The bouncing of droplets on surfaces features the short-time droplet-surface contact, benefiting numerous applications, including self-cleaning, anti-icing, heat transfer control, and so on. Recent studies reported that increasing liquid viscosity inhibits droplet bouncing on nonwetting solid surfaces because of increasing viscous dissipation within the droplet, leading to a divergent contact time when the droplet viscosity is beyond a critical value that is two orders of magnitude higher than that of water. Here, we show that the bouncing of high-viscosity droplets can be promoted when the nonwetting solid surface is replaced by a curved soap film. The contact time of droplets bouncing on curved soap films is found to be almost independent of the droplet viscosity in the high-viscosity regime. It is shown that more than $50\%$ of the initial energy is stored as the surface energy of the soap film during the spreading period, proving the essential role of the deformation of the soap film on the bouncing dynamics. The bouncing promotion mechanism is elucidated by a spring-mass-damper system in which the viscous droplet and the curved soap film are modeled in analogy with a damper and a spring connected in series.

The low-noise commercial aircraft necessitates the meticulous design of acoustic liners within engine nacelles. Acoustic liners, due to their porous wall nature, can substantially affect near-wall turbulent structures, thereby inducing various propagating waves with regular wave number and frequency. In this study, direct numerical simulations (DNS) of channel flow bounded by solid and porous walls were conducted at bulk Mach numbers of $M_b=0.2$, 0.5, and 0.8, where time-domain impedance boundary conditions (TDIBC) were employed to model the porous-wall effects. Longitudinal and oblique acoustic waves within the channel flow were accurately captured under porous wall constraints. The wavenumber-frequency relationships for all reflected waves and surface waves subjected to the specified TDIBC were theoretically developed, inspired by the work of Rienstra and Hirschberg [An Introduction to Acoustics (Technische Universiteit Eindhoven, Netherlands, 2004)]. The accuracy of these theoretical predictions was further validated through high-fidelity DNS results. Compared to the solid wall, it has been observed that the porous wall induces a phase offset in waves reflected from impedance walls and the characteristic wave-number-frequency relationship for surface acoustic waves has been confirmed by DNS. Furthermore, the wavenumber spectrum on the wall was explored, revealing the presence of supersonic ridges distributed along a series of concentric ellipses, but with modified wavenumber relationships. These features stem from the propagation characteristics of reflected waves within the channel flow.

The adoption of cardiovascular simulations for diagnosis and surgical planning on a patient-specific basis requires the development of faster methods than the existing state-of-the-art techniques. To address this need, we leverage the periodic nature of these flows to accurately capture their time dependence using spectral discretization. Owing to the reduced size of the discrete problem, the resulting approach, known as the harmonic balance method, significantly lowers the solution cost when compared against the conventional time marching methods. This study describes a stabilized finite element implementation of the harmonic balanced method that targets the simulation of physically stable time-periodic flows. That stabilized method is based on the Galerkin/least-squares formulation that permits stable solution in convection-dominant flows and convenient use of the same interpolation functions for velocity and pressure. We test this solver against its equivalent time marching method using three common physiological cases where blood flow is modeled in a Glenn operation, a cerebral artery, and a left main coronary artery. Using the conventional time marching solver, simulating these cases takes more than 10 hr. That cost is reduced by up to two orders of magnitude when the proposed harmonic balance solver is utilized, where a solution is produced in approximately 30 min. We show that that solution is in excellent agreement with the conventional solvers when the number of modes is sufficiently large (about 10) to accurately represent the imposed boundary conditions.

Many complex wetting behaviors of fibrous materials are rooted in the behaviors of individual droplets attached to pairs of fibers. Here, we study the splitting of a droplet held between the tips of two cylindrical fibers. We discover a sharp transition between two post-rupture states, navigated by changing the angle between the rods, in agreement with our bifurcation analysis. Depinning of the bridge contact line can lead to a much larger asymmetry between the volume of liquid left on each rod. This second scenario enables the near-complete transfer of an aqueous glycerol droplet between two identical vinylpolysiloxane fibers. We leverage this response in a device that uses a ruck to pass a droplet along a train of fibers, a proof-of-concept for the geometric control of droplets on deformable, architected surfaces.

