The movement and placement of cellular components is crucial for the proper development of egg cells and embryos. These transport processes take place within the fluidic interior of the cell and can yield surprisingly complex fluid-structure interactions. Fortunately, advances in mathematical modeling, multiscale coarse-graining, and the large-scale simulation of fluid-structure interactions have all helped in the understanding of this fundamental cellular biology. This paper discusses how simulations of immersed mobile structures and load-bearing biopolymers within cells helped show how the mitotic spindle finds its proper place inside an embryo approaching its very first cell division. Also discussed is the role played by coarse-grained porous medium models, stability analyses, and large-scale fluid-structure simulation, in revealing the self-organized processes that may underlie large-scale transport flows in developing egg cells.

A rigid body immersed in a fluid will generically move when the latter experiences a local force field. In the creeping flow regime, the body velocities (translational and angular) will be linear functionals of this field (“force representation”). Due to the incompressibility constraint, however, it should be possible to express them equivalently as linear functionals of the curl of the force (“curl representation”). Explicit expressions for this alternative formulation are derived, and illustrated with the example of self-chemophoresis.

We uncover interface-induced turbulence, a striking nonequilibrium statistically steady state with spatiotemporal chaos, emerging from interfacial fluctuations in low-Reynolds-number binary-fluid mixtures. Using direct numerical simulations of the Cahn-Hilliard-Navier-Stokes equations, we reveal a power-law energy spectrum indicative of turbulence without a conventional inertial cascade.

Turbulent flows are difficult to predict due to chaos, which amplifies any uncertainty in the initial conditions. The way this uncertainty grows and propagates is key to understanding the emergence of complexity in turbulence and to assessing the reliability of turbulence forecasts. In this Letter, a novel approach based on massive ensembles of simulations reveals that uncertainty propagates in isotropic turbulence following a simple law that depends only on the average properties of the flow. This result opens avenues to improve current forecasting techniques by efficiently and accurately modeling uncertainty propagation.

Viscoelastic fluids like DNA solutions and polymer melts yield chaotic flows even with small inertial effects (quantified by the Reynolds number). Such turbulent motion is conventionally classified as elasto-inertial turbulence (EIT) or elastic turbulence (ET) when inertial effects are finite or vanishing. Our numerical study investigates the turbulent flow of viscoelastic fluids in planar channel flows over a wide range of Reynolds numbers. We discover that EIT and ET exhibit the same dynamical features and are thus the same. Our finding sheds light on low Reynolds number turbulence, with broader implications for materials science, industrial processes, and biology.

In viscoplastic Poiseuille flows over superhydrophobic surfaces, misalignment between lower and upper grooves alters flow characteristics. Adjusting groove misalignment along with key dimensionless parameters—offset number, Bingham number, slip number, groove periodicity, and slip area fraction—affects velocity distributions, plug morphology, and yielded/unyielded zones. Misalignment intensifies velocity and strain rate deviations, leading to plug deformation, asymmetry, and potential breakage. Four distinct regimes of center plug morphology emerge, highlighting the complex interplay between misalignment and viscoplastic flow behavior.

In this work we show that the polymer diffusive instability is able to trigger viscoelastic turbulence with and without inertia through a secondary linear instability providing a generic supercritical route to viscoelastic turbulence. The reported secondary instability resembles center or wall modes, establishing connections with previous results in the literature.

At which scales do vortices in turbulence effectively stretch polymers? To answer this question, we conduct direct numerical simulations of turbulence and the Brownian dynamics simulations of the finitely extensible nonlinear elastic (FENE) dumbbell model. A scale-decomposition analysis based on a bandpass filter allows us to identify the dominant scale for polymer stretching. Furthermore, we explain the scale-dependent contribution to polymer stretching by focusing on the persistence of the stretching process of polymers induced by each-scale vortices.

The two-dimensional steady flow of a highly rarefied gas through a right-angled corner element is studied, based on the Boltzmann kinetic model and the Maxwell wall conditions. Closed-form expressions for the mass flow rate through the corner are derived, indicating a decrease of more than 40% in its mass transfer permeability due to the bend, compared with a straight channel configuration.

