While electrophoresis and diffusiophoresis are driven by phenomena that share much in common, they are generally treated in conceptually distinct ways: one via an electric force on a charged electric double layer, the other via pressure gradients due to lateral concentration gradients. Here, we develop an alternative formulation of linear osmotic slip and phoretic migration that is conceptually unified, and more easily generalizable than conventional formulas, and can be directly extended to double layers with physics beyond the Poisson-Boltzmann equation. Building on Derjaguin's original approach, we compute the osmotic slip velocity over a solid surface in contact with a multicomponent solution, as a sum of the contributions made by each solute species. Each contribution can be naturally expressed in terms of its chemical potential gradient in the bulk, which is the driving force on those species molecules, and an osmotic slip coefficient that can be computed from the excess solute concentration profile near the surface. This unified approach reproduces published formulas for linear electro-osmosis, chemiosmosis, and diffusio-osmosis involving Poisson-Boltzmann double layers, and results for nonelectrolytes. Osmotic slip mobilities are then connected to phoretic migration mobilities through a generalization of Morrison's argument, generalizing both the driving forces and the Dukhin number criterion for its validity. In addition to intuition and conceptual unification, this approach can be naturally generalized to accomodate Maxwell-Stefan multicomponent solute transport. Finally, phoretic drift velocities are expressed in terms of solute fluxes, rather than local concentration gradients, enabling qualitative and quantitative aspects to be predicted in complex solutions without requiring detailed concentration profiles. Examples include diffusiophoresis in multicomponent, equally valent electrolytes, conditions for positive and negative diffusiophoresis in asymmetric electrolytes, and conditions for diffusiophoretic focusing in reacting solutes.

In this work we experimentally investigate the turbulence modulation in the wake of deforming bubbles in homogeneous and isotropic turbulence, in the regime where the turbulence fluctuation is stronger than or comparable to the bubble rising velocity. The void fraction was kept low enough to focus on the modulation by single deformable bubbles, where the bubble-bubble interaction is negligible. To quantify the flow and bubble deformation, both phases were measured simultaneously in three dimensions, which includes the Lagrangian tracks of tracers along with the 3D geometry of bubbles captured by six high-speed cameras. In a quiescent or weak turbulence, the wake has a persistent direction due to the buoyancy. In turbulence, however, our results suggest that the decorrelation time for the slip velocity roughly equals the bubble-sized eddy turn over time. It suggests that, when turbulence becomes intense enough, the slip velocity changes its direction and magnitude so frequently that a wake barely has time to develop. As a result, both the intensity and length of the wake are significantly modified. Nevertheless, with sufficient bubble Reynolds number, the wake, albeit limited, can still modulate surrounding turbulence. To quantify the modulation, an axisymmetric reference frame with the axis of symmetry aligning with the direction of the slip velocity was employed. The turbulence statistics near a bubble can then be averaged together, and the turbulence modulation in intense turbulence is therefore exposed. The results suggest that the local turbulence is augmented by the bubble wake, and the amount of augmentation depends heavily on the bubble Reynolds number, the orientation of the bubble semimajor axis relative to the slip velocity, and the bubble deformation.

The linear models of complex unstable flow systems serve as essential foundations for conducting model-based flow characteristic analysis and control design. The primary obstacle faced by linear modeling these systems lies in balancing the inherent flow disturbances with the necessary excitation signals. This article develops a linear modeling approach based on the idea of closed-loop identification. To extend the applicability of traditional linear modeling techniques, this method employs time-variant or strongly nonlinear data-driven controllers, such as model-free adaptive controllers and deep reinforcement learning controllers, to automatically adjust the amplitude of the predesigned training signal in real time during the training process. Consequently, the strict requirements for obtaining the unstable steady base flow of unstable systems and for designing training signals are weakened. These data-driven controllers have been validated to fulfill the identifiability conditions of closed-loop systems derived from the uniqueness and convergence consistency of identification parameters. Then, the feasibility of the proposed linear modeling method is validated through two typical examples: low Reynolds number laminar flow around a cylinder and transonic buffet flow around a NACA0012 airfoil. The results confirm that this method successfully identifies the intrinsic linear characteristics of different flow systems, thus facilitating the advancement and application of model-based control design and simplification methods.