We systematically investigate the magnetophoresis of weakly paramagnetic manganese oxide nanoparticles under nonuniform magnetic fields using a combination of experiments and multiphysics numerical simulations. Experiments were conducted in a closed cuvette exposed to a nonuniform magnetic field generated by an electromagnet, covering a wide range of particle concentrations (25–200 mg/L) and magnetic field gradients (0–110 ${\mathrm{T}}^2/\mathrm{m}$). The experimental results reveal that paramagnetic manganese oxide nanoparticles exhibit significant magnetophoretic behavior, leading to particle depletion within the cuvette. The depletion rate is independent of the initial particle concentration but strongly depends on the magnetic field gradient. At low magnetic field gradients, magnetophoresis progresses slowly, while at higher gradients, the particle depletion rate increases significantly before stabilizing. Transient concentration gradients emerge within the cuvette during magnetophoresis, which we hypothesize are driven by magnetic Grashof numbers (${\mathrm{Gr}}_m$) near unity. When ${\mathrm{Gr}}_m>1$, the formation of concentration gradients induces bulk fluid flows that accelerate particle capture at regions of maximum magnetic field strength. In systems where magnetophoresis opposes sedimentation, particle-depleted regions form when the ratio of magnetic to gravitational Péclet numbers exceeds 1. The numerical simulations suggest formation field-induced aggregation for manganese oxide nanoparticles with radii of 130 nm or larger. These insights highlight the potential of magnetic separation for sustainable metal recovery, offering a scalable and environmental friendly solution for recycling critical materials from spent electronics.

This paper considers a simple model for the coupled crystallization and sedimentation of a nucleated particle in a solvent. It is motivated by recent interest in understanding the effects of gravity on crystallization, arising in the context of possible future extraterrestrial manufacture of active pharmaceutical ingredients. The model is based on mass- and momentum-conservation arguments and consists of a nonlinear ordinary differential equation and an integrodifferential equation for the particle radius and its velocity, respectively, as functions of time; the second of these equations contains the well-known Basset integral history term. Nondimensionalization and subsequent asymptotic analysis indicate that there can be up to four different regimes as the growing particle sediments. The results of the analysis are compared with numerical solutions and found to give very good agreement; this is done for the crystallization of L-histidine, an essential amino acid that is used in the food and pharmaceutical industries. The availability of asymptotic solutions is particularly attractive in view of the surprisingly lengthy computational time, which is directly associated with the cumulative computational burden of the history term. An important implication is that the forced convection considered here outweighs any free convection effects arising from solute concentration gradients. Moreover, depending on the strength of the gravitational field, e.g., hypergravity or microgravity, the particle can either sediment, then grow, or grow while sedimenting. This distinction is critical for future models, as determining whether the two processes occur concurrently or sequentially influences the mathematical description of the crystallization dynamics.

We consider the problem of determining the rate of nutrient uptake by a self-propelled spherical squirmer, a model for a microorganism that generates motion along its surface. The tangential velocity induced by the squirmer varies along the surface in such a manner that a region of fluid recirculation is formed on the rear part of the squirmer. This problem was formulated by Magar et al. [Q. J. Mech. Appl. Math. 56, 65 (2003)] who investigated it in detail numerically covering a large range of Peclet numbers, $Pe=aU/D, a$ being the radius of the squirmer, $U$ is its swimming speed, and $D$ is the diffusivity of the nutrient in the surrounding liquid. Their numerical results for large $Pe$ suggested that Sherwood number $Sh$, the nondimensional mass transfer rate, increases in proportion to $P{e}^{1/2}$ but they were unable to theoretically determine the constant of proportionality. The present study reexamines this problem in the limit of large $Pe$ and small Reynolds numbers. The concentration in the bulk of the recirculating region approaches a constant whose value is determined by requiring that the mass transfer of nutrient across the streamline dividing the open and closed streamline regions must equal the mass transfer to the squirmer from the closed streamlines. The analysis of the nutrient concentration in the vicinity of the dividing streamline is complicated by the fact that this streamline originates from the stagnation point at the squirmer surface. The boundary layers formed at the nutrient surface on the either side of this stagnation point continue along the dividing streamline resulting in a discontinuity in the nutrient flux. As a consequence, new boundary layers form within these two larger boundary layers. When the squirmer motion induces the recirculation region ahead of itself, the distribution near the dividing streamline is simpler to determine but that near the squirmer surface involves formation of new boundary layers inside the boundary layers returning from the dividing streamline. Analytical expressions for large $Pe$ are derived in both cases and shown to be in agreement with the numerical results of Magar et al.

