vesicle structures. Linear stability analysis predicts the wavelength and growth rate of the initial buckling instability and shows that the dimensionless buckling time scales as $\varGamma^{-2}$, in quantitative agreement with simulations. At longer times, the energy budget reveals a reversal in elastic energy transfer: bending energy accumulated during buckling is released during relaxation and dissipated by membrane viscosity. A scaling analysis of the folding dynamics predicts that the dimensionless folding time scales as $\varGamma^{-2/3}$, again in excellent agreement with simulations. These results provide a continuum description of the mechanisms and widely separated timescales governing osmotically driven membrane collapse and invagination.