This paper experimentally investigates the transitional response of double-mode Faraday waves in a brimful circular container subjected to vertical vibration with parameters near the overlap of two instability tongues. Special attention is paid to the temporal evolution of primary wave components from the initial rest state to the final resonant state. To characterize the nonlinear pattern-forming dynamics, local amplitude variations are measured using a laser Doppler vibrometer, and spatial changes in surface patterns are reconstructed through a modified free-surface synthetic Schlieren method. With rapid ramping of the forcing acceleration, we find that mode transition occurs in a double-mode system where one mode with a lower natural frequency prevails in the transient pattern competition. Phenomenological analysis of single-mode experiments identifies the linear growth rate $\alpha \propto \epsilon$, where $\epsilon$ is the dimensionless forcing distance, and shows nonlinear coefficients ${\beta }_5>0>{\beta }_8$, indicating supercritical and subcritical excitation for the fivefold and eightfold modes, respectively. Incorporating mode suppression and fifth-order terms, coupled amplitude equations can be completed to describe the observed transitional responses of double-mode Faraday waves. This work provides insights into the complex pattern-forming dynamics of Faraday waves in multimode systems.

Hoppers with inclined walls are commonly used in industrial applications to facilitate the gravity-driven discharge of materials through a bottom outlet. The simplest form of this flow configuration, a wedge-shaped, quasi-two-dimensional hopper with frictionless walls and a gravitational force radially directed toward the apex of the wedge, is considered. A closed form solution of the flow was given in the classical work of Savage [Br. J. Appl. Phys. 16, 1885 (1965)]. Discrete element method (DEM) simulations are performed to analyze the stress and velocity fields for granular flow in a close replica of the system considered in the theory. Results are presented for varying hopper parameters (orifice size and wedge angle) and particle properties (particle diameter, friction coefficient, and stiffness). A detailed comparison of the computational results with the predictions of the Savage model indicates that the model predicts the stress accurately, except near the exit, but predicts velocities significantly higher than the computational values. The deviation is due to the assumption that the stress at the exit is zero, which is contrary to the significant exit stress obtained from computations. The flow is purely extensional and is found to follow the $\mu \text{−}I$ rheology, which includes frictional and collisional stresses. A flow model based on the $\mu \text{−}I$ rheology is presented, and model predictions of the stress and solid fraction profiles closely match the computational results. Correlations for the velocity and the mass flow rate, in terms of the system parameters, are obtained from the simulation data.

Traumatic brain injury (TBI) is a serious health issue. Studies have highlighted the severity of rotation-induced TBI. However, the role of cerebrospinal fluid (CSF) in transmitting the impact from the skull to the soft brain matter remains unclear. Herein, we use experiments and computations to define and probe this role in a simplified setup. A spherical hydrogel ball, serving as a soft brain model, was subjected to controlled rotation within a water bath, emulating the CSF, and filling a transparent cylinder. The cylinder and ball velocities, as well as the ball's deformation over time, were measured. We found that the soft hydrogel ball is very sensitive to decelerating rotational impacts, experiencing significant deformation during the process. A finite-element code is written to simulate the process. The hydrogel ball is modeled as a poroelastic material infused with fluid and its coupling with the suspending fluid is handled by an arbitrary Lagrangian-Eulerian method. The results indicate that the density contrast, as well as the rotational velocity difference, between the hydrogel ball and the suspending fluid, play a central role in the ball's deformation due to centrifugal forces. This approach contributes to a deeper understanding of brain injuries and may portend the development of preventive measures and improved treatment strategies.

