The study of transport phenomena, using nondestructive imaging technologies and simulations of fluid flow through complex geometries, has become increasingly vital, particularly in the biomedical domain. Such approaches provide valuable insight into critical processes, including blood perfusion of tissues, drug delivery, and extracellular transport, contributing to our understanding of physiology and the design of medical interventions. However, significant challenges persist in extracting geometry from imaging to reconstruct flow domains for use in direct simulations. Recent advancements in machine learning offer a promising solution by reconstructing domain geometry based on relatively sparse sampling of flow velocity. Motivated by this, we apply deep learning techniques to predict the shape and location of arbitrary bluff obstacles placed in a two-dimensional (2D) channel flow, utilizing convolutional neural networks (CNNs). A CNN is trained on the velocity or concentration field acquired from 2D Lattice Boltzmann simulations. We investigated various scenarios by adjusting CNN input and sparsity, focusing first on the $x$-component of the velocity field, then showing that the CNN performs similarly when applied to the concentration field. Future work will extend this methodology to experimental data to aid in the development of quantitatively accurate predictive models of transport in complex geometries, with numerous applications in biomedical transport and beyond.

Organisms often swim through fluids that are spatially inhomogeneous. If the fluids are polymeric, gradients in polymer concentration may lead to gradients in both fluid viscosity and elasticity. In this Letter, we present theoretical results for the dynamics of active particles, biological or otherwise, swimming through spatially inhomogeneous viscoelastic fluids. We model the active particles using the squirmer model, and show that spatial variations in fluid relaxation time lead to a mechanism for reorientation and taxis in viscoelastic fluids, which we refer to as a form of durotaxis in fluids.

We present a heuristic derivation of the maximal Lyapunov exponent $\gamma$ of homogeneous turbulence which yields two new relations, a sweeping relation and the scaling of the uncertainty field's integral length $L_{\mathrm{\Delta }}$. These relations and the maximal Lyapunov exponent's scaling that they imply are confirmed by periodic turbulence simulations. As the Reynolds number ${\mathrm{Re}}_{\lambda }$ increases, $L_{\mathrm{\Delta }}$ and ${\gamma }^{-1}$ decrease towards values smaller than the Kolmogorov length and time scales.

Spatiotemporally complex flows are found at the onset of unsteadiness in (axisymmetric) rotor-stator turbulence in the shape of concentric rolls. The emergence of these rolls is rationalized using a homotopy approach, where the original flow configuration is continuously deformed into a simpler, better understood configuration. We deform here rotor-stator flow into an annular flow, thereby controlling curvature effects, and we investigate numerically the transition scenarios as functions of the Reynolds number. Increasing curvature starting from the planar limit reveals a clear path towards a subcritical scenario as a function of the Reynolds number. As the rotor-stator configuration is approached, supercritical branches shift to increasing Reynolds number while a subcritical branch of chaotic states takes over. Modal selection in the supercritical scenario involves the competition between two modal families. It rests on a specific radial localization property of all eigenmodes, linked to the space-dependent convective radial velocity which intensifies as curvature is increased. A nonlinear mechanism for the pairing of rolls is proposed based on multiple resonances. The critical point where the original rotor-stator flow loses its stability to axisymmetric perturbations is identified for the geometry under study.

In deep-sea mining operations, the discharge of sediment plumes significantly impacts the ocean environment, thus necessitating precise evaluation. In this work, we conduct large-eddy simulations to investigate sediment transport in deep-sea mining, focusing on the influence of the vehicle wake and various control parameters, including vehicle speed, discharge rate, and vehicle elevation relative to the seafloor, on the evolution of turbidity current. Our simulation demonstrates that the interaction between turbidity current and vehicle's downstream vortical wake strongly affects the distribution of fluid kinetic energy and sediment concentration. The vehicle wake enhances the sediment diffusion and reduces the descending velocity of the current downstream, resulting in a larger region of sediment contamination. We find that the current propagation in the streamwise direction can be approximately predicted by the axisymmetric box model, while the propagation in the lateral direction is characterized by the two-dimensional box model. Depending on the ratio of vehicle velocity to discharge velocity, the propagation of turbidity current transitions from a constant-rate influx to a fixed-volume influx. In statistically stationary states, both the mean and standard deviation of concentration fields exhibit self-similar behavior with respect to the streamwise location and control parameters. Additionally, by comparing seafloor wall shear stress across different simulations, we provide guidance for mitigating unfavorable operating conditions in deep-sea mining activities. These results, which provide important information for modeling the far-field sediment dispersion, are crucial for accurately assessing the large-scale environmental impact of deep-sea mining.

