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.

When a bubble from air entrapment rises to the liquid-gas interface or a gas cavity formed by impacting droplets collapses, it may burst and form a jet, which leads to surface instability. Here, the effect of an electric field on the dynamics of the bubble bursting at low Ohnesorge number is numerically investigated via an arbitrary Lagrangian-Eulerian method coupled with a leaky-dielectric model. Our results demonstrate that the presence of the electric field will deform the bubble cavity, accelerating the propagation of capillary waves while slowing down the cavity inversion. Furthermore, the electric field disrupts the commonly observed self-similar behavior, resulting in the lifting, thickening of jets, and enlargement of droplets formed from jet breakup. Details of the underlying mechanism, including the variations in jet pinch-off, local curvature, wavelength, and energy, are comprehensively discussed. Finally, the influences of the charge relaxation on the dynamic process are investigated. Both the simulation results and theoretical analysis hold a good agreement with previous studies, providing valuable insights in designing at small scales.

We present laboratory experiments that examine the density and velocity structure of gravity currents encountering an array of closely spaced roughness elements. We largely focus on experiments where the height of the current is significantly larger than the height of the roughness elements, such that the current flows over the top of the roughness array. The Froude number of the gravity current decreases as it flows over the roughness array and the decrease is dependent on the roughness height. The fluid density within the head of the current also decreases as the current travels and we show that the local Froude number, based on the buoyancy within the head, is constant. This highlights that the buoyancy within the head controls the local Froude number of the overflowing current. This contrasts with a gravity current flowing through a roughness array, where the absence of a prominent current head means that the local Froude number is controlled by a pressure gradient within the tail of the current. Finally, we examine the horizontal velocity field and volume fluxes above the roughness array. The volume fluxes allow us to infer the exchanges between the fluid within the roughness array, the current, and the ambient fluid, and for these exchanges to be compared to those of a smooth bed current. These results combine to give a detailed understanding of a gravity current flowing over a roughness array and provide a comparison against both smooth bed and through-flowing gravity currents.

This letter presents a new mechanism of interaction between mineral dissolution and colloidal transport. Using microfluidic experiments, we demonstrate that diffusiophoresis, i.e., the motion of colloidal particles due to solute concentration gradients, offers an appealing solution to drive colloidal particles toward a dissolving mineral. We report that particle aggregation limits the mineral dissolution through the formation of a passivation layer around the mineral. This work could be exploited to turn undesirable mechanisms (e.g., dissolution of confinement barriers and release of toxic components by contaminants trapped in porous formations) into positive feedback as the concentration gradients resulting from these events become the driving force to deliver colloids for remediation.

Coated microbubbles in conjunction with ultrasound have emerged as an important biomedical tool for diagnostic imaging and therapeutics. Here, I offer my perspective based on research spanning over two decades, highlighting the underlying physics of linear and nonlinear bubble dynamics. I will describe our effort at mathematical modeling of contrast microbubble behaviors, specifically our adoption of an interfacial rheological model for the stabilizing shell and a hierarchical approach of model building and improvement using attenuation and scattering experiments. I will describe our collaborative effort at using the sensitivity of the acoustic response of microbubbles to ambient hydrostatic pressure for a subharmonic aided pressure estimation (SHAPE) method for noninvasive organ-level blood pressure monitoring. Other collaborative projects demonstrated microbubbles together with low-intensity pulsed ultrasound (LIPUS) to be an effective tool in tissue engineering, growing bone and cartilage from human mesenchymal stem cells in a 3D printed tissue engineering scaffold. We have theoretically investigated various underlying mechanisms for such bioeffects of ultrasound-insonated microbubbles, specifically microstreaming at low acoustic excitations and cavitating jet formation at high excitations for shelled microbubbles. Finally, I briefly describe my computational research on viscous and viscoelastic emulsions and suspensions of drops, vesicles, and biological cells.