The possibility of encapsulating therapeutic substances with active particles inside droplets, thereby propelling their motion from within, presents exciting opportunities for biomedical applications such as targeted drug delivery. In realistic biological and environmental settings, droplet interfaces often exhibit complex interfacial rheological behaviors due to different molecules or particles laden on the interface. Motivated by this complexity, we investigate the effects of interfacial rheology on the motion of an active droplet consisting of a liquid droplet enclosing an active particle described by the squirmer model. Specifically, we examine theoretically how surface shear and dilatational viscosities impact the propulsion of both the enclosed squirmer and the enclosing droplet. Our results indicate that while surface shear viscosity has no impact on the propulsion speeds, both the droplet and the squirmer swim slower with increased surface dilatational viscosity. The independence of propulsion speeds from surface shear viscosity is a feature shared with the classical problem of a translating droplet with surface viscosities. However, we add a cautionary remark on the subtlety in interpreting the impact of surface viscosities in these two problems. We also examine how the presence of surface viscosities affects the flow field and energetic cost in this active droplet system. These findings represent a first step towards understanding how complexities arising from realistic biological or environmental settings influence the behavior of microswimmer-driven droplets, paving the way for their potential applications in these complex environments.

Direct numerical simulations have been performed to investigate the quasistatic magnetoconvection of a low Prandtl number fluid (Pr = 0.025) within a rectangular cell of varying aspect ratios under the influence of a vertical magnetic field. The Hartmann number (Ha) is fixed at Ha = 200 and Ha = 1000, while the Rayleigh number (Ra) ranges from $2\times {10}^5$ to $1\times {10}^7$, encompassing the entire region of the wall mode. Under a strong magnetic field, sidewall instability triggers convection onset, leading to wall mode states with enhanced heat transfer. As Ra increases, wall mode expands towards the cell center, increasing heat transfer intensity, as indicated by the Nusselt number (Nu). Reducing the aspect ratio and increasing the magnetic field both improve global Nu by enlarging the wall-mode region and intensifying heat transfer within it. This study introduces a root-mean-square velocity-based method for characterizing the wall mode, revealing significant circulation in the bulk. It also analyzes the double-layer structure of the wall mode, where the core and reverse flows are driven by buoyancy with an anomalous weakening of the Lorentz force in the core. A thermal boundary layer is observed in the impact zone, correlating inversely with heat transfer intensity.

Particles at liquid interfaces have the tendency to cluster due to capillary forces competing with gravitational buoyancy (i.e., normal to the distorted free surface). This is known as the Cheerios effect. Here we experimentally and theoretically study the interaction between two submerged particles near an advancing water-ice interface during the freezing process. Particles that are thermally more conductive than water are observed to attract each other and form clusters once frozen. We call this feature the frozen Cheerios effect, where interactions are driven by alterations to the direction of the experienced repelling force (i.e., normal to the distorted isotherm). On the other hand, particles less conductive than water separate, highlighting the importance of thermal conduction during freezing. Based on existing models for single particle trapping in ice, we develop an understanding of multiple particle interaction. We find that the overall efficacy of the particle-particle interaction critically depends on the solidification front velocity. Our theory explains why the thermal conductivity mismatch between the particles and water dictates the attractive or repulsive nature of the particle-particle interaction.

Helicity plays an essential role in the interscale dynamics of turbulence. This paper focuses on the compressible effects on helicity cascades via structure functions. We first investigate the spatial-local dynamics of helicity, revealing that helicity is enhanced by pressure gradients along vorticity lines. Then, structure functions are used to describe the multiscale dynamics. The scaling law $r^{2/3}$ for helicity remains valid in compressible turbulence, as helicity is independent of the compressive components. Additional pressure and divergence terms are introduced in the new third-order relation for helicity in compressible turbulence. The pressure term is related to the pressure gradients along the vorticity lines and plays a dominant role in the dissipative range. The divergence term is mainly induced by the mixed structure function of divergence and helicity, significantly contributing to inverse helicity cascades in the inertial range.

