In a crowded and confined system where many drops interact, how do the interactions give rise to collective behavior? How do these interactions impact the performance of droplet-based microfluidic technology, and how can we overcome or leverage such interactions? This paper reviews our recent work on answering these questions, by studying the collective behavior of droplets in a concentrated emulsion and tracking the dynamics and the fate of individual droplets within the emulsion in a microfluidic system.

Elastic stress in viscoelastic flows, at vanishing inertia, can give rise to elastic instabilities and elastic turbulence (ET), causing an increased frictional drag. Here we show that the measured drag correlates well with elastic waves intensity and wall-normal vorticity above the onset of ET. Further, we demonstrate that increasing frequency of the elastic waves with Weissenberg number (Wi) results in their strong attenuation that hinders ET growth and thereby to drag reduction. Thus, this suggests a possible mechanism of interaction of elastic waves with wall-normal vorticity fluctuations, leading to the drag reduction and relaminarization phenomena at low-Re.

Experiments with circular cylinders in high-speed flow reveal new universal behavior associated with coherent oscillations in the near-wake region. The Strouhal number shows invariance with respect to both the flow Reynolds number and Mach number. Further, flow disturbances in the top and bottom halves of the wake have an anti-symmetric relationship.

We study the dynamics and arrest of two coalescing sessile yield-stress drops. Surprisingly, we find that the height of the bridge evolves similar to a Newtonian fluid. The arrested final coalesced shape is described by a balance between capillary pressure and yield stress, which is predicted from viscoplastic lubrication theory.

An object inserted in a fast-flowing soap film can cause shock-like structures in the film. We show by laser interference that the film thicknesses remain the same across those shocks. The shock fronts are due to the bending of soap films, like pleats in a curtain, rather than increases of film thickness. These shocks are actually caused by antisymmetric waves, rather than elastic symmetric waves.

We present an experimental study of the electrostatic Faraday instability at the interface between a dielectric and a conducting liquid. We study the response of the interface to an ac electric field, which is superposed by either a second ac field of different frequency, or by a dc field. An important control parameter is the mixing ratio, which denotes the relative amplitudes of the different components of the driving signal. For ac/ac driving, gradual variations of the mixing ratio can induce a jump of the pattern wavelength, and for ac/dc driving, the response wavelength can be tuned continuously by adjusting the mixing ratio.

Soft entities can be deformed by Poiseuille flows in thin microfluidic channels. Exploiting this phenomenon, we show that red blood cells exhibit a deformation-induced actuation when being subjected to asymmetric periodic flow fields, whereas rigid beads show a vanishing net drift.

The investigation of the fall of a sphere at finite Reynolds number in a concentrated suspension of small fluidized particles leads to unexpected results regarding the drag force exerted by a suspension on a moving object. These results, which seem to be associated with a slip velocity of the particles near the surface of the sphere, call into question the interpretation of the effective rheology of suspensions.

The development of turbulence closure models is an outstanding theoretical challenge, key to many applications. Despite the significant results obtained by Large Eddy Simulations, their capability to fully reproduce the statistics of resolved scales has often been overlooked. In this work we show that, in the context of the Shell Model for turbulence, it is indeed possible to correctly reproduce the statistics of the energy cascade, intermittency included, encouraging the development of similar approaches for three-dimensional Navier-Stokes turbulence.

Transitions among various states of complex fluid flows are intrinsically nonlinear phenomena. Using the recent theory of data-driven spectral submanifolds, we derive here the first low-dimensional reduced model that successfully predicts transitions from a laminar base state to other steady or time-periodic states in plane Couette flow.

The existence of two inertial ranges of forced homogeneous two-dimensional turbulence was conjectured about half a century ago. Given a forcing, confined to a typical wavenumber $k_f$, a direct cascade with $k^{-3}$ scaling for $k\gg k_f$ and an inverse cascade with $k^{-5/3}$ scaling for $k\ll k_f$ would be established. Using a geometric integrator on a unit sphere we are able to provide robust evidence for the double cascade spectrum at modest numerical resolution.