We experimentally investigate the relationship between heat transport and flow structures in rotating thermal convection. Our results, regarding the geometric and dynamic properties of columnar structures, demonstrate that the behaviors of heat transfer efficiency are intimately related to the changes in the coherent structures in the bulk flow. The sharper transitions of the flow field statistics suggest that, in future studies of regime transitions, flow field measurements may serve as a more definitive criterion than those based on heat transport behaviors.

When a particle-laden droplet impacts a flat surface, the presence of the particles inhibits its maximum spreading and reduces the rebound time.

How does rain initiate from cloud droplets? Drops above 100 μm have large enough inertia to fall, allowing them to grow by capturing smaller droplets during descent. However, rain formation needs to overcome a gap of very low collision rate for droplet sizes between 3-30 μm, where this mechanism is inefficient. We investigate four pathways to rain: the coalescence pathway; the mixing pathway driven by the creation of supersaturated conditions from mixing of cloud and drop-free air; the electrostatic pathway arising from these attractive forces; and the turbulence pathway. Rainfall begins when the drop size distribution broadens enough for a few droplets to create efficient collisions.

We theoretically and experimentally study the propagation of approximately circular pancake-shaped bubbles in a Hele-Shaw cell under a uniform background flow at low Reynolds number. Bubble motion and deformation are determined by an interplay between the Hele-Shaw viscous pressure, the pressure drop due to the thin films surrounding the bubble, and the capillary pressure due to the in-plane curvature of the bubble boundary. Numerical, asymptotic and experimental results indicate that, with all other parameters constant, the in-plane aspect ratio of the bubble varies nonmonotonically with its size. The model is also extended for buoyancy-driven bubbles in inclined or vertical channels.

Bubbly flows are present in a multitude of processes in both natural and industrial systems. One critical phenomenon is bubble fragmentation, which drives interfacial area and mass/momentum transfer. Direct Numerical Simulations (DNS) of turbulent two-phase bubbly flows allow for improved control of physical parameters and access to flow variables which are challenging to obtain from traditional experiments. By performing DNS of turbulent bubble fragmentation at a moderate Weber number and varying the bubble diameter around the integral turbulence length scale, we examine the exchange between turbulent kinetic energy (TKE) and surface energy, as well as other local quantities.

Droplet and cantilever systems are often studied to further applications for energy-harvesting technologies and to model the leaf-raindrop dynamics. This paper examines the interplay between the droplet and cantilevers of varying length by measuring the oscillation frequency, phase shift, maximum displacement, and damping coefficients. There is a significant difference in the measured values when resonance happens between the droplet and cantilever of a certain length. At the cantilever resonance length, high damping coefficients are attributed to the opposing inertial forces of the droplet and cantilever.

We demonstrate that adding an immiscible oil core into impinging water droplets can strongly dampen the surface capillary wave propagation, which suppresses the air bubble entrapment in droplet impact on superamphiphobic surfaces at low Weber numbers; but instead, it facilitates the entrapment of a water drop, resulting in complex water-in-oil-in-water droplet configuration after rebound.

Previous work showed that a floating liquid bridge can be sustained under DC or high-frequency AC voltage, though the effects of frequency remain unclear. We investigated the stability of a micro-floating liquid bridge under periodic voltage pulses. The recorded current reveals the formation and breakup of the bridge as six distinct states of stability beyond high-speed imaging. Our results show that both pulse frequency and the electrocapillary number are crucial for liquid bridge stability. Considering the charging/discharging process of the system, we corrected the formation and breakup time, which well explained the observed delay in these processes.

A dynamically unstable state of the Atlantic ocean circulation in a global ocean model is constructed via an edge tracking algorithm. Such an unstable state is relevant as it mediates the potential future tipping point of the meridional overturning circulation from its present-day state to a collapsed state as a result of climate change. We identify the physical characteristics of the unstable state, which gives insights into the physical mechanisms necessary to induce a collapse, as well as potential fingerprints and early-warning signals of the tipping point.