In oceans, multiple energetic inertia-gravity waves often coexist in a region. In this paper, we study the stability of two coexisting plane inertia-gravity waves (hereafter, primary waves), with the same frequencies (${\omega }_1$) and wave-vector norms, in a region of constant background stratification (denoted by $N$). Specifically, we explore the decay of two primary waves through triadic resonant instabilities in cases in which the primary waves do not resonantly interact with each other. Two coexisting primary waves undergoing triadic resonant instability can force two secondary waves each, and this results in two three-wave systems (3WSs). In some cases, two primary waves can have a common secondary wave, and this results in a five-wave system (5WS) composed of two different triads. We show that 5WSs are the dominant instabilities with higher growth rates than standard triads for a wide range of Coriolis frequency values ($f$). For two-dimensional (2D) cases, 5WSs have higher growth rates than triads for $f/{\omega }_1⪆0.3$ and for primary waves with the same horizontal (vertical) wave number but with the opposite vertical (horizontal) wave number. Similar results are observed for 3D cases in which the primary waves are not on the same vertical plane. Numerical simulations match the theoretical growth rates of 5WSs for a wide range of latitudes, except when $f/{\omega }_1\approx 0.5$ (critical latitude). Using theory and simulations, we show that the maximum growth rate near the critical latitude is approximately twice the maximum growth rate of all triads.

This study employs wall-resolved large-eddy simulation of a NACA 0012 airfoil at a Reynolds number of 400 000, a Mach number of 0.058, and zero incidence angle to investigate the fundamental mechanisms governing trailing-edge noise generation and propagation within turbulent boundary-layer flows. It utilizes wave-number-frequency decomposition and Amiet's trailing-edge noise theory to separate total pressure into two distinct components: hydrodynamic (incident) pressure and acoustic (scattered) pressure. The findings reveal that hydrodynamic pressure consists of turbulent coherent structures characterized by high-energy spectra, but they act as nonpropagating sources due to destructive interference within the streamwise correlation length. In contrast, acoustic pressure exhibits an in-phase nature that facilitates efficient sound propagation. The roles of incident and scattered pressures in Amiet's theory are compared with hydrodynamic and acoustic pressures obtained from a numerical simulation, revealing similarities in magnitude and directivity patterns.

Experiments are performed to investigate the interaction of a vortex ring (Reynolds number based on circulation (${\text{Re}}_{\mathrm{\Gamma }}$ = 10 500) with perforated surface (open area ratio, ${\varphi }_1=0.24$ and ${\varphi }_2=0.44$) with different included angles ($\theta ={60}^{\circ }–{180}^{\circ }$). The phenomenon is characterized using techniques like planer laser-induced fluorescence imaging and particle image velocimetry. Lagrangian analysis using finite-time Lyapunov exponents and ${\mathrm{\Gamma }}_2$ vortex identification methods are utilized to understand flow physics. We observe the development of mushroomlike structures at the holes, driven by the induced flow of the vortex ring. These formations, together with Kelvin-Helmholtz instability, introduce initial instability to the emerging jets. We discern a sequential emergence of the vortex ring in the form of jets at lower $\theta$ value that diminishes at higher values. Notably, a single vortex ring is split into two distinct vortex rings for $\theta \le {120}^{\circ }$. On either side of the perforated plate, the sense of circulation after interaction does not show bias toward the sense of flow on the upstream region for some values of $\theta$. We further show the evolution of circulation by jets in the downstream region aligns with the proposed cumulative slug flow model using the center line peak velocity of individual jets.

The drying rate profile of granular beds can be divided into the constant rate period (CRP), which is characterized by a nearly constant drying rate, and the falling rate period (FRP), in which the drying rate rapidly decays. In order to explain this behavior quantitatively, we proposed a simple one-dimensional power law model in which the product of the water permeability and the pressure gradient are assumed to be proportional to the cube of the saturation. To test this model, we measured the drying rates of glass beads and hierarchical granular materials produced by sintering and breaking glass beads. Our results and those of previous experiments showed consistency with the power law. The obtained proportional constant of the experimental power law also shows a rough agreement with that estimated from previous studies on water permeability and capillary pressure. Drying behavior in FRP also agrees with our model in some points. The remnant deviation of the model from experimental results may be attributed to the inhomogeneity of granular media, which was qualitatively verified.