The human heart pumps in a pulsatile fashion that generates pressure and flow waves in the cardiovascular system. These waves propagate and reflect through a fractal tree network composed of fluid-filled compliant tubes. The resulting complex pressure and flow waves create a pulsatile workload (an important contributor to the pumping efficiency of the heart). Although such load has been shown to be dependent on inflow wave frequency, the fundamental relationship between power and frequency has not been directly explored. Hence the general idea of this work is to address this by modeling wave propagation in a generic pulsatile system through a fluid-structure interaction solver (based on a reduced-order Navier-Stokes formulation) applied to a fluid-filled compliant tube terminated by a controlled reflection site. We analyze the impact of reflection on such pulse waves and their associated power-frequency relationships. Our analysis considers moderate frequencies and large wavelengths as inspired by cardiovascular flows. Examining pressure-flow dynamics reveals two distinct regimes as a function of inflow frequency: a pressure-leading regime and a flow-leading regime. We observe that the latter transitions into the former at particular “optimum frequencies” that minimize the pulsatile load on the inlet and create nonlinearity in power-frequency patterns. Results suggest that the values of these frequencies strongly depend on the reflection coefficient of the tube. Our findings highlight the significance of reflection as a key determinant in design that can provide control of optimum inflow frequencies toward minimizing destructive pulsatile loads.

The coexistence of multiple stationary, spatially localized structures has recently been reported for convection in an inclined porous layer, but the influence of imperfectly conducting boundaries has not been studied. This paper analyzes the traveling behavior of asymmetric, spatially localized convective structures (“convectons”), consisting of one or more pulses, in a two-dimensional inclined layer of a porous medium subject to a fixed temperature at the bottom and an imperfectly conducting boundary at the top, such that midplane reflection symmetry is broken. Extensive direct numerical simulations (DNS) are conducted for a wide range of Biot numbers associated with the upper boundary, revealing nontrivial relationships between the drift velocity $c$ of spatially localized structures and the symmetry-breaking parameter $\kappa \ge 0$ based on the Biot number, with $\kappa =0$ corresponding to perfect midplane reflection symmetry associated with $c=0$. In small domains, the drift velocity $c$ is positive (corresponding to upslope motion) and increases monotonically with $\kappa$, while for localized structures in larger domains consisting of a small number of pulses $c$ can be of either sign depending on parameters. For longer structures $c$ reverts to positive values and again increases monotonically with $\kappa$. We show that the along-slope tails of pulses and the associated long-range interactions are governed by the dominant spatial eigenvalues, whose real part is of the smallest magnitude, and we uncover a transition at a finite symmetry-breaking strength $\kappa ={\kappa }_c>0$: for $\kappa <{\kappa }_c$, both dominant eigenvalues are complex, implying that the upslope and downslope exponential tails are oscillatory. In contrast, for $\kappa >{\kappa }_c$, the dominant spatial eigenvalue with a positive real part becomes real, implying that the downslope exponential tail transitions from an oscillatory profile to a monotonic one. As a result, for $\kappa <{\kappa }_c$, bound states consisting of different numbers of pulses are present. These display rich dynamical phenomena including inelastic collisions leading to other bound states, while for $\kappa \gg {\kappa }_c$, adjacent pulses are found to repel one another and so tend to spread out, eventually becoming equispaced in the finite computational domain. The strength of the repulsive interaction increases with $\kappa$, i.e., with increased symmetry breaking. A reduced description of this behavior is proposed based on the interaction between tails of adjacent localized structures, which accurately reproduces the repulsion and inelastic collisions observed in DNS. The reduced model indicates that the transition from bound states to an equidistant configuration occurs when the monotonic tail and the oscillatory tail have the same slope, which occurs at a value of $\kappa$ greater than ${\kappa }_c$. The results presented here represent a step towards understanding the dynamics of spatially localized patterns in moderate-Rayleigh number convection in an inclined porous medium subject to an imperfectly conducting boundary.