Flow features in branching networks are fundamental for understanding transport processes in respiratory and cardiovascular systems. Specifically for tumor embolization, the ability to predict the fate of finite-size particles in bifurcating vessels is highly desirable for improving embolization efficacy. We use particle tracking velocimetry to investigate the spatial distribution, velocity, acceleration, and dispersion of finite-size particles in a 4-generation bifurcating model. Our results show the remarkable influence of particle concentration on particle transport in several ways, which provides insights relevant to optimizing targeted drug delivery in embolization settings.

The dynamics of dilute solutions of polymers is a paradigmatic case of non-Newtonian flow. We show that the rotational dynamics of rigid rod-like polymers in a viscous fluid at low Reynolds number causes the emergence of a turbulent-like chaotic flow. This regime displays increased drag and mixing efficiency.

We present the continuous kinetic approach to modeling of thermally perfect (non-polytropic) gases with temperature dependent molecular internal degrees of freedom. Starting from the Boltzmann collision operator and a specific choice of the cross section enriched with free parameters, models are developed for transport coefficients, bulk and shear viscosities, and thermal conductivity. A procedure is proposed for simultaneously fitting parameters to match experimental data for temperature dependence of the specific heat, shear viscosity, and Prandtl number. Results for the dynamic pressure relaxation time, or equivalently, the bulk viscosity, are compared with previously existing estimates.

In many convective flows of geophysical relevance the Earth’s rotation is able to provide a control on the rate of heat transfer. The physical mechanisms of this process are the subject of this paper, where a linear model is used to break down the onset of convection into understandable elements that can be quantified and compared. The physical processes acting to control the onset of convection in rotating flows are found to differ depending on the parameters of the problem. Thus no simple universal mechanism can be identified.

Streaks are of interest in mixing intensification. The natural formation of streaks generally takes place in high Reynolds number flows indicating that an external forcing may be required to generate streaks in laminar flows. This paper is focused on the analysis of the use of heating and surface roughness for streak formation in low Reynolds number flows.

How fast ice melts in turbulent flows is key to many natural and industrial processes, most notably the melting of ice in polar regions. To better understand the physical mechanics quantitatively we examine the lateral melting behavior through numerical simulations and theory in a vertical convection system of ice and fresh water. We find that the melting rate of ice as a function of increasing heating temperature undergoes an abrupt transition from a slow- to a fast-melting state, contrary to the intuition of a gradual transition. The abrupt transition of the ice melting rate is due to the emergence of a reversed buoyant flow, due to the density anomaly of water near the melting point.

We experimentally investigate the speed of fragments produced by ligament breakup in laser-induced deformation of tin microdroplets into axisymmetric sheets. A double-frame backlit camera is used to obtain the speed of the fragments and the time of their detachment. We show that by normalizing these speeds to the initial expansion speed of the sheet, all data collapse onto a single universal curve that is a function of the dimensionless time $t_d/{\tau }_c$ only, where ${\tau }_c$ is the capillary time. We further find that this universal curve is explicitly independent of the droplet’s Weber number.

Bubble fragmentation drives up to 40% of the CO2 transfer from the atmosphere to the ocean. However, the small size bubble distribution, mainly responsible for gas dissolution, is still poorly understood. Combining experimental and numerical calculations, we find that capillary effects set small bubble production rate which physically explains the origin of their size distribution.

The thermohaline staircase structure, which is characterized by a series of remarkably homogeneous layers of temperature and salinity separated by sharp interfaces, widely exists in the Arctic Ocean’s main thermocline. In our most recent work (Ma and Peltier (2022), JFM), we have proposed a stratified turbulence-based theory to describe the formation mechanism of the staircase structure. In this work, we test the effectiveness of such theory using a series of body-forced direct numerical simulations. We show that the staircase structure spontaneously forms in our simulations in a way that is consistent with our theoretical predictions.

We present a method to calculate the sensitivity of the two least stable eigenvalues with respect to an external forcing added in a fluid-structure interaction system (FSIS). Sensitivity computations are performed by setting the external forcing proportional to flow velocity applied to a local point in the domain. We find that the sensitivity fields of an FSIS can be very different from its fixed structure counterpart. For an elastic structure the fields vary according to the reduced velocity. These sensitivity fields allow for passive control strategies, as confirmed by nonlinear simulations which result in vortex-induced vibration attenuation or mitigation, depending on the case.

