Mixing in fluids is usually thought of as a process of homogenization, but in some circumstances, such as when dealing with filters, particles can have a tendency to accumulate, even at equilibrium. An example is virus particles kept out by a mask: they are more likely to be found near the filter because of a suction effect. A generalization of what we mean by mixing is called for, involving nonuniform, possibly time-dependent ultimate states.

In an effort to achieve very large Rayleigh numbers when studying turbulence on a Rayleigh–Baposenard configuration, one can carry out simulations and experiments in as high convection cells as possible which involves using convection cells with the smallest possible aspect ratio. However, with the increasing height of the cell, the Rayleigh number grows much slower than the critical Rayleigh number for the onset of convection in the same container. This article discusses how to estimate accurately the critical Rayleigh number for the onset of convection in confined geometries and the optimal shape of the container.

The coupling between turbulent convecting water and the freezing/melting process leads to intriguingly complex phenomena which are of pressing importance for applications in environmental and climatological sciences. Here we study the extent and the morphology of ice forming in a differentially heated cavity filled with water by means of laboratory-scale experiments and numerical simulations. We demonstrate that the characteristic ice shape formed in our system is the result of the competition of two counterrotating convective rolls whose strength depends on the externally prescribed thermal gap.

We examine the spatial energy budget for the plane incompressible mixing layer as the convective instability approaches absolute instability. Near onset of absolute instability pressure transport emerges as the primary mechanism responsible for the growth of disturbances, with the production mechanism making an insignificant contribution. Cross-stream profiles of production and pressure transport terms show significant changes in this limit, which are reflected in their contribution to the energy budget. These results, in particular the enhanced correlation between velocity and pressure disturbances, can help understand the physical processes causing absolute instability in a mixing layer.

The rapid propulsion of metallic microrods at the nodal plane of an acoustic standing wave was first reported in 2012. Previous modeling proposed that the acoustic propulsion of metallic rods arises from the nonlinear inertial coupling between rotational and translational perturbation flows (acoustic streaming), but such a mechanism has yet to reproduce experimental data quantitatively. Here we report experiments on the acoustic propulsion of multi-segment bimetallic rods which are properly modeled by a purely viscous flapping mechanism where inertia plays no role.

The concept of an “odd” coefficient of viscosity appears in some fluid mechanical contexts, including quantum fluids, electron fluids in mesoscopic systems, as well as some classical systems. Here we study the shallow depth limit of weakly nonlinear surface dynamics with odd viscosity and gravitational effects and obtain an integrable Kortweg-de Vries equation, the solution of which admits right- and left-moving disturbances with some differences. The odd viscosity term plays a role similar to surface tension.

This work focuses on characterizing the effects of numerical dispersion error on the energy cascade in large-eddy simulation (LES) of convecting homogeneous isotropic turbulence. Numerical energy and transfer spectra reveal that energy is not transferred at the appropriate rate to wavemodes where significant dispersion error is present, leading to a deficiency of energy in highly dispersive modes and an accompanying pile up of energy in the well resolved modes. An asymptotic analysis indicates that dispersion error causes a phase decoherence between triad interacting wavemodes, leading to a reduction in the mean energy transfer rate for these scales.

This study explores escape motions employed by larval fish using two-dimensional simulations. We demonstrate how a deep reinforcement learning framework, discovers swimming escape motions, not previously obtained through direct optimization, under various energy constraints. The study serves to showcase the richness of flow physics that can be discovered through the use of artificial intelligence.

Clustered contractions are observed in the human small intestine after fatty meals or in patients with gastrointestinal diseases. We present a numerical and theoretical analysis of liquid flow produced by the cluster of peristaltic waves in a circular channel. We show that flow rate is not proportional to the number of peristaltic waves in a cluster, and the flow rates of different numbers of waves collapse onto a single curve of each contraction ratio.