The Euler acceleration is noted to play a dominant role during the transient phase of the rotational maneuver of an insect wing. As such, this study aims to understand the influence of Euler acceleration on the transient loading and flow-field evolution over a rotating wing. By decoupling wing acceleration from steady-state velocity, the individual impacts of these parameters are systematically explored. The results reveal that Euler acceleration affects the transient dynamics differently depending on the steady-state velocity, suggesting the presence of distinct regimes. A new scaling parameter (${\alpha }^{*}$), defined as the ratio of Euler acceleration to convective acceleration, is introduced to delineate these regimes. The plot of the maximum lift coefficient ($C_{L_{\text{max}}}$) against ${\alpha }^{*}$ demonstrates the efficacy of this parameter, nearly collapsing the data into a single curve. This variation leads to the classification of two regimes: the quasisteady and acceleration-dominated regimes. In the quasisteady regime, secondary vorticity generation is crucial in dictating the transient dynamics, while no role of secondary vorticity is observed in the acceleration-dominated regime. The secondary vorticity is further dictated by the interplay between Euler and centripetal acceleration, with the former dictating the latter in the quasisteady regime, resulting in higher secondary vorticity development. This affects the growth rate of the leading-edge vortex (LEV), resulting in minimal variation of circulatory lift. In the acceleration-dominated regime, the absence of secondary vorticity growth leads to a continuous increase in LEV strength and hence the circulatory lift, which, combined with increasing noncirculatory component, results in an increase in $C_{L_{\text{max}}}$ with ${\alpha }^{*}$.

We investigate the slow, second order motion of thin flexible floating strips drifting in surface gravity waves. We introduce a diffractionless model (Froude-Krylov approximation) that neglects viscosity, surface tension, and radiation effects. This model predicts a mean yaw moment that favors a longitudinal orientation of the strip, along the direction of wave propagation. The physical mechanism for this angular drift is analog to that of the standard linear Stokes drift: it originates from a slight imbalance between the stronger acceleration on the wave crests (that favors the longitudinal orientation) and the wave troughs (that favors the transverse orientation). Laboratory experiments with thin rectangular strips of polypropylene show a systematic rotation of the strips toward the longitudinal orientation, in good agreement with our model. We finally observe that the mean angular velocity toward the stable longitudinal orientation decreases as the strip length increases, an effect likely due to dissipation, which is not accounted for in our inviscid model.

Inhomogeneous rotating turbulence is ubiquitous in nature and engineering. However, people are still unfamiliar with the dual cascade of energy and helicity in inhomogeneous rotating turbulence. In this paper, our aim is to study the effects of the inhomogeneous Coriolis force on the evolution of flow structures and the dynamics of helicity. On this issue, we performed direct numerical simulation (DNS) on several cases of the simplified inhomogeneous rotational turbulence with cosine distribution of angular velocity. The DNS results demonstrate the spectra of energy and helicity and the interscale transfer of energy and helicity. The Biot-Savart law exhibits the influences of the Coriolis force. In conclusion, the flow field under the effects of the inhomogeneous Coriolis force can be categorized into three regions, namely, the helicity-dominated region, the dual cascade region, and the rotation-dominated region. The energy cascades downscale through the average transfer effect, while the helicity cascades downscale relying on extreme events. In addition, the decomposition of the Coriolis force shows that the Coriolis force accounts for the formation of dumbbell-shaped columnar structures and the generation of helicity.