Gravity-driven flow of water into unsaturated porous media can form preferential pathways due to the gravity fingering instability. Here, we consider this process in a subfreezing porous medium using numerical simulations. We find that the macroscopic infiltration rate can be well predicted by the freezing Damköhler number. In contrast to the classical instability, the introduction of freezing in this problem gives rise to a new flow regime in which secondary flow pathways form in between the initial channels. This secondary instability homogenizes the otherwise channelized flow field and decreases the effective infiltration velocity.

Adjoint-based approaches were developed for full-order and reduced-order models to mitigate a streamwise or transverse gust and maintain the lift performance of a heaving-pitching wing. Simultaneous optimization of multiple parameters in flow control becomes feasible by solving both the physical model and its adjoint model. With a head-on streamwise gust, adjoint-based optimization suggests reducing the wing oscillation to maintain the original lift force; with a transverse gust, besides the reduced oscillation, the optimal wing motion shows an overall pitching-down motion towards the gust to balance out the additional lift generated by the gust.

The thermal drawing method has been widely used in fiber fabrication with the thickness down to the microscopic scale, where the flow instability plays an important role in obtaining nanowires or many intriguing patterns. Inspired by this, we performed an exploratory second-order nonlinear analysis to investigate the nonlinear instabilities of a planar liquid sheet under dual-mode, which can provide guidance to achieve sophisticated nanostructures for functional devices in a single fiber or integrated fabrics.

We experimentally investigated the drainage of vertical rectangular soap films as they thin under gravity. Drainage dynamics were measured by tracking isothickness interference fringes. We showed that the downward motion of these fringes is self-similar with a power-law time evolution, or equivalently, that the thickness profiles exhibit space-time separation. By combining our data with previous studies, we collapsed all profiles onto a single curve, demonstrating the universality of this phenomenon. These findings are important for studying liquid foams and marginal regeneration instability.

Based on the assumption of a combined parabolic and elliptic velocity profile, the simplified second-order depth-averaged equations are derived. As the parameter A relating to the eccentricity of the ellipse increases, new results adequately capture available findings. However, A = 2.23219 provides a relatively more accurate result. Maximum amplitude and speed of the steady-state traveling wave increase with rising values of A. The backflow phenomenon occurs in the capillary regime. Interestingly, the combined velocity profile detects the point of inflection in the capillary region at A = 2.23219, but it disappears at higher values of A, signaling a strong influence of the elliptic part.

The almost 60-year-old moving contact line problem has generated and driven an abundance of research. A variety of models have been proposed to alleviate the singularity at the three-phase conjunction. However, by design they are phenomenological and fall short of identifying the nanoscale effects that determine the fluid structure and compete to resolve the singularity. Here we put forward an inherently multiscale continuum model founded on first principles that bridges the micro- to the macroscale while retaining all fundamental microscopic information. It unravels the underlying physics of moving contact lines showing that it is much more intricate than previous models suggest.

Liquid jets with insoluble surfactants undergo thinning and acceleration due to gravitational stretching. The evolution of the jet’s basic flow and surface perturbations is influenced by a combination of inertia, surface tension, viscosity, gravity, and Marangoni stress. Global stability analysis results show that the Marangoni effects caused by the surfactants promote thinning of the basic flow and inhibit the growth of perturbations. Gravity, on the other hand, not only suppresses the perturbation development but also increases the optimal forcing frequency in forced falling jets.

A dolphin leaping out of the water. A piece of bread pulled from Swiss fondue. A car emerging from a bath of anti-corrosion fluid. More somberly, a missile launched from below sea level. The question is: how much liquid is carried along? We study the entrainment around a horizontal cylinder and observe that, whether in water or in oil (50 times more viscous than water), higher speeds result in greater liquid entrainment. By tracking the thickness of the liquid film at the top of the cylinder, we measure the drainage process down to a few microns. Remarkably, shortly after crossing the interface (typically within 1 second), the drainage becomes independent of the withdrawal speed.