Elastoinertial turbulence (EIT) in dilute polymer solutions displays tilted sheets of polymer stretch with weak spanwise-oriented flow structures – a sharp contrast to the three-dimensional quasistreamwise vortex structures that make up inertia-driven Newtonian turbulence. We show that at for channel flow at sufficiently high Reynolds number, the Newtonian nonlinear Tollmien-Schlichting (TS) wave evolves continuously into EIT as the Weissenberg number increases, highlighting in particular a “sheet-shedding” process by which individual sheets are born in the Kelvin cat’s eye structure of the TS wave and break up to form the layered multi-sheet structure characteristic of EIT.

The effect of gas rarefaction on the propagation of two-dimensional vibroacoustic disturbances generated by a nonuniformly oscillating plane is studied. Closed-form descriptions are obtained in the free-molecular (left panel of the figure) and continuum (right panel) limits and complemented by direct simulation Monte Carlo results. The impacts of gas rarefaction on signal decay rate and directivity pattern are highlighted and rationalized.

We study Boussinesq convection by computing marginally-stable mean temperature profiles for various Ra which are thermal equilibria of the quasilinear equations. We find these marginally-stable thermal equilibria by solving one-dimensional eigenvalue problems and allowing the mean temperature to evolve according to diffusion and advection by the eigenmodes. The mode amplitudes are chosen such that the mean temperature maintains marginally stability. We find that multiple marginally-stable modes become important for Ra > 10${}^6$, and Nu ~ Ra${}^{1/3}$ up to our maximum Ra = 10${}^9$.

The flow of either particle-laden or surfactant-laden drops through a contraction under an imposed pressure has been investigated in a microfluidic setup. The drop deformation generates surface concentration gradients in adsorbed species, which results in surface tension gradients. Crossing of the contraction is driven by the coupling between the drop flow and surface tension gradients and can result in larger passage times for surfactant-laden drops.

We systematically investigate the dynamics of a free-settling particle driven by a laser-induced bubble near a rigid boundary. Two types of particle-bubble interaction are identified, in terms of the intensity of the influence of the boundary on the particle-bubble dynamics. Two important phenomena where the particle ends up impacting on the boundary at a relatively high velocity are discovered, which provide a potential mechanism for enhanced cavitation erosion in sand-laden water.

The dependence of contact angle on droplet size for droplets of height of the order of a few nanometers has been intensively debated for decades. The size effects are believed to be related to surface forces. In the present work, we use the disjoining pressure concept and solve the Derjaguin equation in order to show that values of the contact angle are dramatically dependent on the droplet height as well as the way the contact angle is defined. For the first time, we demonstrate that different contact angle definitions can even lead to opposite dependencies of the contact angle on the droplet height.

Nanobubble coalescence is a process of great importance to a broad range of applications such as froth flotation of fine or ultrafine mineral particles, detergent-free cleaning of clothes, and de-inking of recycled papers. To investigate the differences between nanobubble coalescence and macrobubble coalescence, we use molecular dynamics simulations and theoretical analysis to study the coalescence characteristics of bulk nanobubbles in water. We provide quantitative evidence showing nanobubble coalescence characteristics universally deviate from macroscopic bubble theories due to the small bubble size and the unique effects of Laplace pressure in nanobubbles.

Bubbles freely rising in a fluid at rest can display a variety of complex paths and shapes. We investigate experimentally their behavior in the inertial regimes obtained for a Hele-Shaw cell, where additional lateral walls are introduced to modify the cell width, and thus the coupling between the bubbles’ velocity and shape. Scaling laws characterizing the different regimes of motion are provided.

The nonlinear evolution of electrohydrodynamic flow subjected to unipolar injection in the dielectric liquid is extended from Newtonian fluids to viscoelastic fluids. The effect of viscoelasticity not only precipitates the onset of chaos but also leads to new transition sequences to chaos. Moreover, an asymmetric steady flow pattern is observed in a perfectly symmetric geometry. In viscoelastic fluids, the electric current transfer is reduced in most cases, but for weakly elastic fluid, it may be enhanced.

