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.

In this study, we experimentally investigate the rotational dynamics of flexible fibers in homogeneous and isotropic turbulence. Three high-speed cameras are used to determine and track the three-dimensional conformation of the fibers. The rotational dynamics is characterized here by both the rotation of the end-to-end vector and the rotation of the eigenframe of the deformed fibers. We observe an increase of the rotation rate when the flexibility of the fiber is increased. To model this increase, we propose a scaling law for the evolution of the mean curvature, which depends on the mechanical properties of the fiber and the properties of turbulence. This model extends the one proposed by C. Brouzet et al. [Phys. Rev. Fluids 6, 024601 (2021)] for relatively stiff fibers. The evolution of the curvature is then used to model the mean shape of a flexible fiber, which determines its rotation rate. Our model is in very good agreement with our experimental measurements as long as the mean conformation can be considered as planar—so for moderately flexible fibers.

There has been much recent interest in the chiral motion of achiral particles that sediment in a viscous fluid in a regime where inertial effects can be neglected. This occurs in a broad range of applications such as those involving biological objects like algae, ultrathin graphene flakes, or colloidal suspensions. It is known that particles with two planes of symmetry can be categorized as “settlers,” “drifters,” or “flutterers,” where the latter sediment along chiral trajectories despite their achiral shapes. Previous work investigated the sedimentation of circular disks bent into a U-shape and identified them as “flutterers.” In this work we analyze the change in behavior of such particles when we break one of their symmetries by pinching the disks isometrically along their axis, a shape change that can arise during the sedimentation of thin elastic sheets. The “fluttering” behavior is found to be robust to such shape changes, with the trajectories now evolving toward helical paths. However, the behavior changes when the degree of pinching becomes too strong, at which point the particles become “drifters” which sediment steadily without rotation. We establish criteria for the transition between the two types of behavior and confirm our predictions in experiments. Finally, we discuss the implications of our observations for the dispersion of dilute suspensions made of such particles.

The motion of a water droplet on a single vertical sugar fiber is analyzed. The fiber is positioned vertically, with the droplet placed at its pending end. If the capillary force is able to balance the weight of the droplet, the droplet remains suspended at the fiber extremity. As sugar is dissolved inside the droplet, the fiber eventually breaks. Subsequently, the droplet may fall down carrying a portion of the not yet dissolved fiber, or, more interestingly, the droplet may be propelled upwards, remaining attached to the fiber. The process can then restart. The upward jump (or motion) of the droplet is caused by the capillary force exerted by the droplet on the fiber. When the fiber breaks (or becomes weakened) due to dissolution, this capillary force is no longer balanced, causing the droplet to jump upward. A phase diagram is constructed based on the droplet volume and the fiber diameter. A model has been built to assess the critical droplet volume for a given fiber diameter, above which the droplet falls. Below this volume, the droplet can move upwards along the fiber.

In this paper, we propose a microflow velocimetry based on particle tracking with the aid of optical trapping of tracers, namely, optically trapped particle tracking velocimetry (ot-PTV). The ot-PTV has two phases: a trap phase, in which individual tracers are trapped by an optical force and held at a measurement position; and a release phase, in which the tracer is released and advected by the fluid flow, without interference from the optical force. The released tracer is subsequently trapped again by the optical force. By repeating the set of trap and release phases, we can accumulate the sequential images of the tracer that have the same initial position. Although the data acquisition rate of ot-PTV is lower than that of standard micro-resolution particle image velocimetry (μPIV) due to the nature of pointwise measurement, an advantage of ot-PTV is that the measurement positions can be chosen by the experimenter. That is, even when tracers are scarce in a test section because of some external effects and/or the small size of the test section—ill-suited cases for μPIV since the experimenter has to wait for tracers to diffuse into the test section (i.e., diffusion-limited situation)—ot-PTV remains efficient. The concept of ot-PTV is validated using a benchmark experiment, i.e., a pressure-driven flow in a straight microchannel with a square cross section. An application to thermally induced microflows is also demonstrated, where tracers can be scarce in a test section due to thermophoresis.