Lagrangian averaging is a valuable tool for the analysis and modeling of multiscale processes in fluid dynamics. The numerical computation of Lagrangian (time) averages from simulation data is challenging, however. It can be carried out by tracking a large number of particles or, following a recent approach, by solving a dedicated set of partial differential equations (PDEs). Both approaches are computationally demanding because they require an entirely new computation for each time at which the Lagrangian mean fields are desired. We overcome this drawback by developing a PDE-based method that delivers Lagrangian mean fields for all times through the single solution of evolutionary PDEs. This allows for an on-the-fly implementation, in which Lagrangian averages are computed along with the dynamical variables. This is made possible by the use of a special class of temporal filters whose kernels are sums of exponential functions. We focus on two specific kernels involving one and two exponential functions. We implement these in the rotating shallow-water model and demonstrate their effectiveness at filtering out large-amplitude Poincaré waves while retaining the salient features of an underlying slowly evolving turbulent flow.

In living materials, collective motion often manifests as flow vortices and jets, forming what is known as active turbulence. Using a continuum theory of active nematics and employing an information-theoretic divergence measure, we report on the existence of an activity threshold, beyond which the behavior of the active nematic system substantially changes. Specifically, we show that at this activity threshold the defect pathlength reaches its maximum, velocity correlation length peaks, and nonlinear dependence of flow mixing rate on activity vanishes. We further show that this activity threshold is well separated from the threshold for topological defects nucleation and is a robust feature of the system across different parameter values, and independent of system size. The results offer new insights into characterizing nonequilibrium evolution of active materials with varying activity levels.

Mixing in an explosion is largely affected by the reshock process and corresponding Rayleigh-Taylor and Richtmyer-Meshkov instabilities (RMI). The conventional understanding of RMI stems from a laboratory-scale channel. However, the reshock process in an explosion is different due to combustion, implosion, and reshock generation from the core. This numerical study quantifies mixing layer growth, mixedness, and turbulence, first within the fireball of a free-field TNT explosion and then within an SF6 curtain placed near the charge. The results show that the postreshock mixing within the fireball is consistent with the conventional understanding of RMI, showing a linear mixing layer growth and a rapid rise in the mixedness within the time frame of the shock passage through the mixing layer. However, the early-time mixing shows a strong effect of implosion and deviation from the conventional understanding of RMI. The SF6 mixing is strongly dependent on curtain placement due to two reasons: (a) stronger shocks near the charge cause a more violent RMI and mixing and (b) implosion and fireball cause a deviation in the mixing behavior from the conventional understanding of RMI if the SF6 placement is within the fireball radius. The curtain thickness is shown to have minimal effects on the mixing behavior, except for interactions between the inner and the outer boundaries of the curtain that lead to a more complex mixing for thinner curtains. The differences in mixing layer growth rates are explained using correlations for shock overpressure decay, Rankine-Hugoniot equations, and mixing models.

The remarkable appearance of self-organized regular and peaked polygonal rotating patterns in shallow Leidenfrost rings is investigated as a balance between surface tension geometry and nonlinear terms of Euler equation. Using the Boussinesq shallow convection approximation and a specialized expansion of the Laplace equation solutions, we derive a nonlinear equation that can be integrated in terms of elliptic functions. The model rigorously accounts for surface tension, the contribution of the poloidal rolling vortex, and the interplay between buoyancy-driven and thermocapillary flows. We obtain cnoidal waves solutions describing the dynamics of the inner free surface of the Leidenfrost ring, to predict polygonal patterns in liquid nitrogen. These predictions are compared with experimental observations. Additionally, we introduce a simplified model based on poloidal averaging of the capillary pressure, leading to a Korteweg-de Vries-type equation. This simplified model not only reproduces the cnoidal wave solutions but also predicts new trigonometric solutions, offering insights into the formation of peaked polygons.

An asymptotic approach is employed to study the swimming speed of a two-dimensional Taylor swimming sheet beneath a Brinkman layer of finite thickness. This configuration is representative of a swimmer confined within a porous non-Newtonian boundary and could model microscopic filter feeders like choanoflagellates and sponges or the mucociliary escalator in the lungs. When ignoring the effects of jump stress and porosity, the swimming speed of the sheet decreases as the thickness and lower boundary of the Brinkman layer increase. The same is true as the permeability of the layer decreases. Including porosity effects with a zero jump stress enhances the swimming velocity of the sheet for porosity values near unity and decreases the swimming velocity for smaller porosity values. In the absence of porosity, the swimming speed of the sheet increases for positive-valued jump stresses and decreases for negative ones. Coupling nonzero jump stress with a variable porosity establishes complex behavior, with the sheet's swimming speed attaining a maximum, surpassing that found for the Newtonian case, particularly in thin or low-permeability Brinkman layers.