Spheres falling into water create fascinating phenomena, such as crown-like splashes and clear cavities that are subsequently pinched off. These phenomena are universal and are generally controlled by the properties of the sphere. In this study, we report a new cavity formed by an air jet that lacks a distinct splash and features a rough cavity interface. We investigate the cavity dynamics, including formation, development, and pinch-off events.

This study explores the flow-structure interaction between the oscillatory boundary layer flow and an array of wall-mounted flexible filaments using a penalty-immersed boundary method. The key finding is that the presence of filaments lifts the boundary layer by the average filament height. A partial slip boundary condition with a complex-valued slip length is introduced to quantify the velocity-velocity gradient relation. It indicates the slip length reaches a stable value at the upper edge of the filaments. This study provides insight into modeling the effective boundary condition of the filament-attached wall.

In angstrom-scale channels, where water forms a two-dimensional (2D) monolayer, interlayer shear force decreases, making traditional viscosity definitions unsuitable. Our findings demonstrate that in channels below 1 nm, water flow does not follow conventional viscosity-driven principles; instead, friction between water molecules and channel walls governs flow behavior. We extend the Hagen-Poiseuille equation by excluding viscosity and emphasizing friction, providing a more accurate model for flow in ultra-narrow 2D spaces. This approach improves understanding of water flow in angstrom-scale channels, with applications in desalination and energy conversion.

Elaborating micro- and nanoscale heat using lasers is an emerging experimental technique to induce fluid flows and to control nanomaterial motions; this paper provides a theoretical tool to explore them. When focused lasers are irradiated to microfluidic systems, we can heat up, selectively and locally, fluids, channels, and/or such as thin-metal films. This localized heat generates various thermally-induced transport of fluids and dispersed objects. Considering that flow computation requires a decent amount of training cost, the easy-access instant analytical tool developed here is helpful for researchers without a fluid-mechanics background to explore complex phenomena in their own fields.

We report the mechanism and modeling for the two-dimensional shock-induced instability of a dual-layer gas-particle mixture. In the mixture, the instability is triggered by the pressure perturbation near the perturbed interface instead of the baroclinic vorticity. The velocity difference of gas induced by the pressure perturbation drives the particle interface to grow via drag coupling effects. Inspired by this interfacial instability mechanism, we estimate the growth of the particle interface in the linear stage.

During the generation of free-surface waves in landslide-tsunami modeling, the importance of grain-fluid interaction is still not well identified. To clarify this, the present study examines experimentally the role of viscous dissipation on the dynamics of dry granular masses collapsing into a liquid pool, by varying both the grain size and liquid viscosity. The experiments reveal a richness in granular collapse regimes, from dilute- and dense-inertial to dense-viscous regimes, that significantly influence the entire wave train, while having limited impact on the leading and largest wave.

We experimentally investigate the effects of helical tail length on the swimming efficiency of artificial robots in granular matter. Using magnetically driven swimmers, we found that longer tails boost forward velocity, challenging the traditional behavior observed in Newtonian fluids. We reveal the crucial role of head size in these dynamics through a modified Resistive Force Theory model. Our results demonstrate the intricate relationship between head drag and tail morphology, showing long-range effects linked to force chain formation and buckling. This important discovery broadens our understanding of locomotion in granular systems, an area where current theories are limited.

We investigate granular flows over an inclined, normally vibrated rigid base using the discrete element method, systematically varying the inclination angle (θ), vibration frequency (f), and amplitude (A). Our findings demonstrate that vibrated bases can amplify the mass flow rate (Q) by 25–100 times compared to fixed bases depending upon the choice of parameters and, further, it is possible to find conditions that maintain Q nearly constant. Finally, Q is characterized by a dimensionless parameter S, also known as the shaking strength, which represents the ratio of vibrational to gravitational energies.

Long-term seasonal weather variations can arise from a misalignment between sunlight and the direction of a planet’s gravitational pull, though plausible reasons are yet unclear. Inspired by such events, we have carried out numerical simulations and unmasked large-scale circulations and their reversals in canonical convection. At optimal orientations, the large-scale motions and core mixing events work against each other to achieve maximum heat transport. Our research findings have potential implications for climate studies and the development of thermal control strategies for device applications.