In a recent paper [Peng et al., Phys. Rev. Fluids 9, 083701 (2024)], the phenomenon of electric charge cap formation on the surface of a leaky dielectric droplet in an electric field was identified. The surface charge caps, which form at the droplet poles when charge relaxation is faster inside the droplet phase than in the ambient, are stagnant and perfectly conducting. Using asymptotic methods, a nonstandard, inhomogeneous, mixed boundary value problem satisfied by the droplet field potential in this high electric Reynolds number limit was derived by Peng et al. and then solved numerically. The present article gives an exact solution to that mixed boundary value problem. This solution resolves fully the square-root singularities in the potential at the edges of the electric caps that can cause convergence difficulties in numerical schemes. Knowledge of the solution in analytical form is valuable because it feeds into a nonlinear problem for the coupled hydrodynamics. Moreover, the theoretical approach here is potentially extendible to finding the fields associated with electric charge cap formation in other settings.

We present a methodology that combines Mach-Zehnder interferometry, a custom relative humidity (RH) controlled chamber, and a confined two-dimensional droplet geometry to enable precise investigations of drying of complex fluids and the associated transport mechanisms. This approach is applied to a model binary mixture, water-glycerol, the concentration-dependent thermodynamic and transport properties of which are relatively well documented. High-resolution interferometric imaging ($6\mu \mathrm{m}{\mathrm{pixel}}^{-1}$, 1 $\mathrm{frame}{\mathrm{s}}^{-1}$) allows simultaneous measurement of drying kinetics and internal concentration fields with $\pm 0.5\%$ accuracy, characterized here over a wide range of RH (25–95%), and thus Péclet numbers. The experimental results closely match a quasisteady, isothermal model of vapor-diffusion-controlled evaporation coupled to diffusion within the droplet. These data enable extraction of both the concentration-dependent mutual diffusion coefficient $D\left(\phi \right)$ and the water chemical activity $a_w\left(\phi \right)$ over almost the entire range of glycerol volume fraction $\phi$, even from a single low-RH experiment. While $a_w\left(\phi \right)$ agrees well with literature values, our measurements yield a consistent fit for $D\left(\phi \right)$. Complementary experiments with fluorescence microscopy confirm that buoyancy-driven convection, although present, remains negligible, so that mass diffusion dominates solute transport in this confined geometry. The overall agreement validates the methodology, demonstrating its robustness as a quantitative framework for probing drying dynamics and transport in complex fluids, with broad applicability to controlled evaporation studies.

Worthington jets ejected after the impact of a solid or liquid object on a liquid surface have extensive applications in natural, industrial, and scientific contexts. Here, we present a combined experimental and theoretical investigation of the jet generated by sphere impact with no cavity formed. Experiments identify three distinct pinch-off modes, whose regime boundaries are independent of sphere wettability and density, and are theoretically determined by the Rayleigh–Plateau instability. From momentum and energy conservation, a new scaling law is derived for the dimensionless maximum jet height and agrees remarkably well with experiments across various impact conditions, thus validating its universal character and clarifying its dependence on the Froude, Weber, and Reynolds numbers, as well as the density ratio. Coupling self-similar solutions with a kinematic condition at the jet tip yields good predictions for the evolution of jet height and shape, revealing gravity-dominated jet dynamics, with a modification from surface tension that is most pronounced without pinch-off. These findings demonstrate that the upward jet is sustained by the collision of converging flow behind the sphere, a generation mechanism fundamentally distinct from the cavity collapsing forced case.

We study laser-induced bubble dynamics near the free surface of a viscoplastic fluid through controlled experiments, examining the effects of stand-off distance ($h$), laser energy ($E$), and fluid rheology on bubble behavior. Four distinct flow regimes are identified: swelling, trapped, bullet jet, and vapor jet. When the stand-off distance is much smaller than the maximum bubble radius ($h/R_0<0.1$), no bubble forms and only an open cavity is generated, defining the swelling regime. In the intermediate range ($0.1<h/R_0<0.7$), transitions are governed by a modified Reynolds number (${\mathrm{Re}}^{*}$); bullet jets form when ${\mathrm{Re}}^{*}>150$, while ${\mathrm{Re}}^{*}\lesssim 150$ leads to a trapped regime dominated by viscoplastic forces. For $h/R_0\gtrsim 0.7$, cavitation consistently produces vapor jets. A simplified force-balance-based model is proposed to predict the temporal evolution of bubble penetration depth, showing reasonable agreement with experiments in the trapped and bullet jet regimes.