A depth-averaged numerical model is developed to understand the experimentally observed interplay of induced charge electroosmosis and electrothermal flow in an insulator-based dielectrophoresis microdevice. The experimentally measured nonlinear fluid velocity matches asymptotically the predicted velocity of the electroosmotic flow in a low-concentration buffer and that of electrothermal flow in a high-concentration buffer. This agreement is consistent with a scaling analysis.

The viscodiffusive McIntyre instability has been suggested as a possible source for density layer formation around laboratory and oceanic floating vortices. This suggestion is here quantitatively addressed using idealized, axisymmetric, numerical simulations of a simple Gaussian-like vortex in thermal wind balance, floating in a rotating, stratified flow.

This work revisits the liquid bridge, which was observed by Lord William G. Armstrong in 1893, from a fresh perspective of its stability and final fate in terms of its lifetime. Remarkably, a water fall and the associated effective length are strongly correlated with the breakup of the liquid bridge. The linear stability analysis of an electrified jet agrees with experiments well. These results shed light on the underlying physical mechanism and on promising technological applications via active regulation and control of a liquid bridge.

We investigate vortex shedding off an airfoil generated by pulsed actuation (or pulse modulation) of synthetic jets. This technique is shown to shed circulation in a controlled manner during dynamic stall, reducing many of its detrimental effects.

The flow of a submerged water jet directed toward the liquid interface is investigated both experimentally and theoretically. We find evidence that the presence of a small amount of surfactants can trigger an azimuthal instability. Our theoretical model reveals that surfactant advection in the Stokes regime contains the minimal ingredients to explain the instability.

The deposition of homogeneous and patterned films of partially wetting liquid from a liquid meniscus driven by Rayleigh surface acoustic waves (SAW) is analyzed with a thin-film model. Employing path continuation and time simulation we investigate, in particular, how the time-periodic states corresponding to line deposition and the related bifurcations emerge when changing the Weber number or the SAW strength describing scenarios relevant for a class of deposition and coating processes.

We show a standalone power-free technique for transporting and splitting a droplet on an open surface using continuous wettability-gradients. A three-dimensional phase-field Cahn-Hilliard model for interfaces and Navier-Stokes equations for transport are employed and solved numerically using the finite element method. We can control the droplet splitting ratio by manipulating the widths of the Y-branches. The physics of the droplet transport, flow pattern inside the droplet, and the splitting mechanisms have been explained through detailed numerical studies and scaling analysis.

We study collective motion of two hydrodynamically coupled identical pushers at a planar fluid/air interface in the presence of self-induced Marangoni flow, which is generated by insoluble surfactant, excreted by the pushers at a constant rate. Surfactant decomposes homogeneously at a constant rate. Under specific initial conditions, the pushers form a stable rotational equilibrium, whereby each pusher follows a circular path and the distribution of surfactant in the co-rotating frame of reference is stationary. In the absence of the Marangoni flow, the rotational equilibrium becomes unstable and the pushers move away from each other.

Self-similarity is a universality phenomenon exhibited from large scales (e.g., supernovae) to small scales (e.g., spreading of droplets). Viscous gravity currents in nonuniform passages exhibit an “incomplete” version of such universality. This combined theoretical–numerical–experimental study provides a theory of the dependence of the universal dynamics on the initial and boundary conditions, and demonstrates two distinct incomplete self-similar regimes in the spreading and leveling of a viscous gravity current.

Using molecular dynamics simulations we study the splash of water nanodroplets (ND) on hydrophilic to hydrophobic surfaces. Mechanisms for internal breakup and prompt splash are found to be different from those of macroscale (MS) impacting droplets. Breakup is attributed to initial air holes on solid surfaces for MS, but to vibration of a nanometer spreading film for ND. The prompt splash is initiated by air bubbles under spreading lamella at MS, but for ND by Rayleigh-Taylor instability of ejected rims from rapidly decelerated spreading lamella. ND internal breakup depends on surface wettability because vibration attenuation is larger on hydrophilic than hydrophobic surfaces.

