We investigate leaky dielectric droplet dynamics in a superposed electric field consisting of alternating and constant electric fields using both analytical and numerical approaches. In the present study, an analytical formulation is developed within the framework of small deformation theory to describe the mean and amplitude of the steady-state-time-periodic droplet deformation. In addition, a phase field interface tracking numerical method is employed to accurately capture the droplet interface evolution and to explore the parametric space governing the oscillatory response of the droplet subjected to the superposed electric field. The influence of the mixing ratio of the alternating and constant electric field components on both the mean deformation and oscillation amplitude is systematically examined. It is shown that the frequency of the mechanical response of the droplet is twice the frequency of the alternating electric field and corresponds to the base frequency of the superposed electric field. The droplet deformation exhibits a phase difference to the applied superposed electric field, and the effects of electrical relaxation and mechanical response on this phase difference are established. The dependence of mean droplet deformation on the mixing ratio is analyzed for low forcing frequencies and for frequencies at which surface charge polarization remains unaffected. The present work bridges droplet dynamics in alternating and constant electric fields and identifies conditions where superposed fields produce larger mean deformation and oscillation amplitude than a pure ac electric field.

This study utilized direct numerical simulation to investigate the bypass transition over a flat plate featuring isotropic, protruding rough surface and subjected to a favorable-to-adverse pressure gradient. The rough surface was positioned at one of two locations, upstream of or in proximity to the separation point, while the inlet free-stream turbulence (FST) was characterized by two distinct intensities and fundamental frequencies. Through proper orthogonal decomposition, dynamic mode decomposition, local stability, and transient growth analyses, the effects of rough surfaces and inlet FST with varying intensities and fundamental frequencies on the bypass transition process and its disturbance growth mechanism were elucidated. The results indicate that the intensity and fundamental frequency of the inlet FST, along with the rough surface position, have negligible effects on the quasistreamwise vortices and velocity streak structures in the transition region. The rough surface placed upstream of the separation point interacts with the inlet FST to generate a resonant mode. For an inlet FST with a turbulence intensity of 3% and a fundamental frequency of $2\pi /7$, this interaction produces a novel resonant mode distinguished by a more elongated wave packet and an upstream-shifted resonant onset. This new mode comprises numerous high-frequency components that make a significant collective contribution to the system's nonlinear dynamics. Conversely, a rough surface positioned near the separation point markedly amplifies the inlet FST. The second harmonic of the inlet FST demonstrates insensitivity to the rough surface's position, the FST intensity, and its fundamental frequency. A lower fundamental frequency of the inlet FST results in increased nonlinear structural strength within its third and fourth harmonics, an effect that is further augmented when the rough surface is located near the separation point. The novel resonant mode creates extensive regions of linear stability within the transition zone. Within these regions, disturbances at multiple frequencies undergo optimal transient growth, and the spatial distribution of these optimal disturbances mirrors the fibrous morphology of the corresponding energy structure. Regarding the transient growth of wave disturbances in general resonant modes, a higher fundamental frequency yields the maximum energy gain, albeit within the most spatially confined optimal disturbance distribution. Furthermore, an increase in the streamwise wave number of the travelling wave also serves to enhance the gain.

The unlike-doublet impinging jets atomization behaviors in hypergolic liquid rocket engines are crucial for reliable ignition and combustion efficiency, while their flow mechanisms under different jets inertia disparity are not well understood. Through high-fidelity volume of fluid (VoF) simulations with intraliquid species transport, this study comprehensively quantifies the inertia disparity (characterized by diameter and momentum ratios) influence on atomization characteristics. Results show that the elevated inertia disparity reduces the spray angle and shortens the impinging liquid sheet breakup length. The primary breakup induced Sauter mean diameter distribution becomes uniform and the mixing efficiency is reduced with higher impinging jest inertia disparity. Phenomena in terms of deflection angle collapse near the central axis and mutual penetration of jets are observed at high inertia disparity conditions, causing a special trimodal flow rate distribution. The pair vortices and rotated bubbles are found after unlike jets impingement. To interpret the numerical results, further flow topology and structure analysis are conducted and it reveals that inertia disparity initiates Kelvin-Helmholtz type shear instabilities at the impingement point of jets. These shear effects then evolve into vortex structures that propagate radially from the central axis, entraining liquid sheets and generating collapse.