We study the conditions under which large-scale vortex flow patterns appear in electromagnetically driven conducting horizontal soap films created between two coaxial cylindrical electrodes and placed in a vertical magnetic field. For large Marangoni and Peclet numbers, the two-dimensional flow in a flat free film is effectively incompressible and the surface concentration of an insoluble surfactant plays the role of the pressure away from the boundaries. If the direct radial electric current flows through the film, the Lorentz force arising in a uniform field drives the azimuthal flow. Its stability is investigated in cases of slip and no-slip boundary conditions at the edges of the film in the limit of a small Hartmann number. Flow stability changes nontrivially depending on the slip length, and the flow stabilizes for perfect-slip boundaries. In contrast, if the vertical axisymmetric field is strongly nonuniform, the flow may become linearly unstable at much smaller Reynolds numbers than the critical value for no-slip boundaries,- leading to the formation of large-scale circulation cells. Our experiments conducted using a piecewiseconstant magnetic field detect the formation of vortex structures that are in qualitative agreement with those predicted by the performed analysis.

Through switching contraction patterns driving digestive flows, the small intestine balances nutrient uptake and waste removal. Complex segmentation contraction patterns are associated with higher nutrient uptake, while peristaltic contractions primarily serve to flush out unused remnants. However, the impact of the non-Newtonian behavior of digestive fluids on the efficacy of these contraction patterns remains unclear. Here, we present finite-element simulations that model nutrient transport, diffusion, and uptake within both segmentation and peristaltic contractions along the small intestine for Newtonian and non-Newtonian fluids. Our simulations reveal that diffusion plays a key role in uptake, with nutrient absorption directly linked to fluid viscosity, which governs molecular diffusivity. Further, we present an analytical prediction for uptake in peristalsis as a function of molecular diffusivity, which aligns closely with our simulation results. Notably, we find that shear-thinning properties of non-Newtonian fluids enhance nutrient uptake, particularly in segmentation contractions compared to peristalsis. Our results demonstrate the fluid dynamical principles underlying intestinal digestion, showing how shear-thinning non-Newtonian fluids promote efficient nutrient uptake without compromising the clearance of waste. This physical insight advances our understanding of digestive processes and provides a foundation for exploring the prevention of intestinal diseases such as bacterial overgrowth.

We study the flow induced by the periodic forcing on a fluid bounded in a millimeter-sized channel with a wedge obstacle on one of its walls. This geometry is an upscaled version of an acousto-microfluidics setup, previously investigated for its potential for efficient mixing. Combined with the harmonic response consisting of an unsteady viscous boundary layer of thickness $\delta$ along the walls, and deflected by the obstacle, there exists a streaming jet flow shooting out from the tip of the obstacle, which in turn generates vortices outside the boundary layer. While it is known that the jet velocity is strongly influenced by the sharpness of the wedge tip—quantified by its radius of curvature $r_c$, much less is known under conditions when the jet velocity becomes strong enough to perturb and deflect the unsteady boundary layer. With finite-elements numerical simulations of the Navier-Stokes equations, we investigate the steady and unsteady flows in an unprecedentedly large range of forcing amplitudes. We encompass different sharpness conditions varying the ratio $\frac{r_c}{\delta }$. We confirm previous results showing the occurrence of an asymmetric streaming flow at $r_c<\delta$—with an imbalance of vorticity on each side of the obstacle, above a threshold in forcing velocity $v_{ac}$. We find that this regime is observed also when $r_c>\delta$, although above a higher threshold. Importantly, we could experimentally reproduce this asymmetric regime, as well as transitional regimes, in parameter ranges corresponding to those of the simulations. We examine more carefully the different stages between symmetric and asymmetric flows, at increasing forcing amplitude. Depending on $\frac{r_c}{\delta }$, the streaming flow near but below the threshold $v_{ac}$ shows long transient stages (50 to 200 periods) with asymmetric fields or slowly evolving symmetric ones. The final state shows slow periodic oscillations, with a wobbling streaming jet. Similar slow oscillations can also be observed in asymmetric regimes for $v_a>v_{ac}$. At even higher $v_a$, an unstable behavior of the asymmetric flow is observed, with nonharmonic fluctuations of the jet and the associated vortices. Careful examinations of the corresponding unsteady flows reveal that the basic symmetric regime remains stable as far as the unsteady boundary layer is attached to the wedge.