We experimentally investigate the flow behavior of viscous oil threads in a a variety of miscible and immiscible low-molecular weight alcohols in microchannels. A comparative study is conducted between diffusive and capillary regimes using simple functional relationships for the thread characteristics, including diameter and detachment length. We develop a comprehensive classification of immiscible and miscible fluid dynamics in square microfluidic channels and provide a quantitative analysis of the evolution of multiphase flow properties across flow patterns.

Simultaneous application of flow and electric fields along a microfluidic channel can focus flexible polyelectrolyte molecules. Electrohydrodynamic interactions drive the migration to the center. Though migration velocity increases monotonically with electric field strength, the polyelectrolyte concentration at the center of the channel diminishes after exceeding a critical electric field. The mean-field model developed here demonstrates that dispersion, induced by the electric field interacting with Brownian fluctuations in the polyelectrolyte configuration, causes this phenomena.

The effect of grain size on the critical shear stress required to initiate sediment transport in erodible granular beds is typically described by the Shields number which compares the hydrodynamic stress to the particle weight. Although this framework works well for beds composed of grains of the same size, we find that it does not capture the behavior of polydisperse beds. In particular, we find that larger grains are mobilized by nominally subcritical stresses when small grains are present. Our results highlight the importance of granular contact and force networks in controlling the onset of sediment transport.

A thermodynamics-based phase-field model is developed to simulate phase separation of a binary mixture under a temperature gradient in a constant shear. The effects of meaningful dimensionless numbers, such as the capillary number, the Lewis number, and the dimensionless heat capacity are explored. The temperature gradient breaks the symmetry of phase separation compared to instantaneous quenching while different phase separation patterns, ranging from stripes to drops, can be obtained or even suppressed by a proper choice of parameters.

The torque experienced by a circular cylinder rotating steadily about an axis passing trough its centroid and perpendicular to its symmetry axis is computed over a wide range of Reynolds number and aspect ratios using fully resolved simulations. In the creeping-flow regime, numerical results are shown to match predictions of an improved slender-body approximation. In strongly inertial regimes, flow symmetries and boundary layer arguments are employed to derive scaling laws for the various contributions to the torque. We finally obtain an empirical formula for the total torque, valid throughout the parameter range explored in the simulations.

A ternary phase-field simplified multiphase lattice Boltzmann method (TPF-SMLBM) is developed in a numerical investigation of a compound droplet placed on solid substrate in shear flow at moderate Reynolds numbers. Three major kinematic modes are recovered: quasi-steady sliding (QSS), tumbling-sliding, and tumbling-detachment. Analysis of QSS dynamics explains the wetting length exponential shrinking rate in the early evolution stage. A new dimensionless parameter, the Tumbling number (Tu), is proposed to identify the mode transition towards tumbling. The dynamics of detachment is also investigated, showing that the critical Capillary number of detachments can be described by a scaling law.

Modeling realistic fluid and plasma flows is computationally intensive, motivating the use of reduced-order models for a variety of scientific and engineering tasks. However, it is challenging to characterize, much less guarantee, the global stability (i.e., long-time boundedness) of these models. In this work, we illustrate how to modify the objective function in machine learning algorithms to promote globally stable data-driven models of fluid and plasma flows. This innovation significantly extends the applicability of sparse system identification for complex dynamics, such as models of turbulent boundary layers.

In many complex fluids, the geometry of particles in suspension can be complex, prompting the need to understand how shape influences their bulk transport. We consider the Taylor dispersion of passive, elongated Brownian rods subject to a background Poiseuille flow. Monte-Carlo simulations demonstrate that elongated particles exhibit enhanced longitudinal dispersion compared to their spherical counterparts, in excellent agreement with integral expressions derived from asymptotic analysis. For particles of high aspect-ratio, the dispersion coefficient can be collapsed along a single curve, providing a simple correction factor that extends Taylor’s seminal results to elongated particles.