The transport of matter by turbulent flows plays an important role, in particular in a geophysical context. Here, we study the relative movement of groups of two (pairs) and four (tetrahedra) Lagrangian particles using direct numerical simulations of the stably stratified Boussinsesq equations, with Brunt-Väisälä frequency $N$ and Coriolis parameter $f$. We cover regimes close to homogeneous isotropic turbulence, to flows dominated by stratification and rotation, keeping fixed the ratio $N/f=5$. The flows studied are anisotropic, so the relative motion between two particles depends not only on the initial separation between the particles, but also on their orientation with respect to the vertical axis. In all cases considered, we demonstrate that the relative particle motion differs depending on whether dispersion is considered forward or backward in time, although the asymmetry becomes less pronounced when stratification and rotation increase. On the other hand, the strong fluctuations in the dispersion between two particles become more extreme when $N$ and $f$ increase. We also find evidence for the formation of shear layers, which become more pronounced as $N$ and $f$ become larger. Finally, we show that the irreversibility on the dispersion of a set of particles initially forming a regular tetrahedron becomes weaker when the influence of stratification and rotation increases, a property that we relate to that of the perceived rate-of-strain tensor.

Data-driven RANS modeling is emerging as a promising methodology to exploit the information provided by high-fidelity data. However, its widespread application is limited by challenges in generalization and robustness to inconsistencies between input data of varying fidelity levels. This is especially true for thermal turbulent closures, which inherently depend on momentum statistics provided by low- or high-fidelity turbulence momentum models. This work investigates the impact of momentum modeling inconsistencies on a data-driven thermal closure trained with a dataset with multiple fidelity (DNS and RANS). The analysis of the model inputs shows that the two fidelity levels correspond to separate regions in the input space. It is here demonstrated that such separation can be exploited by training with heterogeneous data, allowing the model to detect the level of fidelity in its inputs and adjust its prediction accordingly. In particular, sensitivity analysis and verification show that such a model can leverage data inconsistencies to increase its robustness. Finally, the verification with a CFD simulation shows the potential of this multifidelity training approach for flows in which momentum statistics provided by traditional models are affected by model uncertainties.

Superhydrophobic surfaces (SHS) are textured hydrophobic surfaces, which have the ability to trap air pockets when immersed in water. This can result in significant drag reduction, due to substantially lower viscosity of air resulting in substantial effective slip velocity at the interface. Past studies of both laminar and turbulent flows model this slip velocity in terms of a homogenized Navier slip boundary condition with a slip length relating the wall slip velocity to the wall-normal velocity gradient. In this work, we seek to understand the effects of superhydrophobic surfaces in the context of mean scalar and momentum mixing. We use the macroscopic forcing method (Mani and Park, 2021) to compute the generalized eddy viscosity and slip length operators of a turbulent channel over SHS, implemented as both a pattern-resolved boundary condition and homogenized slip length boundary condition, for several pattern sizes and geometries. We present key differences in the mixing behavior of both boundary conditions through quantification of their near-wall eddy viscosity. Analysis of transport in turbulent flow over pattern-resolved surfaces reveals substantial nonlocality in the measured homogenized slip length for both scalar and momentum mixing when the Reynolds and Peclet numbers based on pattern size are finite. We present several metrics to quantify this nonlocality and observe possible trends relating to Reynolds number, texture size, and pattern geometry. The importance of nonlocality in the slip length operator and eddy diffusivity operator is demonstrated by examining the impact on Reynolds-averaged solutions for the mean scalar and velocity fields.