A fundamental relation in Lagrangian Kolmogorov theory is concerned with inertial range scaling of the second-order velocity structure function over intermediate time lags at sufficiently high Reynolds numbers. Significant theoretical support for asymptotic constancy of the scaling constant $\left(C_0\right)$ is known, but limitations in the range of time scales accessible in direct numerical simulation make unambiguous testing of the scaling challenging. In this paper, direct numerical simulations of forced isotropic turbulence at Taylor-scale Reynolds numbers between 140 and 1300 are used to improve understanding in this subject, including scaling at time lags shorter and longer than those associated with inertial-range-like behavior. Uncertainties arising from modest simulation time spans in the high Reynolds number data are addressed by expressing the velocity structure function in terms of the acceleration autocorrelation, which suggests that $C_0$ may be sensitive to the effects of Lagrangian intermittency but does not rule out asymptotic constancy at Reynolds numbers beyond those that may be feasible in simulations in the foreseeable future. The Lagrangian velocity increment is examined further from a spatial-temporal perspective as a combination of convective (spatial) and local (temporal) contributions, which are subject to a strong but incomplete mutual cancellation dependent on Reynolds number and time lag. The convective contribution is strongly influenced by the particle displacement, which is driven by large-scale dynamics and can thus grow into inertial range dimensions in space within just a few Kolmogorov time scales, without fully satisfying classical Lagrangian inertial-range requirements. An overall conclusion in this work is that both the limited range of time scales (narrower than that for length scales) and the effects of particle displacements have significant roles in the observed behavior of the second-order Lagrangian velocity structure function.

The generative mechanism of the pressure field is fundamental in turbulence research and flow control, especially when subject to turbulent separation at high Reynolds numbers. To this end, we propose a physics-based framework—momentum decomposition of the pressure field—which uses the momentum equations to decompose the spatial pressure gradient into quantifiable momentum budgets. Each momentum budget corresponds to a distinct physical mechanism, enabling a rigorous decomposition and quantitative evaluation of the inherent mechanisms governing pressure generation. Incorporating results of a direct numerical simulation of laminar cylinder flow, this method is first demonstrated, after which the three-dimensional large eddy simulation results of a complex turbulent bluff body wake at ${\text{Re}}_D=1.88\times {10}^5$ are analyzed with a comparison of flow control. In the near wake, the bulk of low pressure originates from the streamwise convection of the centripetal flow outside the wake, which manifests as a streamline curvature effect from the term $\overline{u}\partial \overline{v}/\partial x$, while the pressure variation inside the wake receives main contributions from Reynolds stresses. Under flow control, due to the streamline curvature modification near the base edge, the pulsed jet produces favorable pressure gradients from the mean flow term $\overline{u}\partial \overline{v}/\partial x$ contributing to the bulk of base-pressure recovery. Overall, the proposed framework provides a fundamental flow diagnostic tool and a rigorous foundation for designing and analyzing flow control strategies, since pressure control can be rationally linked to the momentum budgets manipulation, generally applicable to flow regimes governed by the Navier-Stokes equations.

Direct numerical simulations are performed to investigate the countergradient transport of heat and momentum in homogeneous shear turbulence under stable thermal stratification. The simulations are conducted at a Reynolds number of $\mathrm{Re}=5000$, with Richardson numbers set to 0, 0.1, and 0.2. The clustering method is employed to analyze $Q1$ and $Q3$ structures, which drive the countergradient transport in the quadrant classification of vertical heat flux and momentum. The structural characteristics and spatial distributions of these structures are systematically evaluated and compared with previous research findings. The results reveal that most countergradient transport originates from structures larger than the Corrsin scale, and their volumetric contribution increases with stratification intensity. Furthermore, the paired $Q1$ and $Q3$ structures are characterized by analogous spatial patterns and exhibit a strong association with vortical structures. Specifically, the countergradient transport of heat is driven by the interaction between the cold and hot fluid parcels or the vortex-induced rotation, whereas the countergradient transport of momentum is solely attributed to the vortex-induced rotation. These findings provide improved insight into the dynamics of countergradient transport under stable thermal stratification and highlight the critical role of vortical structures in driving these processes.