Here we employ direct numerical simulation to examine the transitional flow characteristics influenced by a three-dimensional rough surface and pressure gradient. Three types of skewness are designed for the rough surface, strategically positioned upstream of the laminar separation bubble (LSB), adjacent to the separation point, and within the bubble itself, aiming to elucidate the disparities in the transition mechanisms beneath varying skewness and surface locations, as well as the underlying reasons. The findings indicate that the frictional resistance associated with positive skewness exceeds that of negative skewness, and the surface force is more sensitive to negative skewness than to positive skewness. These are independent of the rough surface's location relative to the LSB. Negative skewness not only enhances the continuity of the transverse secondary flow, but also amplifies the spatial heterogeneity in streamwise and wall-normal directions when the rough surface is positioned in proximity to the separation point. The underlying mechanism is an increase in the velocity gradient within the free shear layer (FSL), which provokes spanwise rollers at the LSB's trailing edge and fosters the growth of inviscid instability. Conversely, positive skewness has a contrasting impact. Provided the overall height of the rough surface does not transcend the FSL, positioning the rough surface within the LSB markedly extends the LSB and postpones the downstream onset of transition, a phenomenon unaffected by skewness or the flow characteristics over the rough surface. Within the context of linear dynamic approximation, rough surfaces located near the separation point may augment the intensity of disturbances, yet the degree of quasiorthogonality in the modes is inferior to that observed with rough surfaces situated ahead of the separation point. This aligns with the resonant disturbance induced by positive skewness, essentially indicating that convective instability is mitigated by backflow.

A drop impacting on a superhydrophobic surface acquires an electrical charge. The magnitude of this charge depends both on the hydrodynamics of the impact and on the physicochemical properties of the liquid. Despite its relevance in nature and industry, fundamental understanding of the mechanisms at play in liquid-solid contact electrification remains elusive. Here, we measure the charge acquired by an impacting drop and perform a parametric study by varying drop size, impact speed, salt concentration, viscosity, and liquid conductivity. Our results for pure water confirm that the contact surface area is the dominant hydrodynamic control parameter for charge acquisition [Diaz et al., Soft Matter 18, 1628 (2022)], but drops with varying chemical composition stray away from these predicted trends. We then demonstrate that the amplitude of acquired charge depends directly on a coupling between electric charge transport and hydrodynamic parameters, and more specifically on the ratio of the hydrodynamic impact time and the electrical discharge time.

Direct numerical simulations have been conducted to investigate the influence of shear effects on the Rayleigh-Bénard convection of liquid metal in a cuboid vessel within an aspect ratio of 4 under strong horizontal magnetic fields, where the Rayleigh number is fixed at ${10}^6$, Prandtl number $\text{Pr}=0.025$, Hartmann number varying from 1000 to 4000, and the wall shear Reynolds number ranging from 0 to 60 000. According the intensity of the shear effects, three typical flow regimes, i.e., competition regime, buoyancy-dominated regime, and shear-dominated regime, have been detected. In the buoyancy-dominated regime, multiple turbulent states emerge, with changes in magnetic field strength influencing the stability regions of these states and altering the large-scale circulation (LSC) structure. The underlying mechanisms governing these turbulent states have been thoroughly explained through elliptical instability analysis. During the competition regime, characteristic phenomena such as “vortex reconnection” and “vortex proliferation” occur, characterized by alternating four-vortex and five-vortex patterns, which influence the flow and heat transfer characteristics. And proper orthogonal decomposition analysis is employed to examine structural changes caused by instability, identifying dominant modes responsible for the observed changes in vortex patterns. When shear becomes dominant, the LSCs undergo reorganization, leading to reduced flow fluctuations and enhanced heat transfer performance. In addition, energy budget analysis reveals that increasing magnetic field strength extends the shear-dominated regime while contracting the energy competition phase.