We studied the transient motion of single oil droplet dispersed in paramagnetic rare-earth dysprosium salt solution in a strong magnetic pressure gradient $\left(\mathbf{\nabla }{B}^2\right)$. For that purpose, we used a concentric ring-rod NdFeB permanent magnetic assembly and oriented its axis parallel to gravity. The resulting $\mathbf{\nabla }{B}^2$ field stratifies monotonically along its symmetry axis, reaching $\approx 600{\mathrm{T}}^2/\mathrm{m}$ at the magnet surface. Initially, an oil droplet rises in a stagnant aqueous solution driven by buoyancy force. As the droplet approaches the magnet, the Kelvin force acting on the droplet becomes dominating. Consequently, the droplet starts to oscillate vertically rectilinearly. Dynamically, the trajectory of the oscillating droplet is resembled perfectly with a damped linear harmonic oscillation system. The phenomenon is robust for all four experimented organic phases despite that their momentum dissipation time scales differ in two orders of magnitudes. Correlating hydrodynamic forces with damping terms in the linear harmonic oscillation system, an experimentally quantifiable constraint is derived for the memory kernel of the droplet's Basset-Boussinesq force. The droplet's memory kernel, different from that of spherical gas and particle that decays at the dimensionless time following $\propto t^{\prime -1/2}$, decays exponentially $e^{t^{\prime }}$. This is found valid for the highest experimented droplet Reynolds number up to 45. Statistics from experiments show that the droplet memory kernel is correlated with droplet diameter instead of the viscosity ratio between the two phases. After hydrodynamic forces have dissipated kinetic energy, the droplet is magnetically levitated statically, where the Kelvin force is counterbalancing buoyancy. By incorporating magnetic pressure into the Young-Laplace equation, we calculate the interfacial tension between the two phases based on the deformation of droplet which agrees well with measurements validated by a tensiometer.

Understanding and optimizing the design of helical microswimmers is crucial for advancing their application in various fields. This study presents an innovative approach combining Free-Form Deformation with Bayesian Optimization to enhance the shape of these swimmers. Our method facilitates the computation of generic swimmer shapes that achieve optimal average speed and efficiency. Applied to both monoflagellated and biflagellated swimmers, our optimization framework has led to the identification of new optimal shapes. These shapes are compared with biological counterparts, highlighting a diverse range of swimmers, including both pushers and pullers.

Understanding the transition between fluid-like and solid-like regimes of granular materials requires elucidating its hysteretic behavior. Yet, the origin of this hysteresis, defined as the difference in external stress necessary to induce flow or jamming of a granular medium, is still debated. While the origin of this hysteresis has long been attributed to grain's inertia, recent studies have shown that it depends on interparticle friction. To clarify the role of the different effects and possible interplays between them, we study the fluid-solid transition through three-dimensional discrete element simulations of dry and model-immersed granular flows down an inclined plane. In the dry case, a finite hysteresis is observed at the static-flowing transition even for frictionless particles. The hysteresis amplitude is shown to depend both on interparticle friction and particle inertia. Decoupling the effects of friction and inertia allows us to rationalize in a coherent picture the different results found in the literature. In particular, hysteresis is shown to become negligible when both friction and inertia are small, while it cannot be disregarded when at least one of them is present. The link between hysteresis amplitude and the discontinuous jump of compaction at the jamming transition is discussed. While the presence of hysteresis for frictionless particles is not associated with notable dilatancy and compaction at transitions, the coordination number exhibits discontinuous jumps at both transitions. Also, it is shown that the avalanche angle is directly linked to the static coordination number, and that the hysteresis amplitude is related to the coordination number discontinuity observed at jamming. These results highlight the strong link between the jamming-unjamming transition and the evolution of the granular microstructure through friction and inertia.