Droplets, solid particles, and gas bubbles in unsteady flows experience the Basset–Boussinesq history force (BBH) in addition to steady viscous drag, added mass, and buoyancy. Although physically relevant, the BBH term is often neglected because its inclusion is analytically and numerically demanding. To assess when this approximation fails, we revisit unsteady Stokes flows around spherical droplets of finite viscosity and derive, from first principles, the velocity fields and hydrodynamic forces, including both the classical rigid-particle limit and the free-slip (zero-viscosity) bubble limit. The resulting expressions also encompass cases with time-dependent bubble radii. We further illustrate how the BBH force arises from transient, diffusion-driven vortex structures around accelerating particles. Applying these results to droplets or particles in horizontally shaken liquids (periodically accelerated flows), we find that in the transition regime between the quasisteady Stokes limit and the inertia-dominated regime, BBH can lead to a reduction of the droplet deflection amplitude by more than 60% compared to predictions that neglect memory effects. We also derive a characteristic scaling of the displacement amplitude in the low-frequency limit, providing an unambiguous, experimentally verifiable signature of the BBH. For light particles and gas bubbles, the BBH contribution becomes more significant (relative to the other hydrodynamic forces) compared to that of heavy particles, such as droplets in air.

We investigate the ejection of satellite bubbles during the coalescence of two air bubbles in water. Using magnetic levitation we suspend the bubbles, with diameters in the range 3–15 mm, in a stable, neutrally buoyant state, free from mechanical constraints. Our experiments reveal the simultaneous ejection of twin satellite bubbles from the poles of the bubble formed from the coalescence of equal-sized precursors. More generally, we find that the number and size of the ejected satellites are dependent on the initial size ratio of the precursor bubble pair. Numerical simulations, which agree well with our experiments, show that satellite production is governed by the combined effect of two distinct processes: the arrival of a capillary wave crest at a pole and the rapid retraction of that polar region. We propose a timing model that successfully predicts the range of size ratios for which single, double, or no satellites are formed. Our analysis also offers insight into the absence of satellite ejection in similarly sized liquid drop coalescence. Furthermore, we report the experimental observation of toroidal bubble ejection from precursor bubbles with approximately 2:1 diameter ratios, and we show that the formation of these toroidal bubbles is also governed by our timing model.

Hydrodynamic flows and swimming trajectories of microswimmers are strongly influenced by nearby surfaces and geometric confinements. The far-field hydrodynamic flow of a microswimmer in bulk can be effectively represented by a force dipole due to the swimmer's propulsion and drag forces, where the source dipole due to body-size effect is subdominant. In contrast, the source dipole becomes the dominant flow contribution when the microswimmer is confined strongly in two dimensions, irrespective of the propulsion mechanism of the swimmer. Recent experimental works demonstrated that this understanding is not completely correct. For microswimmers under slightly weaker confinement, its flow field has a strong dependence on the spatial arrangement of the swimmer's propulsion and drag forces as well as the swimmer's geometry. In this case, the modified far-field hydrodynamic flows of the swimmer should be approximated by placing Stokeslets and source dipoles at proper positions of the swimmer. Here we employ this flow field modification and investigate how the spatial arrangement of Stokeslets and source dipoles influences the dynamics of a microswimmer in a confined liquid film. We observe versatile swimming trajectories, including boundary collision, boundary sliding, centerline sliding, amplified oscillation, and damped oscillation, depending on the relative strengths and positions of the Stokeslets and source dipoles at different confinement heights. These results highlight the enriched dynamics of microswimmers due to the diversity of flow fields in confined geometries.

An antibubble is an object in which a liquid core is separated from a surrounding liquid by a thin spherical gas shell. Such structures can be generated when a droplet crosses a soap film with sufficient kinetic energy to become wrapped by the film, which then merges upon contact with a liquid bath. When droplets fall through multiple soap films, multilayer antibubbles can be generated. In this paper, the conditions required to successfully generate monolayer and multilayer packed droplets are studied in order to optimize the formation of monolayer and multilayer antibubbles. In particular, the geometrical factors and the composition of the liquid that makes up both the droplets and the soap films are discussed. The stability of antibubbles generated using this method is also investigated as a case study. The robust formation of monolayer and multilayer antibubbles is a key to open opportunities in drug delivery without the use of either oil or solid compounds. Moreover, this method allows for the production of monodisperse, millimetric, and multilayered antibubbles.