We develop a two-dimensional mathematical model that investigates the processes of erosion and deposition in an elastic porous medium. To simplify, we assume homogeneity and nondimensionalize the parameters, including Darcy velocity, particle concentration, and shear stress before reducing the continuum model via asymptotic analysis by exploiting its small aspect ratio. Our results illustrate the evolution of the medium under a prescribed constant flux of particles, wherein we draw conclusions on how total volume changes based on varying coefficients that dictate the tendency of particles to adhere to or be eroded from the walls of the medium at varying values of shear stress.

When searching for recurrence in turbulent flows a well-known issue is an inability of simple distance measures to identify solutions exhibiting high dissipation bursting behaviour. By constructing novel recurrence functions based on the nonlinearity of the governing equations, recurrent flows (unstable periodic and relative periodic orbits) are now able to be computed which cover the full range of turbulent dynamics. This has enabled much improved reconstructions of the flow statistics and indicated simple heuristic weightings of the individual solutions.

Coupled heat and momentum transfer in a porous medium saturated by a near (super) critical fluid is shown to take place under three different regimes depending on the distance to the critical point (CP). Far enough from the CP, transfer is governed by the classical piston effect (PE). While nearing the CP, the PE is hindered by a pressure gradient that builds up in the bulk of the medium. Exceedingly close to the CP, viscous effects are present in the whole domain, including the boundary layer close to the heated boundary, so that the PE is faded away and heat transfer takes place in a diffusive regime.

Wavy channels are widely used to enhance heat transfer in various applications, but their nonlinear dynamics under mixed convection remain poorly understood. Our numerical study reveals that mixed convection fundamentally alters the routes to chaos in wavy-channel flows: symmetric channels show both the Ruelle-Takens-Newhouse and degenerate period-doubling routes, asymmetric channels show only the latter route, and semi-wavy channels show no routes to chaos. The Pomeau-Manneville intermittency route, previously observed in isothermal conditions, is notably absent. These insights into the nonlinear dynamics of wavy-channel flows provide crucial guidance for optimizing heat transfer devices.

When the Faraday instability is induced in floating droplets in a viscous bath, a wave radiation pressure is exerted on the droplet boundary, causing it to evolve until a new equilibrium shape is reached. Different shapes are obtained by varying the forcing amplitude and frequency, though the system is highly hysteretic. We develop a theoretical model for the time evolution of the droplet boundary through the separation of timescales, with a strong agreement between the predicted equilibrium profiles and experimental observations.

This paper uncovers how freestream turbulence (FST) affects the wakes of porous discs with varying porosities, often used as wind turbines surrogates in wind tunnel studies. Low-porosity disks behave similarly to solid bodies in terms of entrainment behavior and scaling laws. FST reduces both wake growth and entrainment rates in the far wake, with turbulence intensity and length scale playing distinct roles. Intriguingly, as porosity increases, these “solid body” FST effects gradually diminish and are reversed above a critical porosity. This study also sheds light on the influence of disc porosity and FST on the presence of equilibrium and nonequilibrium turbulence in the wakes.

Bedload transport in vegetated channels, especially sparsely vegetated channels, is highly complex. As flow intensity varies, bedload transport can be divided into two stages: local and global bedload transport. In this study, the Engelund formula, which is typically used for bedload transport in bare beds, has been extended to calculate the bedload transport rate in sparsely vegetated channels. The results show that the bedload formula based on bed shear stress is more appropriate for medium and high bedload transport rates (global bedload transport), while the bedload formula based on grain shear stress is more suitable for weak bedload transport rates (local bedload transport).

Recent studies have used optimization to determine fluid flows that can efficiently cool heated objects. This paper examines recently discovered steady optimal flows through a heated channel, and uses a perturbation method to find nearby unsteady flows that convect more heat - up to 80% - for a given amount of power needed to move the flow. The unsteady perturbations consist of vortices, small or large, that move along the channel walls and disrupt the thermal boundary layer.

