The interaction mechanisms among detonation waves, shock waves, and liquid droplets play a critical role in advancing propulsion technologies such as rotating detonation engines. This study conducts a detailed comparison of wave dynamics, cavitation phenomena, and droplet deformation during the detonation wave and the shock-wave interactions with a water droplet, employing a high-resolution numerical model that integrates multicomponent compressible fluid dynamics, chemical reactions, and phase transition effects. Numerical simulations reveal distinct characteristics between detonation and shock-induced phenomena. Unlike the shock wave, detonation-induced reflected shock waves exhibit significantly higher propagation velocities while maintaining nearly identical wave configurations, a phenomenon this study mechanistically explains by the unique postwave conditions. A fundamental distinction arises in cavitation dynamics between the detonation wave and the shock wave, with the detonation-wave triggering cavitation zone collapse at significantly higher rates compared with the shock wave. This difference is attributed to the shorter persistence of low-pressure regions behind the detonation front, where rapid attenuation of postwave pressure and flow velocity occurs. Moreover, detonation-induced flow interactions create unique droplet fragmentation patterns. The rapid postwave velocity reduction prevents Rayleigh-Taylor instability-driven forward jet formation, instead causing leeward-side flattening of the droplet through the vortex in the recirculation zone.

Bicuspid valves with crescent-shaped leaflets are found in lymphatic vessels and veins, where their primary function is to prevent reflux and ensure unidirectional flow toward the heart. These valves are passive, and their functionality emerges spontaneously from a complex interplay between the properties of the valve leaflets and the flow patterns developing within the vessel sinus region surrounding the valve. The main function of the valves is to limit retrograde flow, or reflux, but the optimal valve structure has not been well characterized. Here we investigate numerically how the length of the leaflets affects the valve efficiency in preventing reflux. The valves are subjected to backward flow, akin to that imposed by gravity. We report the flux through the valve orifice as a function of key parameters: valve length, leaflet length, and leaflet rigidity. We monitor the transition in the flow regime—from reflux to complete flow blockage—by varying only the leaflet length. The transition threshold is found to depend strongly on the valve shape and stiffness. We captured these control parameters numerically to evaluate the ability of the valve to close and prevent reflux. This study allowed us to explain reflux observed experimentally in certain incompetent abnormal and immature valves, particularly those with shorter leaflets.

The accurate prediction of pressure drop across randomly packed beds is critical for the design of chemical reactors, adsorption columns, and thermal energy storage systems, yet existing semiempirical correlations often lack consistent accuracy across diverse geometric and flow regimes. This study presents a residual-driven sensitivity analysis framework that systematically evaluates the influence of key operational and geometric parameters, namely, superficial velocity $U_s$, normalized bed length $L/D$, and normalized column diameter $D/d_p$, on the prediction error of classical pressure drop models. Using an extensive experimental dataset collected in our laboratory, comprising over 3000 measurements across four column diameters (50–200 mm) and six particle sizes (2.5–42.6 mm), we integrate robust outlier detection, iterative data sanitation, and multimethod sensitivity assessment combining Pearson correlation, tree-based feature importance, and partial dependence analysis. Results show that for the raw dataset, errors are collectively influenced by all three parameters, with no single factor dominating. Through successive cleaning iterations that progressively remove data with strong wall effects ($D/d_p<4$), low length-to-diameter ratios, and extreme geometries, the analysis reveals a clear transition: Superficial velocity emerges as the overwhelmingly dominant driver of residual error, accounting for 74.6% of the normalized Gini importance in the final filtered dataset. This evolution demonstrates that after mitigating geometric confounders, the core limitation of widely used models such as the Ergun equation lies in their inability to accurately capture flow-regime-dependent behavior. The work provides a validated methodology for sensitivity analysis in packed-bed flows and offers practical guidance for model selection and experimental data-quality assurance, highlighting that future model improvements should prioritize velocity-dependent corrections rather than further refinement of geometric terms.