We conduct direct numerical simulations (DNS) to investigate the dynamics of a non-Newtonian shear-thickening fluid in a turbulent plane channel. The primary parameter governing the non-Newtonian flow rheology is the Carreau number ($\text{Cu}$), defined as the ratio of the fluid's characteristic timescale, $\mathrm{\Lambda }$, to the flow characteristic timescale, $h/u_{\tau }$, where $h$ is the channel half-height and $u_{\tau }$ is the friction velocity at the wall. Starting from a Newtonian turbulent channel flow at ${\text{Re}}_{\tau }=180$, we examine the impact of increasing $\text{Cu}$ on turbulent statistics and coherent structures. The shear-dependent rheology is described using a Carreau viscosity model, with $\text{Cu}$ values spanning two orders of magnitude ($\text{Cu}=0.1,1,5,10$). While maintaining a constant mean pressure gradient ($\nabla \overline{p}$) that drives the flow—ensuring a fixed shear Reynolds number based on the zero-strain-rate reference viscosity ${\text{Re}}_{\tau ,0}=180$—we observe varying effective Reynolds numbers (${\text{Re}}_{\tau ,w}=111,76,58,52$) due to the altered viscosity distributions. Our findings reveal that shear thickening generally reduces the mean flow velocity and enhances the isotropy of velocity fluctuations compared to the Newtonian reference case. As $\text{Cu}$ increases, the strength of vortical structures diminishes, accompanied by a decline in turbulence intensity. This behavior is primarily attributed to elevated wall viscosity, which shifts turbulent stresses towards viscous stresses. Notably, at subcritical effective shear Reynolds numbers for which a Newtonian fluid would exhibit laminar flow, the shear-thickening fluid retains unsteady behavior (turbulence) but lacks a logarithmic layer.

We study experimentally a symmetrical rigid foil performing pitching oscillations around a mean incidence angle (${\alpha }_m$) with respect to an incoming flow in a hydrodynamic channel at a constant velocity where the Reynolds number based on the chord of the foil is ${\mathrm{Re}}_c=\rho U_{\infty }c/\mu =14400$. The problem is inspired by the pumping maneuver used by athletes on the new hydrofoil-based windsurf boards. In windsurfing, the pumping mode is used by athletes to produce unsteady propulsion. Because of the complex kinematics and the sail's position relative to the perceived wind, the sail produces thrust or drag, and lift. In sailing, the wind perceived by the sail is not parallel to the mean chord. Even if the sail is in a steady mode, it can propel the board by adjusting the mean incidence angle. Few studies investigate the impact of ${\alpha }_m$ on the mean values of aerodynamic force. The goal of this study is to quantify the forces on this configuration by varying the pitching kinematics characterized by the Strouhal number (${\text{St}}_A=fA/U_{\infty }$, with $f$ and $A$ the frequency and amplitude of pumping, respectively, and $U_{\infty }$ the wind velocity perceived by the sail) from 0 to 0.27, and the mean incidence angle ${\alpha }_m$, from 0° to ${30}^{\circ }$, of the foil. The force measurements show a high lift production and the delay of the stall angle according to ${\text{St}}_A$ which can be linked to previous studies about the generation of vortices at the trailing edge. A general trend of decrease is observed for the drag force coefficient in pitching compared to the static case. For the highest Strouhal numbers tested, the drag coefficient can become negative (thrust) in a range of ${\alpha }_m$ up to ${15}^{\circ }$ in specific cases. By using a sport-mimetic approach, we transform the measured lift and drag forces into propulsive and drifting forces, which are the decomposition of the aerodynamic force in the board frame. It is the reference frame in sailing to characterize and optimize physical parameters of the boat such as speed and trajectory. We investigate the impact of unsteady propulsion in upwind conditions. Doing so allows us to investigate race strategies because the generation of propulsion resulting from the drive force is linked to a sideways motion caused by the drift force. We also discuss the impact of using the pumping maneuver rather than the steady propulsion and show several behaviors that could help athletes with decision making.