The injection of fluid into the wake of a bluff body, commonly referred to as base bleed, is a well-known method of drag reduction. In the current paper we demonstrate that this method provokes a complete suppression of the steady asymmetry which otherwise dominates the natural Ahmed body wake and causes additional drag. Independent force measurements corroborate the suppression of the wake asymmetry. Different scales of base blowing reveal similar maximum drag reduction and asymmetry suppression, where the optimal blowing coefficient is found to scale with bleed-to-base area ratio as $(S_j/S{)}^{1/2}$.

A solution method for a nonlinear integro-differential equation is proposed and conducted on the problem of a boundary hair exposed to shear flow. While bearing resemblance to the pendulum problem from mechanics, this equation has not been analytically solved until now. We obtain this solution by treating the integral term as a parameter which we later constrain after obtaining the prospective trajectories. Our analytic solution circumvents the difficulties one can have with finite difference along with other numerical approaches and we argue that it could be used as a basis for understanding weakly time-dependent systems.

Here, we consider the spreading of polymer solutions with a flexible blade that deforms during spreading as a brush or a finger would. Using scaling laws and numerical simulations, we predict the value of the deposited film thickness. We show that normal stresses, which usually lead to remarkable behaviors (such as the swelling of the jets during extrusion, or the rise of the fluid on a rotating rod) have no effect here. Their impact is indeed reduced by the geometry of the experiment.

What happens when a drop of water first contacts a slippery solid infused with oil? We find that the spreading dynamics is not as universal as has been claimed for other kinds of substrates.

Dynamic organization of rod-like proteins and filaments in the cell membrane occurs in many cellular processes, including membrane transport and cell division. The dynamics of a single membrane-bound filament is determined, in part, by its hydrodynamic interactions with the membrane lipids and the surrounding bulk fluids. This study presents the first computation of the translational and rotational resistance of a single filament in a spherical membrane/cell. The boundedness of the spherical geometry gives rise to novel flow confinement effects that increase in strength with increasing the ratio of the filament’s length to membrane radius.

This paper presents simplified simulations, using the shallow-water equations (top panels) and a box model (bottom panels) of the particle-laden gravity currents generated by a vehicle moving along the seafloor. It analyzes the resulting deposits and their dependence on the two dominant parameters in the system: the ratio of the vehicle to spreading current speed (vehicle Froude number $Fr$) and the ratio of particle settling to vehicle speed. Estimates of the maximum extent of these deposits as a function of those two parameters are also computed, in both the supercritical regime, $Fr>\sqrt{2}$, and the subcritical regime, $Fr<\sqrt{2}$.

Different regimes are observed in the unchannelized collapse of wet granular columns. The initial aspect ratio of the column and the dimensionless macroscopic cohesion, which contains the particle size and the water content, are two relevant variables in the formation of different regimes and in the collapse dynamics. Generalized scaling laws are developed to characterize the deposit of wet collapsing material for which morphological quantities may be conveniently expressed by adding variations caused by the cohesion effect to the results of dry granular material.

Fluctuations in frictionless granular flows transition with inertial number $I$. The transition for stress properties and fabric anisotropy fluctuations depends on the pressure. The fluctuations scale self-similarly with number of particles $N$ and pressure $P$. A similar transition is observed for the average coordination number.

We study granular flows with grains of different sizes (i.e., polydispersity) in the granular column collapse configuration, in both dry and immersed systems with a Discrete Element Method - Finite Element Method (DEM-FEM) model. We show that polydispersity has an stronger effect on immersed cases than in dry cases, and propose a unified model that links the runout with the column collapse energy. Our results contribute a novel perspective in the study of immersed polydisperse flows.

An experimental investigation of cavitation in aviation fuel (JP-8 and JP-5) in a converging-diverging nozzle geometry is presented. A novel enhanced gradient shadowgraphy image processing technique is developed and employed in order to characterize the fundamental processes involved in unsteady bubbly shock wave generation and evolution, both with and without micro-air bubble injection at the inlet. We clarify the sequence of unsteady processes at play in aviation fuel cavitation and provide new perspectives regarding the damaging impact of shock waves that will lead to improved design of fuel system components.

The underlying physics of nonlocal granular flow within quasistatic, cohesive, split-bottom cells have been investigated. The evolution of macroscopic quantities, e.g., nonlocal granular fluidity, with respect to cohesiveness has been analyzed by coupling microscopic-level discrete element method (DEM) simulations with a coarse-graining procedure. As a result, tentative constitutive relations for wet granular flows have been uncovered and discussed.