We perform a linear stability analysis to investigate the double diffusive convection stability of a density-stratified fluid contained in an inclined slot subjected to a lateral temperature gradient. The inclination angle ($\theta$) changes from −80° to ${80}^{\circ }$ relative to the vertical. The results reveal an asymmetrical behavior in stability with respect to $\theta =0^{\circ }$. The base flow is less stable when heating is applied to the upper wall (negative $\theta$) compared to heating the lower wall (positive $\theta$). For small solute gradients, there is a critical inclination angle, $\theta =65.8^{\circ }$, at which the thermal gradient required to initiate instability undergoes a steep decline. At intermediate solute gradients, the thermal and solute gradients compete to dominate stability, leading to multiple transitions at which different instability modes emerge and replace one another. For large solute gradients, the critical thermal and solute gradients increase simultaneously following a relationship that approaches an asymptotic limit, which is hardly influenced by inclination angle.

The fluid-structure interactions (FSI) generated by impinging shock boundary-layer interactions (SBLI) over a flexible panel are studied to capture the panel vibration effects on the flow field and vice versa. A 1-mm-thick steel panel was employed to generate the FSI and the flow conditions ensured that the panel oscillation amplitude was much smaller than the boundary-layer thickness and plate thickness. An impinging oblique shock was generated by an $8^{\circ }$ shock generator placed incident on a Mach-2.5 flow. Two-dimensional pressure fields over the panel surface and wall-normal deflection at discrete panel locations were simultaneously measured at 10 kHz. Proper orthogonal decomposition and spectral proper orthogonal decomposition (SPOD) methods were employed on the measured pressure fields to analyze the dynamics of the SBLI unit and its feedback coupling with the panel oscillations. Analysis of the eigenspectrum revealed elevations in the vicinity of the panel elastic modes. Visualization of the dominant SPOD modes at the panel elastic frequencies revealed an increased spanwise correlation in the intermittent region that extended almost across the entire panel span. The time evolution of the first SPOD mode at panel elastic modes revealed a streamwise propagating modal peak; by contrast, a predominantly spanwise motion was observed at other frequencies. These observations evidence the promotion of two-dimensionality in the SBLI unit at the panel elastic modes due to the fluid-structure interactions.

We experimentally investigate how vortex rings, generated and propagating within a water tank, interact with the water-air interface. Near-perfect reflections of these vortex rings occur when they approach the interface at a sufficiently large incident angle. To understand this interaction, we employ a vortex-sheet-vortex-pair model in numerical simulations, which captures the essential dynamics. Additionally, a simplified model based on the conservation of flux or momentum provides further insight into the mechanism behind the vortex-ring reflection. Through combined approaches—experimentation, numerical simulation, and detailed analysis—we gain a deeper understanding of how vortex rings interact with free boundaries.

We analyze the representation of viscous stresses in the one-fluid formulation of the two-phase Navier-Stokes equations, the model on which all computational approaches making use of a fixed mesh to discretize the flow field are grounded. Recognizing that the Navier-Stokes-like equations that are actually solved in these approaches imply a spatial filtering, we show by considering a specific two-dimensional flow configuration that the proper representation of the viscous stress tensor requires the introduction of two distinct viscosity coefficients, owing to the different behaviors of shear and normal stresses in control volumes straddling the interface. Making use of classical results of continuum mechanics for anisotropic fluids, we derive the general form of the constitutive law linking the viscous stress tensor of the two-phase medium to the filtered strain-rate tensor, and take advantage of the findings provided by the above two-dimensional configuration to close the determination of the fluid-dependent coefficients involved. Predictions of the resulting anisotropic model are then assessed and compared with those of available ad hoc models against original experimental results obtained in a reference flow in which some parts of the interface are submitted to shear while others are mostly controlled by stretching. The selected configuration corresponds to a viscous buoyancy-driven exchange flow in a closed vertical pipe, generated by unstably superimposing two immiscible fluids with a large viscosity contrast and negligible interfacial tension and molecular diffusivity. Using different levels of grid refinement, we show that the anisotropic model is the only one capable of predicting correctly the evolution of the front of the ascending and descending fingers at a reasonable computational cost. We confirm this conclusion on a one-dimensional counter-current channel flow with a large viscosity contrast, and use this simple configuration to establish that the anisotropic model converges quadratically as the grid is refined, while the familiar ad hoc model based on an arithmetic averaging of the fluid viscosities only converges linearly.