In many environmental flows, an air-water free surface interacts with a turbulent flow in the water phase. To mimic this situation, we propose an original experimental setup, based on the randomly actuated synthetic jet array forcing used to study turbulence with almost no mean flow. By using a central pump connected to jets, we generate a turbulent flow of tunable intensity, with good isotropy and horizontal homogeneity, up to a maximal turbulent Reynolds number of 8800. The aim here is to characterize how turbulence is modified by the presence of a free surface. We show that the free surface affects turbulence for fluid depths smaller than the integral length. We report that the turbulent fluctuations become strongly anisotropic when approaching the free surface. The vertical velocity fluctuations decrease close to the surface whereas the horizontal ones increase, as reported in previous theoretical predictions and numerical observations. We also observe a strong enhancement of the amplitude of the temporal and spatial power spectra of the horizontal velocity at large scales, showing the strengthening of these velocity fluctuations near the free surface. In addition, these behaviors are studied for various levels of turbulence.

Oscillating foil turbines (OFTs) can be used to produce power from rivers and tides by synchronizing their heaving motion with the strong lift force of vortices shed at their leading edge. Prior work has shown that compliant membrane OFTs, which passively camber, exhibit enhanced leading edge vortex (LEV) stability and improved lift and power compared with rigid foil OFTs for specific kinematics. This work seeks to understand (a) the performance of compliant membrane OFTs over their full kinematic parameter space and (b) separate the roles of membrane camber and extensibility in LEV stabilization. We characterize the performance of a compliant membrane OFT over a wide range of kinematic parameters through prescribed motion experiments in a free-surface water flume. The optimal frequency of the compliant membrane OFT is found to be lower than that of a rigid foil OFT due to the enhanced LEV stability of the membrane. The lift and power of compliant and inextensible membrane foils are then compared to determine whether camber alone is effective for LEV stabilization or if extensibility plays an important stabilizing role. The deformation of the compliant membrane OFT is measured using laser imaging. We observe that the role of extensibility changes for different angles of attack. At low angles of attack, membrane deformation is consistent through the half cycle coinciding with similar performance to the inextensible foil. At higher angles of attack, the compliant foil has a larger deformation and dynamically decambers corresponding with delayed stall and enhanced lift and power.

We present numerical simulations investigating the evolution of liquid droplets into baglike structures in turbulent airflows. The droplet bag breakup problem is of significance for many multiphase processes in scientific and engineering applications. Turbulent fluctuations are introduced synthetically into a mean flow, and the droplet is inserted when the air-phase turbulence reaches a statistically stationary state. The morphological evolution of the droplet under different turbulence configurations is retrieved and analyzed in comparison with laminar aerobreakup results. While the detailed evolution history of individual droplets varies widely between different realizations of the turbulent flow, common dynamic and morphological evolution patterns are observed. The presence of turbulence is found to enhance the drag coefficient of the droplet as it flattens. At late times, the droplet becomes tilted and increasingly corrugated under strong turbulence intensity. We quantify these phenomena and discuss their possible governing mechanisms associated with turbulence intermittency. Lastly, the influences of liquid-gas viscosity ratio are examined and the implications of air-phase turbulence on the later bag film breakup process are discussed.