The turbulent wake behind a square-back Ahmed body in close proximity to the ground exhibits bimodal switching. This manifests as the center of the wake randomly switching side-to-side between one of two asymmetric positions. This work is the first attempt to employ nonlinear model-based feedback control to suppress this wake bimodality. High fidelity simulations are used to develop and implement the control strategy and investigate the resulting effect on the wake and aerodynamic drag.

How the complex emerging patterns of bacterial or algal suspensions impact their mixing and transport properties is largely unexplored. Using an experimentally validated continuum model, this study shows that ideal mixing conditions are observed close above the transition from an ordered flow pattern to active turbulence when the interplay of spatial and temporal correlations is just right.

Transport of sediments via turbulent flows is common in nature and industry. We find that long deformable fibers transported by turbulent flows settle faster under the action of gravity than when in a still fluid. The settling statistics are surprisingly unaffected by the fiber’s ability to deform and depend only on its weight. Complementarily, the tumbling dynamics of the sedimenting fiber is governed solely by its elasticity.

We experimentally investigate the effect of shape on finite-size particles long term trajectories and observe that particles with an anisotropic shape can be attracted to coherent regions of the flow with a higher rate than spherical particles. We present a simple model that combines finite-size effects with orientation-dependent drag forces, and show that the aggregation rate and final particle concentration depend on both the particle’s Stokes number and aspect ratio.

We present a computational study of the effect of hydrodynamic slip at the surface of a particle on the statistical behavior of an ensemble of spherical particles in a two-dimensional von Karman flow in the wake of a cylinder. We predict that slip can lead to significant differences in escape rates, more initial positions that lead to vortex trapping at long times, and a greater uncertainty in scattering predictions. Thus, our work highlights that hydrodynamic slip significantly affects particle trajectories in unsteady flows.

Separating turbulent boundary layers exhibit unsteady motions at various frequencies. Using numerical and analytical techniques we identified the distinct strong responses of the flow to actuations at its natural unsteady frequencies. The low-frequency motion of the separating shear layer can be modulated by small streamwise perturbations thus leading to a smaller mean separation region. The key control mechanisms are the strong structural changes dominated by two-dimensional roller vortices. The stress/load unsteadiness on the wall is a possibly harmful outcome of flow control.

The Force Partitioning Method is employed to decompose the hydrodynamic drag in rough-wall turbulent channel flows. The contributions of vortex and strain dominated regions on the pressure drag are quantified using an auxiliary surface-dependent potential field $\varphi$. Different sources of drag are identified, and their relative importance quantified. The 𝑄-induced force (where 𝑄 is the second invariant of the velocity gradient tensor) is responsible for about 50% of the rough-wall drag, and is mainly generated by the strain-dominated (𝑄 < 0) regions before each roughness element. The equivalent sand-grain height $k_s$ is also characterized using $\varphi -$dependent norms.

A multiscale proper orthogonal decomposition (mPOD) has been used to decompose the multiscale features of very long turbulent channel flow. The very-large-scale motions (VLSM) can be clearly visualized, even for flow at relatively low Reynolds number. A new energetic mode, called eVLSM, has been identified, which contains substantial energy. The large-scale structures (apart from eVLSM) are inclined to the streamwise direction and appear to be responsible for the typical meandering behavior or even for the breakup of VLSM.

The internal energy equation for a compressible fluid can be cast in a form that relates the wall heat flux for a turbulent boundary layer to various terms integrated across the layer. We derive and utilize such a relation to investigate the ability of several Reynolds-averaged Navier-Stokes turbulence models to predict wall heat flux in a Mach 11 turbulent boundary layer. Data from a Direct Numerical Simulation (DNS) provide a means for assessing detailed contributions of the integrated model terms to the wall heat flux, helping to determine whether each model is able to obtain the “right answer for the right reasons.”

This study analyzes the effects of shocklets on sound source characteristics by analyzing source terms of the Lighthill equation, which is obtained from the results of direct numerical simulations. The results show that shocklets become main sound sources at high turbulent Mach numbers and the two main source terms of Reynolds stress and entropy cancel each other out across shocklets. The behavior is explained analytically by using a one-dimensional shock relation. This paper also provides a possible explanation for the link between shocklets and the generation mechanism of crackle noise as well as the applicability of the present findings to source modeling of a nonlinear acoustic analogy.