In this study, a white-noise stochastic forcing model is proposed for the eddy-viscosity-based linearized Navier-Stokes equations of turbulent channel flow. The white-noise stochastic forcing is first optimized by minimizing the relative errors of the generated energy profiles of velocities compared to the direct numerical simulation results with ${\text{Re}}_{\tau }=186$ to 934. For different tested eddy-viscosity models, the optimized forcing energy profiles all show self-similar properties in the near-wall region, where the optimized forcing profiles with different flow scales show a good collapse when the wall-normal coordinate is normalized by the spanwise wavelength ${\lambda }_z$. For higher regions beyond the maximum points of the optimized forcing energy profiles, their values all decrease by more than $75\%$ at the centerline of the channel compared to their maxima. Based on the optimized results, a stochastic forcing model is proposed by describing the modeled forcing energy profile with squared mean-quantity-based eddy-viscosity profiles in the near-wall region after scaling and linearly decaying profiles in the higher region beyond the maximum points. The proposed white-noise forcing model is validated for its predictions of the covariance of velocity fluctuations. For different eddy-viscosity models, the prediction errors of the covariance tensor are reduced by $35.3\%$ to $86.4\%$ when adopting the forcing model compared to the results with spatially uniform white-noise forcing. Moreover, the forcing model is also applied to predict the coherent structures specified as the proper orthogonal decomposition (POD) modes, which provides rational results for both the shapes and energy distributions of the leading three pairs of POD modes. Finally, the new model is applied to evaluate the transfer functions for estimations of large-scale structures, which exhibit notable improvements compared to the results based on spatially uniform white-noise forcing, with a reduction in relative estimation error by more than $80\%$.

The Lamb vector appears in the rotational form of the Navier-Stokes equations and is the source of vortical flow nonlinearity that results in the cascade of energy from large to small scales. We investigate the three-dimensional spatial structure of this vector in the near wake of a NACA0018 wing with square wingtip profile at ${10}^{\circ }$ angle of attack and chord-based Reynolds number of 5000. At these conditions, a large recirculation zone forms in the wake and the flow transitions in the separating shear layer. We analyze the spatial footprint of the three components of the Lamb vector and its divergence (the latter for both the mean and the fluctuating velocity fields). By integrating the vertical component of the Lamb vector across the cross-stream direction (which is equal to the vorticity flux for two-dimensional flows) we obtain the local aerodynamic loading along the wing. The vorticity flux is equal to zero at the trailing edge, thereby confirming the Taylor-Sears condition away from the wing tip. We also apply Helmholtz decomposition to extract the potential and solenoidal parts of the Lamb vector. The former part is dominant in the attached and separated shear layers, while the latter is present downstream of the recirculation zone where the flow is turbulent. We decompose the Euclidean norms of the Lamb vector and its potential part into terms that are determined by the time-average field only, the fluctuating field only, as well as mixed terms. We find that the mixed terms play a dominant role and are the slowest to decay.

We consider viscous flow and solute transport in a tube with a corrugated surface, whose topology cannot be accurately described due to either a scarcity of data or measurement errors (or, more frequently, both). This uncertainty can be addressed by modeling the geometry of the roughness as a stationary random field. Consequently, flow and transport equations become stochastic. To solve these equations, the irregular boundary of the flow domain is mapped onto a smooth one (no roughness), with the impact of the original geometry encapsulated in the components of the contravariant tensor associated with the mapping. A perturbation expansion is then employed to compute the statistics of the velocity field, which is used to derive the effective viscosity and quantify the diffusion mechanism of an advected passive solute. It is observed that the effective viscosity depends on the degree of disorder in the roughness geometry and, therefore, cannot be regarded solely as a property of the fluid. Instead, the concentration is shown to satisfy a diffusion-type equation with time-dependent effective parameters. In particular, the effective diffusion coefficient converges to a constant (asymptotic) value after a transitional period, which depends on the correlation scale of the random signal describing the surface topology. The analytical nature of the solutions allows for the treatment of surfaces with, among other characteristics, short correlation lengths—an issue that cannot be effectively addressed using Monte Carlo simulations.