Capillary suspensions are commonly encountered in a wide array of applications, but their stability in flow is not fully understood. Here, we investigate the stability of a two-particle capillary cluster in extensional flow using a combination of theory and experiments. A linear stability analysis reveals the existence of a critical capillary number ${\text{Ca}}_c=(8/45)cos\theta$ that depends only on the contact angle $\theta$. For $\text{Ca}>{\text{Ca}}_c$, clusters are unconditionally unstable, regardless of initial conditions. For $\text{Ca} < {\text{Ca}}_c$, a nonlinear analysis shows the existence of a $\text{Ca}$-dependent minimum interparticle separation beyond which breakup occurs. The analytical model further supports the experimentally observed slowdown in relaxation dynamics. Theoretical predictions are supported by precise flow experiments using a Stokes trap, where active flow modulation is used to stabilize an initially unstable cluster in extensional flow. Overall, these results provide a quantitative understanding of capillary suspension stability in flow.

Stereo inhalation draws ambient fluid into a pair of spatially separated siphons. The ubiquitous mammalian nose morphology of two separated nares uses stereo inhalation to enhance respiration and olfaction. Previous studies have found that stereo inhalation improves the spatial extent of odor capture and success of source localization. However, direct quantification of the spatial extent of inhaled fluid has received less attention, which may provide context for evolutionary adaptations to sensory appendages and design of biologically inspired sniffing devices. We numerically modeled idealized stereo inhalation through a pair of round siphons and evaluated the effects of siphon separation, proximity to boundaries, and inhalation Reynolds number (Re) on the inhaled fluid structure. We find that siphons closer together have approximately three times the lateral perception of sensory information relative to pairs of single siphons. Siphons that protrude above a solid boundary inhale fluid farther away from the orifice relative to siphons flush with the boundary. Additionally, the Reynolds number alters the axial distance that fluid is inhaled from the siphon orifice. As Re decreases from 100 to 1, outward viscous diffusion of suction-driven momentum increasingly dominates its inward advection, enhancing axial biases to inhale fluid more directionally. Organisms may alter morphology (siphon separation and extraction height) and inhalation dynamics (Reynolds number) at behavioral or evolutionary timescales to adapt to their surrounding environments. Our findings can inform principles for engineering applications and provide physical mechanisms that govern sensing enhancements from stereo inhalation.

Ultrasound-driven microbubbles are increasingly being investigated for both molecular imaging and therapeutic applications. To be effective, these bubbles must be brought into close proximity or direct contact with the target site. Leveraging the acoustic radiation force provides a powerful strategy to direct their movement. In this study, we examine the translational dynamics of a microbubble with unprecedented accuracy by simultaneously time-resolving both its radial and translational responses and by using optical tweezers to study the bubble in free space. Our experimental results show excellent agreement with theoretical predictions for the bubble sizes considered, provided the history drag force is included in the force balance. For the Reynolds numbers considered (up to $\text{Re}\approx 2$), the zero-Reynolds-number history force performs as well as its finite-Reynolds-number extension. Although nonspherical modes may arise at larger bubble expansions, they do not appear to significantly influence the bubble translational motion. A major finding is that the normalized transport distance of the bubble scales linearly with the normalized volumetric expansion during its oscillation, greatly simplifying the design and analysis of transport strategies. We also investigated bubble stability during transport and observed a marked increase in dissolution rate once a threshold in bubble expansion is exceeded. These insights can be leveraged to develop optimal transport strategies that balance both transport speed and bubble stability for targeted delivery applications.