We study the dynamics of sail membranes during a model of a tacking maneuver, when the sail angle of attack is reversed in order to sail upwind. In successful tacking the sail flips to the mirror-image shape, while in unsuccessful tacking the sail remains stuck in a metastable state close to the initial shape. We investigate whether the sail flips, and if so, how long it takes and the subsequent dynamics, over a parameter space that describes the sail membrane properties and the kinematics of tacking. We find that the “steady” parameters—stretching rigidity, pretension, and angle of attack—mostly determine whether a membrane flips or not. Flipping is more likely with larger values of the stretching rigidity, pretension, and angle of attack. The dynamical parameters—membrane mass density, concavity of angle-of-attack transition kinematics, and time length of the tacking maneuver—mainly affect how long flipping takes. With large membrane mass the membrane can maintain the momentum from the tacking motion long enough to reach the flipped state, but it may also take longer to converge to a steady shape. Concave-down angle-of-attack profiles and small tack times are generally associated with shorter flip times but a few exceptions exist, because these kinematics can also give a larger acceleration to the fluid-sail system that persists for longer times. We also investigate slack sails and find that they are more difficult to flip.

The mixing properties of vapor content, temperature, and particle fields are of paramount importance in cloud turbulence as they pertain to essential processes, such as cloud water droplet evaporation and entrainment. Our study examines the mixing of a single cloudy air (which implies droplet-laden) filament with its clear air environment, a characteristic process at the cloud edge, in two ways. The first consists of three-dimensional combined Euler-Lagrangian direct numerical simulations which describe the scalar supersaturation as an Eulerian field and the individual cloud water droplets as an ensemble of Lagrangian tracers. The second way builds on the recently developed diffuselet method, a kinematic Lagrangian framework that decomposes a scalar filament into a collection of small sections subject to deformation by local stirring and cross-sheet diffusion. The Schmidt number is $\text{Sc}=0.7$. The entrainment process causes a deformation of the supersaturated cloud filament in combination with diffusion until the system reaches a well-mixed equilibrium state, which implies for the present configuration that all droplets are evaporated. We compare the time dependence of the mean square and probability density function of the supersaturation field. For the initial period of the mixing process, they agree very well; at later stages, deviations caused by nonzero mean of the conserved scalar are observed. For the cases including cloud water droplets, we also investigate the impact of droplet number density and condensation growth response. Turbulence causes deviations from the $d^2$ law similar to recent experiments in sprays. A simulation at a Schmidt number that is by a factor of 100 larger than in clouds improves the agreement between simulation and diffuselet method significantly. The latter result promotes the diffuselet framework as an efficient parametrization for turbulent high-$\text{Sc}$ mixing which can reduce the resolution efforts of the viscous-convective range of scalar turbulence.

Fluid-structure interaction (FSI) in elastic vessels occurs in a wide range of systems in nature and technology. A difficulty in the development and validation of FSI models is the lack of quantitative measurements of vessel response to unsteady flow forcing. We here investigate the canonical case of an elastic tube subject to laminar pulsatile flow. For this purpose, we develop an experimental setup comprising a high-precision piston, a three-dimensional (3D)-printed elastic pipe, and a camera equipped with a microscope objective to determine the wall displacement. We find that for weak forcing the response is similar to a forced damped harmonic oscillator. Near resonance and for moderate forcing amplitudes, the wall motion exhibits complex dynamics, including multiple frequencies and nonaxisymmetric tube deformation. When the amplitude of the response exceeds a threshold, the tube collapses nonaxisymmetrically during parts of the cycle, thereby drastically reducing the cross-sectional area of the tube. We additionally perform fully coupled axisymmetric numerical simulations based on the solution of the Navier-Stokes equations and a thin-shell model for the tube. Our simulations agree with experimental results, except near resonance and under large amplitude forcing, where a 3D model accounting for structural damping would be necessary. Our results shed light on the rich nonlinear dynamics of this canonical system and serve as a basis to validate future models.

A systematic asymptotic analysis of the Boltzmann equation for monatomic ideal gases is carried out under the conditions that the mean free path of gas molecules and the external force are both small, and the results are compared with the Boussinesq approximation of the conventional fluid dynamics. Under a suitable scaling that recovers the finite Rayleigh number, a fluid-dynamic-type set of equations similar to the one for the Boussinesq approximation is obtained. However, the obtained energy equation is not the same as that in the usual Boussinesq approximation. The difference implies that the usual Boussinesq approximation fails to correctly take account of the work done by the pressure. This difference affects the flow field as well through the buoyancy effect. Numerical simulations are carried out to demonstrate the quantitative impact of the difference.

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

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

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

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