The problem of scaling in isotropic magnetohydrodynamic (MHD) turbulence has remained unresolved, with competing predictions of $k^{-5/3}$ (Kolmogorov) and $k^{-3/2}$ (Iroshnikov-Kraichnan) scalings. In this paper, we address this long-standing controversy using high-resolution numerical simulations on ${8192}^2$ and ${1536}^3$ grids. We show that the total energy and cross-helicity spectra are closer to $k^{-5/3}$ than $k^{-3/2}$. The fluxes and structure functions of the total energy and cross helicity also demonstrate robust support for Kolmogorov scaling. The magnetic energy shows the $k^{-5/3}$ spectrum, but the kinetic energy exhibits the $k^{-3/2}$ spectrum; the latter spectrum is due to the energy transfers from the magnetic field to the velocity field.

The two leading models of isotropic magnetohydrodynamic (MHD) turbulence have competing predictions: $k^{-5/3}$ (Kolmogorov) and $k^{-3/2}$ (Iroshnikov-Kraichnan) scalings. This paper identifies the valid MHD turbulence model using high-resolution numerical simulations and diagnostics—structure functions, intermittency exponents, and energy spectra and fluxes of imbalanced MHD. The energy spectra of our forced MHD simulations on the ${8192}^2, {4096}^2, {1024}^3$, and ${512}^3$ grids support Kolmogorov's $k^{-5/3}$ spectrum over Iroshnikov-Kraichnan's $k^{-3/2}$ spectrum, but the difference in the spectral exponents is small. However, the numerically computed third-order structure functions and intermittency exponents support Kolmogorov scaling in both two and three dimensions. Also, the energy fluxes of the imbalanced MHD follow the predictions of Kolmogorov scaling. These results would help in a better modeling of solar wind, solar corona, and dynamos.

Flows of viscoelastic fluids in narrow nonuniform geometries, such as contraction, expansion, and contraction-expansion configurations, are ubiquitous in various engineering applications and physiological flow systems. For such flows, one of the key interests lies in understanding how fluid viscoelasticity affects the dependence of the pressure drop on the flow rate, which remains not fully understood compared to Newtonian flows. In this work, we analyze the creeping flow of the Oldroyd-B fluid in slowly varying contraction-expansion channels, commonly referred to as constrictions. Unlike most previous theoretical studies that focus on contracting channels, we consider instead a constriction geometry and present a theoretical model for calculating the elastic stresses and flow rate-pressure drop relation at low and high Deborah ($\text{De}$) numbers. We apply lubrication theory in orthogonal curvilinear coordinates and consider the ultradilute limit, in which the velocity approximates a parabolic and Newtonian profile. This results in a one-way coupling between the velocity and elastic stresses, allowing us to derive closed-form expressions for the elastic stresses and pressure drop for arbitrary values of the Deborah number. We validate our theoretical predictions with two-dimensional numerical simulations and find excellent agreement. We identify the physical mechanisms governing the pressure drop behavior and compare our results for the slowly varying constriction with previous predictions for the contraction. We reveal that, at low Deborah numbers, the pressure drop in the constriction monotonically decreases with $\text{De}$, similar to the contraction geometry. However, at high Deborah numbers, in contrast to a linear decrease for the contraction, the pressure drop across the constriction reaches a plateau due to the vanishing contribution of elastic normal stresses, leaving elastic shear stresses as the sole driver of the reduction. Furthermore, we elucidate the spatial relaxation of elastic stresses and pressure gradient in the exit channel following both constriction and contraction geometries, showing that the relaxation length is significantly shorter in the case of a constriction.