The single droplet under shear is a foundational problem in fluid mechanics. In computational fluid dynamics (CFD), the two-dimensional (2D) problem offers advantages in both computational efficiency and relevance, yet it lacks a comprehensive theoretical treatment equivalent to that of the three-dimensional (3D) case. In this brief note, we present an analytical treatment of this problem beginning with a derivation of the Lamb solution for 2D Stokes flows and then applying it to obtain the flow field around a droplet in a purely extensional flow. Using these flow fields, expressions are obtained for the apparent viscosity, ${\mu }^{*}$, of a dilute 2D emulsion as well as a small deformation theory. We show that in the limit of both zero Reynolds number ($\text{Re}\to 0$) in which inertia is negligible and zero capillary number ($\text{Ca}\to 0$) in which surface tension prevents any droplet deformations, ${\mu }^{*}=\mu (1+f\left(\lambda \right)\varphi )+\mathcal{O}\left({\varphi }^2\right)$ with $f\left(\lambda \right)=(2\lambda +1)/(\lambda +1)$ where $\lambda$ is the ratio of the droplet viscosity to the matrix viscosity and $\varphi$ is the area fraction covered by the suspended phase. In addition, we show that in the capillarity-dominated regime ($\text{Ca}\ll 1$), the steady-state value, $D_T^{\infty }$, of the Taylor deformation parameter obeys $D_T^{\infty }=g\left(\lambda \right)\text{Ca}$, where Ca is the capillary number and $g\left(\lambda \right)=1$. This contrasts with the 3D case, where $g\left(\lambda \right)$ depends on $\lambda$. These results are then validated through direct numerical simulations (DNSs) of a single droplet at the center of a periodic square box undergoing simple shear. The DNS and theory are compared across a wide range of viscosity ratios ($0.01\le \lambda \le 100$) and area fractions ($0.002\le \varphi \le 0.125$) and they are found to agree asymptotically in the limit $\varphi \to 0$ for $\text{Ca}\ll 1/(\lambda +1)$. Our results provide a basic theoretical framework for interpreting 2D droplet simulations and provide clear benchmarks for CFD codes in 2D.

In this paper, we investigate the dynamics of Hele-Shaw flow in a multiply connected domain. We consider multiple fluid domains enclosed by a moving outer interface in a radial Hele-Shaw cell, with several inner interfaces separating these fluid regions. To compute the long-time evolution of interface morphologies, we develop a spectral-accurate boundary integral method and a nonstiff time updating scheme, together with a time adaptive scheme to speed up the computation. Our numerical results reveal that interface instabilities are strongly influenced by the initial configuration of fluid domains and physical parameters such as fluid viscosities. Notably, at early times, the fingering instability observed on the outer interface—triggered by the presence of inner interfaces—differs fundamentally from the classical perturbation-initiated growth in single-interface scenarios. Depending on their configuration, the inner interfaces can either promote or suppress the development of fingering on the outer boundary, offering a potential strategy for morphological control in practical applications. Motivated by the self-similar theory and the shape-control concept introduced in Li et al. [Phys. Rev. Lett. 102, 174501 (2009)], where self-similarity is only realized at large interface sizes under time-dependent flux, we demonstrate that one can preselect a self-similar limiting morphology and promote its formation at significantly smaller scales. This is achieved through a carefully designed multi-interface setup that promotes the desired symmetry while suppressing other unfavorable instabilities.

We examine flow and transport through an orifice in a flat wall separating semi-infinite atmospheres of two dissimilar gases. The analysis assumes steady conditions and order-unity values of the Schmidt number $\mathit{\text{Sc}}$ and Péclet number $\mathit{\text{Pe}}$, such that advection and diffusion contribute comparably to mass and momentum transport. Mixing between the two gases induces order-unity variations in viscosity and density, resulting in coupled concentration and velocity fields. The solution yields the mass transfer rates of both gases, expressed in terms of an appropriately defined Sherwood number, as well as the overpressure required to sustain the flow, all as functions of $\mathit{\text{Sc}}$ and $\mathit{\text{Pe}}$. An explicit analytical solution is obtained in the limit of small $\mathit{\text{Pe}}$, while numerical integration is used to describe flows with $\mathit{\text{Pe}}=O\left(1\right)$. The mixing of hydrogen and air is used as an illustrative example that serves to highlight the influence of large gas-molecular-weight differences on the flow structure and associated mixing rate, with additional selected results given for the case of hydrogen and water vapor.

In this work, we propose a phase-field-lattice-Boltzmann-based interfacial mass transfer model to better demonstrate the species transfer across the two-phase interface. In the model, the two-phase dynamics is governed by the Allen-Cahn equation, and the interfacial mass transfer behavior is described by a self-derived convection-diffusion equation, which shows a standard form with no source term compared with the available models. Then, we devise a multiple-relaxation-times (MRT) lattice Boltzmann scheme for their numerical solving. The simulations on typical interfacial mass transfer benchmarks indicate that the proposed phase-field-lattice-Boltzmann model shows superior interfacial mass transfer prediction performance when compared with the available models, particularly in the vicinity of the two-phase interface. The predicted concentration profile across the interface appears independent of the interface width. This model also shows the capability of predicting the interfacial mass transfer in large-density-ratio two-phase flows.