We investigate the nonlinear axisymmetric shape oscillations of inviscid droplets, focusing on the modal coupling between different oscillation modes. The research builds upon the geometrically exact nonlinear theory for droplet shape oscillations by Plümacher et al. [Phys. Fluids 32, 067104 (2020)], which allows for large deformations and superimposed initial deformations. The theory rests on the potential flow assumption and the usual momentum jump condition at the droplet surface including the surface tension. Using the unified transform method of A. S. Fokas [Proc. R. Soc. London Ser. A 453, 1411 (1997)], the governing equations are transformed into a system of integrodifferential equations defined on a unit sphere. These equations are then solved numerically with a Galerkin method that uses spherical harmonics and exhibits overall spectral convergence. The frequency shift and the extended time spent in the prolate state within an oscillation period are analyzed for different initial deformation modes and show good agreement with existing literature. The results demonstrate that for large initial deformations, the modal coupling significantly influences the oscillation dynamics, particularly in the interaction between even and odd modes. To study modal coupling in detail, superimposed initial deformations are investigated in which a large-amplitude even mode is superimposed with various individual small-amplitude odd modes. It is shown that the initially excited large-amplitude even mode remains nearly unaffected by the superimposed small-amplitude odd modes. The initially superimposed small-amplitude odd mode, however, is altered by the large-amplitude even mode without being significantly amplified or damped. This nonlinear modal coupling is not present in single even initial deformation modes, where it is shown that an even initial deformation mode cannot excite odd modes.

The flow of a hyperpycnal river plume into a lake with a sloping bed and without any lateral confinement is a common occurrence in nature. A characteristic example of such geophysical fluid flow system is the inflow of river Rhone in Llake Geneva. In this work, we study the near-field plunging dynamics of an unconfined hyperpycnal plume at laboratory scale, over an idealized bed, with a slope that is similar to the one of the natural system. The study is based on large-eddy simulation of the Navier-Stokes equations in the Boussinesq approximation. We focus on the effect of varying the inflow conditions and in particular the densimetric Froude number, ${\mathrm{Fr}}_d$, which is the nondimensional parameter describing the ratio between inertial and buoyancy forces acting on the plume. Three simulations were performed at different values of ${\mathrm{Fr}}_d$, within the range encountered in the natural system. Similarly to previous works, we are able to identify lateral slumping as the main mechanism that leads to plunging of the dense river water and the formation of the characteristic triangular pattern at the lake surface. We are able to further identify the formation of a wake downstream of the vertex plunge point, due to the transport of mixed river-ambient water from the converging mixing layers across the plunge curve on both sides of the plume. The extent of both the wake and the overall plunge region increases significantly with increase of ${\mathrm{Fr}}_d$. This mechanism can be associated to the changes of the surface patterns of the plume observed in the field. In addition, we compute the total entrainment, $E$, of ambient lake water as the streamwise increase of volumetric flow rate downstream of the river mouth. $E$ is found to increase with distance from the mouth, as the plume continuously entrains ambient lake water. We find that for the same distance from the river mouth, $E$ is larger for lower ${\mathrm{Fr}}_d$. This increase of $E$ with decreasing ${\mathrm{Fr}}_d$ is attributed to two mechanisms. First, in the plunge region, lower ${\mathrm{Fr}}_d$ leads to greater lateral spread and therefore increased interface area between plume and ambient water. Second, in the underflow region, lower ${\mathrm{Fr}}_d$ results in higher mean streamwise plume velocity, enhancing entrainment intensity.

Research studies conducted over the years have demonstrated that wall suction is a highly effective laminar flow control (LFC) technique to delay laminar to turbulent transition. In this work, we investigated efficient LFC configurations. These are evaluated both in terms of the drag and power exerted by the flow and demanded by the LFC system. To derive the LFC power, the literature analyses on drag reduction for turbulent flows were adapted for the LFC applications hereby considered, leading to the identification of the relevant power-contributing terms. Two methods, originally developed to predict the transition location for uncontrolled flows, were employed to explore LFC configurations. These are specifically the so-called $e^N$ method, derived from the linear stability theory, and the $\gamma \text{−}{\text{Re}}_{\theta }$ model. Only the $\gamma \text{−}{\text{Re}}_{\theta }$ approach gave more robust results for LFC applications. As such, it was embedded in an iterative framework exploiting Bayesian optimization to find the most beneficial configurations, for uniform suction LFC, to control the archetypal, bidimensional, and incompressible flat plate flow. Overall, 700 configurations were explored. Efficient LFC configurations were found with the optimal configuration delivering 34% of total power saving. This study, establishing a robust and computationally affordable methodology, while developing the power budget breakdown, paves the way for efficient LFC for aeronautical flows, possibly considering nonuniform suction, pressure gradients, surface curvature, the third spatial direction as well as flows at different Reynolds and Mach numbers.