We report hot-wire measurements in flows of high and low turbulence intensities, both in normal and superfluid helium, at 1.6 K, 2 K, and 2.3 K. Consistent with previous studies, we observe a spectral bump at high frequency. Surprisingly, the bump frequency is found to depend on the turbulence intensity of the flow. Using the turbulent Reynolds number rather than the velocity as a control parameter collapses results from both flows.

We introduce a counter-flow turbulent channel configuration, amenable to simulation and modeling. It has periodic streamwise and spanwise boundaries and isothermal no-slip walls. A tangent hyperbolic forcing function drives the flow in opposite directions on the upper and lower halves of the channel, forming an antisymmetric mean shear velocity profile. Compared to conventional channel flows, the mean flow is inflectional and the maximum turbulence intensity relative to the maximum mean velocity is nearly an order of magnitude higher. The counter-flow channel can sustain high turbulent Mach numbers which is useful for studying high Reynolds and Mach number turbulent flows.

Swirling turbulent plumes are investigated with the Morton, Taylor, and Turner model (MTT) and the $\mathrm{\Gamma }$-approach. We derive the asymptotic solutions using regular perturbation methods, and discuss the influence of swirling motions on the plume properties for lazy and forced plumes, respectively. Specially and intriguingly, by introducing a swirl, a forced plume can even be turned into a lazy one in the near field during the vertical evolution.

We study the effect of both uniform spanwise and streamwise magnetic fields on the near wall region of a turbulent channel flow. Previous results have shown that the spanwise magnetic field leads to flow relaminarization for magnetic intensity significantly smaller than the streamwise magnetic field. In order to explain these results, a deep analysis of the fine turbulence structure is needed. We perform a detailed analysis through the Reynolds shear-stress transport equations and the conditional averaging deduced from the near wall active eddies, thus connecting the magnetic field orientation effect to the coherent electric current topology.

We develop a wavelet-based adaptive wall-modeled large eddy simulation (WA-WMLES) method to overcome the stringent restriction on step size for time integration, caused by mesh resolution requirement to resolve inner viscous sublayer, which becomes computationally expensive as the Reynolds number increases. This approach uses a wavelet-based adaptive large eddy simulation, incorporated into the anisotropic-adaptive wavelet collocation framework, to resolve the outer region of turbulent boundary layer, while the inner part is approximated by the wall-shear-stress model, and extends the application of the wavelet-based adaptive methods to a realistic wall-bounded turbulent flow configuration at a relatively high (order of a million) Reynolds number.

Reduced models describing the Lagrangian dynamics of the Velocity Gradient Tensor (VGT) in Homogeneous Isotropic Turbulence (HIT) are developed under the Physics-Informed Machine Learning (PIML) framework. We construct the pressure Hessian and sub-filter contributions using the integrity bases and invariants of VGT and express them with extended Tensor Basis Neural Network (TBNN). We observe that the PIML model provides an improved representation for the magnitude and orientation of the small-scale pressure Hessian contributions. Statistics of the flow, as indicated by the joint PDF of second and third invariants of the VGT, show good agreement with the “ground-truth” DNS data.

How water surface waves grow under wind forcing has long been an interesting and challenging question. For short gravity-capillary waves, the viscous effects are important but have not been well studied. In this paper, we simulate the wind-wave growth by directly solving the two-phase Navier-Stokes equations. The numerical method features a momentum conserving scheme, interface reconstruction using Volume of Fluid, and adaptive mesh refinement (AMR). As a result, we observe concurrent growth of the irrotational traveling wave and the rotational drift layer (current). The growth rate of the wave and the evolution of the drift layer under different forcing parameters are discussed respectively.