We investigate the mechanisms underlying the generation of broadband trailing-edge noise from an airfoil, focusing on the role of hydrodynamic structures with nonzero spanwise wavenumbers and the development of a corresponding reduced-order model. A wall-resolved compressible large-eddy simulation (LES) of a NACA0012 airfoil at 3° angle of attack, Reynolds number $\mathrm{Re}$ = 200 000, and Mach number $\mathrm{M}$ = 0.3 is performed. The simulation replicates the experimental setup of Demange et al. [AIAA Aviation Forum (2023)], including the tripping elements ensuring turbulent boundary layer development. The numerical domain has a large spanwise extent (43.75% of the chord) to allow for the investigation of large spanwise coherent structures. Validation against experimental data shows good agreement. The simulation results show that acoustic radiation from the trailing edge follows the scattering condition, whereby only hydrodynamic waves with spanwise wavenumbers lower than the acoustic wavenumber can generate propagative sound. Notably, the contribution from nonzero spanwise wavenumber modes becomes significant beyond the cut-on frequency at which the first nonzero spanwise acoustic mode becomes propagative. Through spectral proper orthogonal decomposition (SPOD), the associated flow structures are identified as streamwise-travelling wave packets convecting obliquely across the trailing edge. Reduced-order models based on acoustic-domain extended SPOD accurately reproduce the LES sound pressure levels within 2 dB, using only two modes per frequency–wavenumber pair. This compact representation paves the way for targeted noise-reduction strategies based on the control of the identified coherent structures.

We investigate the influence of expansion geometry on the flow field and turbulence structure in axisymmetric pipe flows through comparative analysis of abrupt (${90}^{\circ }$) and gradual (${45}^{\circ }$) area expansions with an area ratio of 2.56 at step-height Reynolds numbers of 25 000 and 35 000. Using refractive-index-matched stereo particle image velocimetry, we extract turbulence statistics with high spatial resolution. The gradual expansion consistently yields elevated turbulence levels, broader shear layers, enhanced Reynolds stress anisotropy, and stronger out-of-plane fluctuations. In contrast, the abrupt expansion generates a secondary vortex that disrupts the return flow, reducing shear layer interaction and turbulent kinetic energy (TKE) production. The governing mechanism is attributed to the geometry-induced modulation of the return flow. In the gradual case, the return flow is aligned with the sloped surface and impinges obliquely on the free-stream, generating a distributed region of high shear and sustained turbulence production leading to intensified TKE and anisotropy in the near-expansion region. These findings reconcile prior observations of increased pressure loss in sloped expansions and reveal the fundamental role of expansion slope in controlling turbulence generation and energy redistribution in separated flows. The observed trends suggest a generalizable mechanism relevant to a broader range of expansion angles and flow conditions.

A rotating stall occurring in the reversible pump turbine operating within the S-shaped region significantly impairs hydrodynamic stability, leading to severe torque oscillations and pressure pulsations. Currently, theoretical frameworks and quantitative predictions for stall inception are still lacking. This study develops a theoretical model for rotating stall based on small-disturbance theory. The model analyzes the resonance conditions and stability characteristics of disturbance waves by coupling internal flow perturbation dynamics with the external characteristics of the pump-turbine system. Key stall parameters, including the onset point, rotational speed, and the number of stall cells, are predicted based on the finite-difference-based numerical implementation. The results show that single-cell stall patterns are more dominant than two-cell patterns, with the former exhibiting a clear critical stability threshold. Complementarily, an unsteady flow simulation approach is adopted to capture transient flow behavior from runaway to low-flow conditions under four guide-vane openings. Pressure fluctuations in the vaneless area are analyzed using wavelet transform to identify the onset of rotating stall. Comparison between the numerical simulation and theoretical predictions confirms the model's accuracy and utility in predicting stall onset.