The effect of spanwise aspect ratio ($AR$) on flow characteristics over backward-facing steps with extended streamwise length and external corners is investigated experimentally. For intermediate $AR$, a unique wake pattern is observed, where there is no separation bubble, and the flow after reattachment ejects from, rather than impinging on, the central plane bottom floor, leading to intensified fluctuations and a broader region of high turbulence. This flow feature may be attributed to strong interactions of separated flows from all open edges with possible contributions from corner vortices that develop alongside the step. We also discuss the influence of these corner vortices for varying $AR$.

We revisit the amplitude modulation phenomena, as defined by Mathis et al. (J Fluid Mech. 628, 311-337; 2009), in the context of non-canonical wall-turbulence. A unique set of published, high-Reynolds number turbulent boundary layer datasets, from the same experimental facility are considered. It is found that nonlinear interactions, across the turbulence scale hierarchy, may become significant with the introduction of various non-canonical perturbations, in contrast to previous observations for canonical flows. The implications of these findings on the interpretation of amplitude modulation effects, and near-wall flow prediction models, for non-canonical wall-turbulence are discussed.

We propose a nonequilibrium wall model for improving the predictions of flow separation in complex, turbulent boundary layers. Improved predictability of smooth body separation at multiple Reynolds and Mach numbers in flows over the NASA/Boeing speed bump and the Bachalo-Johnson bumps is demonstrated at resolutions where the equilibrium model fails to separate. Scaling arguments, followed by $a$ $posteriori$ verification suggest a weaker scaling of the required resolutions to capture flow separation using the proposed model compared to standard equilibrium closures.

Parametrization of the probability density function (PDF) of streamwise wall-shear stress (WSS) in turbulent channel flows at the friction Reynolds number from 180 to 5200 is investigated. Lognormal parametrization is found to be more accurate than Gaussian for both the original and rescaled PDF of WSS. The original PDF of the inner WSS fluctuations can be well parametrized by a lognormal distribution. The rescaled PDF of the outer WSS fluctuations can be precisely parametrized by a Gaussian distribution.

This paper discusses the transformative potential of self-exploring automated experiments for the discovery, optimization, and control of unsteady vortex-dominated flow phenomena. By minimizing experimentalists’ input in the actual performance of fluid experiments, the potential for scientific discovery is maximized.

Though internal waves cannot propagate vertically through weakly stratified fluid, if the depth of the weak stratification is sufficiently shallow, these waves can partially transmit through it. This paper quantitatively extends previous results on Cartesian internal wave tunneling to the case of axisymmetric wave fields and proposes a simple three-layer model. We show that there exists a smooth transition between the fully propagating and the tunneling regimes. We further reflect on the challenges set by the measurement of internal wave mode amplitudes in confined domains, and we discuss an innovative method to measure said amplitudes in this experimental and numerical context.

By employing local geometrical optics stability analysis adapted to visco-diffusive flows, we derive novel explicit instability criteria for isothermal and non-isothermal swirling flows, induced by the combination of rotation and shear in orthogonal directions and ubiquitous in various natural phenomena, such as tornadoes and tropical cyclones. Our advance stems from an observation overlooked in previous research: the neutral stability curves in these problems possess an envelope, which we have analytically determined using the connection between envelopes and polynomial discriminants. Our analytical results offer a general theory of instabilities across a wide range of swirling flows.

Orbital sloshing, a common technique in fluid mixing for processes like cell cultivation and fermentation, generates complex wave dynamics at the interface and a hidden Lagrangian mean flow in the fluid bulk. Distinguishing between the Eulerian viscous streaming and Stokes drift contributions to the overall Lagrangian motion has remained challenging, particularly in highly viscous fluids. This study presents a weakly nonlinear analysis, revealing that Stokes drift and Eulerian viscous corrections can be equally important in the mean flow generation, offering new insights into orbital sloshing wave dynamics beyond traditional inviscid models.