Optical images of transparent three-dimensional objects can be different from a replica of the object's cross section in the image plane due to refraction at the surface or in the body of the object. Simulations of the object's image are thus needed for the visualization and validation of physical models. We report ray-tracing image simulations that achieved high physical fidelity, reproducing optical behaviors and image features not rendered in previous studies. We replicated brightfield microscopy images of drops with complex shapes and images of pressure and shock waves traveling inside them. For high physical fidelity, the simulations must replicate the spatial and angular distribution of illumination rays, and both the experiment and the simulation must be designed for accurate optical modeling. The simulations are highly sensitive to the properties of the drops and can be used to diagnose and refine fluid dynamics models. The simulated images can also be optimized to extract multiple 3D properties from experimental images. Compared to specialized single-shot 3D imaging methods, this approach has the advantage that it preserves the experimental simplicity, the high resolution, and the visual interpretability characteristic to basic optical imaging. The techniques introduced here are directly applicable to optical microscopy, so they can be used in other fields, such as microfluidics and biology, to expand the type and the accuracy of three-dimensional information that can be extracted from basic optical images.

Flag models have recently emerged as promising flexible vortex generators for enhancing heat transfer in laminar channel flows; however, systematic comparative studies of their thermohydraulic performance remain limited. In this work, a comprehensive numerical investigation is conducted on three representative flag configurations—the standard flag model (SFM), the inverted flag model (IFM), and the wall-mounted flag model (WFM)—to examine their heat transfer enhancement characteristics over a wide range of bending stiffnesses ($K_b^{*}$), channel Reynolds numbers (Re), and vertical placements ($h^{*}$). The comparative analysis reveals that the three models enhance heat transfer through distinct vortex-generation mechanisms. The SFM is dominated by wake-induced mixing, the IFM by leading-edge-generated coherent vortices with deep core penetration, and the WFM by persistently wall-attached vortical motions that strongly interact with the thermal boundary layer. The bending stiffness $K_b^{*}$ determines whether unsteady flapping dynamics can be activated, while Re and $h^{*}$ further regulate the coherence and transport effectiveness of the induced vortical structures once such dynamics are established. For all three configurations, the heat transfer efficiency increases with Re; however, the location of the high-efficiency regime in the $K_b^{*}\text{−}\mathrm{Re}$ parameter space is strongly configuration dependent. Among the three models, the IFM achieves the highest peak heat transfer efficiency with its high-efficiency region occurring at intermediate $K_b^{*}$ values and high Re. Nevertheless, this superior performance is confined to a relatively narrow operating window and exhibits pronounced sensitivity to $h^{*}$. In contrast, the WFM exhibits a broader and more robust high-efficiency regime at comparatively larger bending stiffness under high-Re conditions, whereas the SFM provides more modest enhancement with weaker sensitivity to parameter variations. Overall, these results clarify how flag-induced dynamics and vortex organization govern thermal transport in laminar channel flows.

The aim of the present study is to perform a comprehensive theoretical and numerical investigation of pressure and flow waves in compliant arteries in order to understand their physiological implications for detecting vascular stiffness. A model of a compliant artery, consisting of a viscoelastic tube containing a Jeffreys-type non-Newtonian fluid and surrounded by external tissue, is studied. The purpose of the work is to understand the coupled influence of fluid and arterial wall viscoelasticity on wave dynamics, flow impedance, and energy dissipation in a compliant artery. The arterial wall deformation is modeled using the Green-Rivlin constitutive law, which accounts for memory kernel and nonlinear viscoelastic effects. With regard to their coupling, the governing equations for the radial and longitudinal motion of an arterial wall are derived separately. The analytical expressions for flow distribution, impedance to flow, and energy estimate are obtained in terms of the frequency functions and the system parameters. A two-dimensional numerical experiment is presented to illustrate the energy distribution, and it utilizes physiological arterial parameters to assess the frequency-dependent impedance and energy dissipation behavior within the fluid-structure model. The obtained results highlight the importance of including both the viscoelasticity of fluid and the arterial wall in the modeling of fluid-structure interaction in arteries. Our results suggest that increasing the vessel radius and stretch ratio enhances damping and dissipates energy more effectively at lower frequencies, while higher stiffness and relaxation times amplify oscillations. Compared to the Newtonian and Maxwell models, the Jeffreys model more accurately captures physiological energy dissipation and dispersive wave behavior in the cardiovascular system for diagnosis and treatment. This study presents a comprehensive model for detailed profiling of vascular mechanics that captures the coupled influence of fluid and arterial wall viscoelasticity, the distribution and dissipation of the energy delivered to arteries, wave impedance, and system stability, with applications in basic future clinical diagnosis.