This study presents a spectral-fundamental solution (SFS) method which enables efficient simulation of large-scale nonlinear wave-body interactions. The SFS method combines spectral basis functions and fundamental solutions to achieve both global efficiency and local accuracy. Based on the linearity of the Laplace equation, it decomposes large-scale boundary-value problems into independent subproblems, enabling efficient full-domain computation. Numerical validations show that SFS achieves higher accuracy than the high-order spectral method for short, steep waves and outperforms the method of fundamental solutions in long-wave conditions. Applications to nonlinear ship waves in large-scale domains yield results in good agreement with experimental data, successfully capturing higher-order nonlinear effects. The simulations reveal the physical origins of distinct energy bands in the wave spectrogram and demonstrate how ship acceleration influences the ship-generated wake field. Furthermore, the simulations explain why high-speed ships exhibit wake angles that are narrower than classical predictions. Beyond ship waves, this efficient SFS framework can be extended to a wide range of unsteady wave-structure interaction problems in ocean engineering.

We show that floating ice blocks with asymmetric shapes can self-propel with significant speeds due to buoyancy-driven currents caused by melting. In water baths with temperatures between $10{}^{\circ }\mathrm{C}$ and $30{}^{\circ }\mathrm{C}$, model right-angle ice wedges are found to move in the direction opposite to the gravity current which descends along the longest inclined side. We describe the measured speed as a function of the length and angle of the inclined side, and the temperature of the bath in terms of a propulsion model which incorporates the cooling of the surrounding fluid by the melting of ice. The heat pulled from the surrounding liquid by the melting ice block generates a thermal convection flow, leading to momentum exchange and a net propulsion force. The translation velocity is explained by balancing the propulsion force by drag. We further show that the ice block moves robustly in a saltwater bath with ocean-like salinity and maintains the same direction of motion as in freshwater. A simplified model is further developed to describe the propulsion of asymmetric ice blocks in saltwater, incorporating the effects of rising meltwater and the sinking of the surrounding bath water due to cooling. For sufficiently large temperature, we find that the cooling-induced sinking flow generates a stronger force than the upward flow from the meltwater. Consequently, the net propulsion force is in the same direction and nearly the same magnitude as that observed in freshwater. These findings suggest that melting-driven propulsion may be relevant to the motion of icebergs in sufficiently warm oceanic environments.

In this article, the Green function for the Stokes flow in the interior, exterior, and annular regions bounded by cylindrical walls is derived as a function of the pole position and expressed in an invariant form at both the field and pole points. Specifically, the Green function, assuming no-slip boundary conditions, is obtained using a cylindrical harmonic expansion of the Stokes flow within the bitensorial formulation introduced in Procopio and Giona [Math. Eng. 5, 1 (2022)]. This formulation allows us to obtain higher-order singularities within the same domains and under the same boundary conditions, such as the confined couplet and stresslet, by simply differentiating the Green function at its pole. Moreover, the confined sourcelet (or point source) and its associated multipoles are derived from the Green function through a new method that enforces the reciprocal properties of the Stokes flow. The resulting singularities are then employed to address hydrodynamic problems involving active and passive colloids interacting with cylindrical and planar walls, such as sedimenting particles in an annular cylindrical region and between two parallel plane walls, and the attractive or repulsive hydrodynamic forces exerted by cylindrical boundaries on microswimmers.

We study the dimensionality of two-dimensional Kolmogorov flows over a wide range of Reynolds numbers and forcing wave numbers $k_f=\{2,4,8\}$ using two complementary approaches: convolutional autoencoders and a Kaplan-Yorke estimation based on Lyapunov analysis. As the Reynolds number increases, two distinct transitions are observed: the first corresponds to the destabilization of a periodic orbit, while the second marks the saturation of the large-scale motions. When expressed in terms of the forcing Reynolds number, these transitions occur at nearly the same value for all forcing wave numbers, suggesting a universal scaling with respect to the forcing scale. By filtering the data to retain only the large-scale range ($k<k_f$), we show that the dimensionality estimated by the autoencoders also saturates at the second transition, implying that once the large scales are fully developed, the subsequent increase in dynamical activity occurs predominantly at smaller scales. At higher Reynolds numbers, the Kaplan-Yorke dimension ceases to grow, revealing its limited sensitivity to the nonlinear interactions that dominate in this regime. Both the Kaplan-Yorke saturation dimension and the filtered large-scale dimensionalities exhibit a linear dependence on $k_f$, indicating that the number of active degrees of freedom scales with the forcing scale rather than with the total number of available Fourier modes.