Direct numerical simulation over porous walled channel flows with computational domain size constraints were performed to clarify the role of spanwise rollers associated with the Kelvin–Helmholtz instability on turbulent flows over a porous wall. The spanwise rollers contribute to an increase in turbulence inside the porous wall and modify the logarithmic law in the clear flow region.

A general flux model describing the transport of kinetic energy and scalar variance in turbulence driven by a multiscale force has been established, with a universal conservative equation. In a complete cascade picture of turbulence there exist four different cases, with fluxes of kinetic energy and scalar variance being either constant or nonconstant.

Fluid-particle acceleration in turbulent flows is related to turbulent kinetic energy and its rate of dissipation into heat. Focusing on the statistics of the fluid-particle acceleration conditioned on both the local dissipation rate and the kinetic energy, it is shown that the acceleration grows exponentially with kinetic energy and presents a power law dependence on the dissipation. Based on these observations, we propose a vectorial stochastic model for the dynamics of a fluid particle giving the essential characteristics of Lagrangian turbulence.

In the logarithmic layer of boundary-layer turbulence, velocity structure functions scale as power and logarithmic functions of displacement at small and large scales, respectively. Using measured clear-air and sand-laden data from the atmospheric surface layer with friction Reynolds number up to ${10}^6$, we justify the balance between the third-order structure function divergence and shear production in the Kármán-Howarth-Monin equation in the logarithmic regime. The relative ranges of the two regimes depend on the ratio between the energy production and dissipation rate, which captures the relative strength between the anisotropic wall effect and near-isotropic dissipation.

Training/retraining a model against new data often breaks its good behavior. This left machine learning models open to criticism: machine-learned models do not fully preserve, e.g., the law of the wall (among other empirical facts), and they do not generalize to, e.g., high Reynolds numbers (among other conditions). This paper establishes a paradigm for machine learning, namely, progressive machine learning, allowing one to preserve the good behavior of an existing model in retraining. This paradigm is applied to progressively model flows in the constant stress layer, the wake layer, and with system rotation, with success.

Large eddy simulations are performed to study tonal noise generation by a NACA0012 airfoil for Reynolds numbers in the range $0.5\times {10}^5\le Re\le 4\times {10}^5$. Different flow patterns responsible for noise generation originate from laminar separation bubbles over the airfoil surface. Intermittency and flow transition to turbulence plays a key role in the noise spectrum.

We examine the effect of an incoming boundary layer state (laminar vs. turbulent) on the near wake of a surface-mounted square cylinder with a height-to-width aspect ratio of 4 at a Reynolds number ~${10}^4$. The mean wake structure for both cases is a dipole structure consisting of a counter-rotating pair of streamwise vortices extending from the recirculation region. For the laminar boundary layer case, the wake contains an additional vortex pair. We use oil-film flow visualizations over the base plate, reconstructed 3D phase-averaged velocity fields, and energy transfer between coherent and incoherent fields, to elucidate the influence of the boundary layer state.

We numerically show that traveling wave-based surface-undulations on a hydrofoil generates thrust. Simulations demonstrate that the pressure suction mechanism generates thrust beyond a threshold ratio of the wave to free stream flow speed. This mechanism is reminiscent of thrust generation in whole body undulation, as seen in prior studies. Within the examined parameter space, two distinct vortex patterns are revealed: almost steady vortex-sheet and periodic vortex-street. Both forward and reverse types of vortex-sheet and vortex-street are found behind the hydrofoil.

Global and regional ocean simulations rely on eddy viscosities and diffusivities to account for irreversible mixing of momentum and scalars due to unresolved scales of motion. These closures are often sensitive to the values of the mixing coefficient, whose shape has been well characterized in terms of turbulence parameters. In this paper, we connect this well-established shape of the mixing coefficient curve to the underlying physics of stably stratified turbulence as a function of the turbulent Froude number.

This paper examines the theoretical modeling of a steady horizontal gravity current. The differential equations obtained reveal a mathematical singularity which no longer allows them to be solved. To circumvent this problem, we introduce a jump into the model. We then compare the theoretical results with large eddy simulations and find good agreement.