A phenomenological model for the heat transfer coefficient in turbulent pipe flow of power-law (PL) fluids is developed. The analysis employs a two-layer approach, separating the flow into a viscosity-dominated inner region and a turbulence-dominated outer region. By leveraging a scaling framework rooted in Kolmogorov's theory of turbulence, we derive a semi-empirical heat transfer correlation analogous to the Prandtl-Taylor analogy for Newtonian fluids. A key contribution is the introduction of a new dimensionless group, the power-law Prandtl number (${\mathrm{Pr}}_{PL}$), defined to be independent of the Reynolds number, thereby allowing for a more fundamental characterization of heat transfer in these systems. The model incorporates a single calibration function, $c_h\left(n\right)$, which depends on the power-law index $n$ and captures the influence of non-Newtonian rheology on the sublayer-to-core thermal resistance partitioning. This function is calibrated using established literature data for Carbopol solutions. The proposed correlation demonstrates excellent agreement with experimental results across a wide range of Reynolds and Prandtl numbers, achieving a normalized root-mean-square error of 1.14% with the polynomial calibration and exhibiting superior predictive accuracy compared to classical models.

Ionic liquids (ILs), characterized by high electrical conductivity, negligible vapor pressure, and wide physicochemical tunability, hold promise for applications in cooling, coating, and energy systems where droplet impact is critical. We experimentally investigate the effect of an external electric field, $\mathbf{E}$ (0–10 kV/cm), oriented parallel to the impact velocity, on the deformation and impact dynamics of high-conductivity IL droplets across a broad range of Weber $(31\le \mathrm{We}\le 629)$ and Ohnesorge $(0.11\le \mathrm{Oh}\le 1.19)$ numbers. The results show that IL droplets undergo pronounced prolate deformation driven by field-induced Maxwell stresses, with the deformation magnitude increasing with electric field strength and travel time but decreasing with surface tension and viscosity. Despite substantial preimpact deformation $(0\le \mathcal{D}\le 0.62)$, the impact outcomes—spreading and splashing—remain largely unchanged. The maximum spreading factor $\left({\beta }_{\text{max}}\right)$ and splashing threshold exhibit negligible changes compared with spherical droplets. No field-induced jetting or breakup is observed, in contrast to previous findings for water droplets under $\mathbf{E}$. The data for ${\beta }_{\text{max}}$ collapse onto the semiempirical scaling ${\beta }_{\text{max}}=0.61{(23.3+\mathrm{We}/\mathrm{Oh})}^{1/6}$, derived from a simplified energy conservation model in which the initial kinetic energy is dissipated by viscous losses. These findings demonstrate that while electric fields strongly alter droplet morphology in flight, the high viscosity of ionic liquids suppresses electrostatic coupling during impact.

Rare and extreme events in turbulent flows play a critical role in transport, mixing, and transition, yet they are notoriously difficult to capture experimentally. Here we report, to our knowledge, the first direct experimental detection of an upstream-directed jet burst in a backward-facing-step (BFS) flow at ${\text{Re}}_h=2100$, using long-duration live optical flow velocimetry (L-OFV). Continuous monitoring over 1.5 h enabled a data-driven definition of extremes as rare velocity probes excursions deep into the observed distribution's tails; in practice, large negative events ($u:Z<-6$, $v:Z<-5$ at $(x,y)=(2h,h/2)$, where $\left|Z\right|\gg 0$ stands for large deviations from the mean value) triggered the live capture of surrounding velocity fields. The recording is triggered when the probes surpass the defined threshold, using live analysis of the velocity fields. The detected event features a jetlike intrusion into the recirculation region initiated by the collapse of a merged Kelvin–Helmholtz vortex and sustained by counterrotating vortices and is accompanied with heavy-tailed probe statistics and simultaneous amplification of fluctuating kinetic energy and enstrophy. While a single event was recorded, underscoring its rarity, the results establish L-OFV as a viable platform for rare-event detection in separated shear layers and document a previously unreported mechanism of upstream jet bursting in BFS flow.