The general system of images for regularized Stokeslets (GSIRS) developed by Cortez and Varela [J. Comput. Phys. 285, 41 (2015)] is used extensively to model Stokes flow phenomena such as microorganisms swimming near a boundary. Our collaborative team uses dynamically similar scaled macroscopic experiments to test theories for forces and torques on spheres moving near a boundary and uses these data and the method of regularized Stokeslets (MRS) created by Cortez et al. [Phys. Fluids 17, 031504 (2005)] to calibrate the GSIRS. We find excellent agreement between theory and experiments, which provides experimental validation of exact series solutions for spheres moving near an infinite plane boundary. We test two surface discretization methods commonly used in the literature: the 6-patch method and the spherical centroidal Voronoi tessellation (SCVT) method. Our data show that a discretization method, such as SCVT, that uniformly distributes points provides the most accurate results when the motional symmetry is broken by the presence of a boundary. We use theory and the MRS to find optimal values for the regularization parameter in free space for a given surface discretization and show that the optimal regularization parameter values can be fit with simple formulas when using the SCVT method. We also present a regularization function with higher-order accuracy when compared with the regularization function previously introduced by Cortez et al. [Phys. Fluids 17, 031504 (2005)]. The simulated force and torque values compare very well with experiments and theory for a wide range of boundary distances. However, we find that for a fixed discretization of the sphere, the simulations lose accuracy when the gap between the edge of the sphere and the wall is smaller than the average distance between discretization points in the SCVT method. We also show an alternative method to calibrate the GSIRS to simulate sphere motion arbitrarily close to the boundary. Our computational parameters and methods along with our matlab and python implementations of the series solution of Lee and Leal [J. Fluid Mech. 98, 193 (1980)], MRS, and GSIRS provide researchers with important resources to optimize the GSIRS and other numerical methods, so that they can efficiently and accurately simulate spheres moving near a boundary.

In this study, we experimentally measure and characterize the behavior of water droplet impact on the center of superhydrophobic surface, focusing on the dynamics in the retraction stage. The circumferential velocity in the retracting liquid film rapidly amplifies, generating a centrifugal force which either induces rapid rebound by changing the shape of the bouncing droplet into a spinning-top or inhibits the rebound of the droplet. We measure the flow field in the retracting liquid film and reveal the coupling between the increasing circumferential velocity and droplet's decreasing radius in the retraction stage. We adopt a simplified approach to calculate the retraction velocity and the development of the circumferential velocity in the retracting liquid film. Finally, we reveal that the rebound of the droplet is weakened by the centrifugal force with a transition to nonbouncing around a critical Froude number $(\mathrm{Fr}\approx 2.4)$. Good agreements are found between the theoretically predicted parameters and the experimentally measured ones.

In the past, two families of statistical mechanics approaches have been applied to the two-dimensional Euler equations. The first one is formulated in Fourier space and considers the Galerkin-truncated dynamics. The other one is formulated in physical space and considers either point vortices or coarse-grained vorticity. We show that in a Galerkin-truncated system, both methods describe a part of the flow. A condensate can be identified, assuming that it can be characterized by an unspecified functional relation between the vorticity and the stream function. It is shown, a posteriori, that this function is a hyperbolic sine relation, as predicted by point-vortex statistical mechanics. The energy spectrum associated with the condensate is well described by an exponential function and the tails of the probability density function of the vorticity follow a power law. Analytical arguments to explain these observations are proposed. After removing the condensate, the remaining field can be described by Fourier-statistical mechanics.

The presence of gas or vapor bubbles may strongly influence the forces that occur during the impact of a liquid mass onto a solid. Here, we study this effect numerically, in a well-controlled manner, by simulating the short-time interaction between an impacting droplet and a solid surface, mediated by the gas layer between droplet and solid just before collision, in the presence and absence of bubbles. A boundary integral method is used to simulate the falling droplet, the mediating air layer is modeled using lubrication theory, whereas uniform gas bubbles are added to the droplet that obey a polytropic equation of state. We show that the presence of gas bubbles inside the droplet can have a significant influence on the force exerted on the substrate, even before touchdown. This is due to the transmission of load from the solid, through the gas layer, and finally into the bubbly droplet, buffering the impact. We simulate different bubble configurations, modifying their number, size, shape, and initial position. It is found that larger bubbles, as well as those close to the impact zone, dampen the collision more as compared to small bubbles or the ones that are far from the droplet's surface. In addition, multiple small bubbles are shown to have a similar or even greater effect as a single large bubble.