Vortex shedding is an important physical phenomenon observed across many spatial and temporal scales in fluids. Previous experimental and theoretical studies have established a hierarchy of local and global reduced-order models for vortex shedding based on the Stuart-Landau and Ginzburg-Landau equations. In this work, we employ data-driven methods to discover a new Landau variable for the complex Ginzburg-Landau equation (CGLE) for periodic two-dimensional vortex shedding past a cylinder. We first coarse-grain vorticity field data from direct numerical simulations of the fluid by integrating over the vertical spatial dimension, and then time-delay embed this new variable to obtain phase information necessary for CGLE analysis. Finally, we use the sparse identification of nonlinear dynamics (SINDy) algorithm to learn an interpretable system of coupled real partial differential equations that balance model complexity and prediction error. We develop local homogeneous models in key regions of the wake, as well as global heterogeneous models that are parameterized by the streamwise coordinate across the entire wake. After computing the normal-form parameters from the discovered equations, we classify the different models and determine behavior and stability in the different regions of the wake, demonstrating the validity of these models across a range of spatiotemporal subdomains. Different dynamics are found to dominate at different stations within the wake. In addition to introducing a novel Landau variable for vortex shedding, this work may also help characterize other vortex shedding systems and inform the design of control schemes.

Two-dimensional turbulence with linear (Ekman) friction exhibits spectral properties that deviate from the classical Kraichnan prediction for the direct enstrophy cascade. In particular, for sufficiently small viscosity and large friction, the enstrophy flux is suppressed in the cascade and, as a consequence, the small-scale vorticity field becomes passively transported by the large-scale chaotic flow. We numerically address this problem by investigating how the statistics of the Lagrangian finite time Lyapunov exponent (FTLE) in 2D Ekman-Navier-Stokes simulations are affected by the friction coefficient and by the other parameters of the flow. We derive a simple phenomenological model that interpolates the dependence of the Lyapunov exponent on the flow statistics from the large friction limit, where analytical predictions are available, to the small friction region. We find that the distribution of the FTLE around this mean value is always close to a Gaussian, and this allows us to make a simple prediction for the correction of the spectral slope of the direct cascade, which is in very good agreement with the numerical results.

We consider fluctuating Sabra models of turbulence, which exhibit the phenomenon of spontaneous stochasticity: Their solutions converge to a stochastic process in the ideal limit, when both viscosity and small-scale noise vanish. In this paper, we develop a renormalization group (RG) approach to explain this phenomenon. Here, RG is understood as an exact relation between the stochastic properties of systems with different dissipative and noise terms, in contrast to the Kadanoff-Wilson coarse-graining procedure, which involves small-scale integration. We argue that the stochastic process in the ideal limit is represented as a fixed point of the RG operator. The existence of such a fixed point confirms not only the convergence in the ideal limit but also the universality of the spontaneously stochastic process, i.e., its independence from the type of dissipation and noise. The dominant eigenmode of the linearized RG operator determines the leading correction in the convergence process. The RG eigenvalue $\rho \approx 0.84exp\left(2.28i\right)$ is universal and it turns out to be complex, which explains the rather slow and oscillatory convergence in the ideal limit. These universality predictions are accurately confirmed by numerical data.

We study the mobilization of an oil droplet in a deformable, actuated constricted tube subjected to two different actuation mechanisms: hydrodynamic actuation (oscillatory body force in the fluid) and dynamic-wall actuation (oscillatory traction on the tube walls). Using high-resolution fluid-structure interaction simulations, we analyze the effects of actuation frequency and amplitude on droplet transport through the constriction. Our simulations show that hydrodynamic actuation leads to a monotonic increase in the droplet's mobilization time with increasing actuation frequency, and a decrease with increasing actuation amplitude. In contrast, dynamic-wall actuation exhibits a resonance effect—the mobilization time reaches a minimum at a frequency near the tube's resonant frequency. Our study highlights the potential of actuation mechanisms in deformable tubes for precise control of droplet transport in biomicrofluidic applications.