This study explores the swimming behavior and hydrodynamics of an unconstrained, intermittently pitching foil using two-dimensional numerical simulations over a broad range of kinematic parameters. In contrast to continuous swimming, intermittent motion, characterized by alternating periods of active propulsion and passive gliding, achieves higher energy efficiency, but induces substantial trajectory deflection. The swimmer develops a nonzero lateral velocity, leading to a path deviation whose direction is sensitively dependent on the pitching amplitude and duty cycle. A sharp transition in the deflection angle is observed as the amplitude increases, with a reversal in the deflection direction occurring near a critical amplitude. Linear scaling between the flapping and propulsive Reynolds numbers is identified, underscoring the dominant influence of the Strouhal number on propulsive performance. In addition, the wake structures of the intermittent swimmer vary significantly with the flapping parameters. Different vortex modes emerge during the burst and coast phases, and their alignment plays a key role in determining the stability of the trajectory direction. These findings provide insights into the hydrodynamic principles of intermittent locomotion and its advantages in propulsion efficiency.

Peristalsis is the driving mechanism behind a broad array of biological and engineered flows. In peristaltic pumping, a wavelike contraction of the tube wall produces local changes in volume which induce flow. Net flow arises due to geometric nonlinearities in the momentum equation, which must be properly captured to compute the flow accurately. While most previous models focus on radius-imposed peristalsis, they often neglect longitudinal length changes—a natural consequence of radial contraction in elastic materials. In this paper, to capture a more accurate picture of peristaltic pumping, we calculate the flow in an elastic vessel undergoing contractions in the transverse and longitudinal directions simultaneously, keeping the geometric nonlinearities arising in the strain. A careful analysis requires us to study our fluid using the Lagrangian coordinates of the elastic tube. We perform analytic calculations of the flow characteristics by studying the fluid inside a fixed boundary with time-dependent metric. This mathematical manipulation works even for large-amplitude contractions, as we confirm by comparing our analytical results to COMSOL simulations. We demonstrate that transverse and longitudinal contractions induce instantaneous flows at the same order in wall strain but in opposite directions. We investigate the influence of the wall's Poisson ratio on the flow profile. Incompressible walls suppress flow by minimizing local volume changes, whereas auxetic walls enhance flow. For radius-imposed peristaltic waves, wall incompressibility reduces both reflux and particle trapping. In contrast, length-imposed waves typically generate backflow, although trapping can still occur at large amplitudes for some Poisson ratios. These results yield a more complete description of peristalsis in elastic media and offer a framework for studying contraction-induced flows more broadly.

The transport of ${\mathrm{CO}}_2$ across the air-water interface is central to physical oceanography and carbon sequestration. A comprehensive understanding of this process requires high-resolution diagnostics of diffusion, absorption, and reaction across a wide range of spatial and temporal scales. The current study presents a measurement method to quantify the ${\mathrm{CO}}_2$ distribution at the air-water interface. This method combines the advantages of tunable diode laser spectroscopy and rapid spatial beam scanning for in situ, nonintrusive, and spatiotemporally resolved measurement of the ${\mathrm{CO}}_2$ concentration distribution above the interface. The performance of this method was examined in a series of quasi-1D experiments in a miniature gas chamber, where the diffusion and absorption of ${\mathrm{CO}}_2$ into pure water and alkaline solutions of different pH values were continuously monitored. A time resolution of 5 ms and a spatial resolution of 1 mm were achieved. The observed gas-phase ${\mathrm{CO}}_2$ distribution evolution agreed with the classic one-dimensional diffusion model, which validated the accuracy of the current method. PH-dependent dynamics of interfacial ${\mathrm{CO}}_2$ concentration was also observed: the ${\mathrm{CO}}_2$ depletion rate is highly pH-sensitive at low pH and saturates at pH $\approx$ 10, revealing complex competition between the gas-phase and the liquid-phase transport processes. The current method's high spatial and temporal resolution holds promise for studying cross-interface gas transport under more complex flow conditions, in both field measurements and laboratory studies.