We simulate a spheroidal swimmer through a complex fluid, modeled by the Giesekus constitutive equation incorporating fluid inertia. We develop a spheroidal swimmer model and exert it in a direct-forcing fictitious domain method framework. This model extends the conventional spherical “squirmer,” representing a microswimmer generating self-propulsion through tangential surface waves at its boundaries. We vary the swimmer's aspect ratio (AR) and Weissenberg number (Wi; the ratio of fluid elastic force to viscous force), respectively, in the range of $1.5\le \mathrm{AR}\le 8$ and $0.5\le \mathrm{Wi}\le 10$. Our results show that, an inertial spheroidal puller with a small $\left|\beta \right|$ (a swimming intensity parameter) swims faster than the counterpart subjected to the Stokes flow regime—a departure from the observed pattern in spherical pullers. Within the Giesekus fluid medium, an augmented mobility factor α correlates with an increased squirmer velocity, while a larger AR contributes significantly to the speed enhancement of a neutral squirmer in the presence of fluid inertia. Meanwhile, we explore the squirmer's energy expenditure and hydrodynamic efficiency, finding that a slenderer, inertial squirmer with a vigorous swimming intensity expends more energy, contrasting with the reduced energy expenditure associated with a smaller intensity. Notably, a larger AR positively correlates with squirmer efficiency, displaying an advantageous relationship with swimming speed.

This work investigates impacting nanodroplets on pillared surfaces via molecular dynamics (MD) simulations, especially to understand the intrusion effect of liquid in pillar gaps at the nanoscale, by comprehensively revealing outcome regimes and modeling the maximum spreading factor $\left({\beta }_{\max }\right)$. A total of six outcomes, including first sticky (1S), second sticky (2S), first nonbouncing (1NB), second nonbouncing (2NB), first bouncing (1B), and second bouncing (2B), are identified. The 1S, 2S, and 2B regimes take place on monostable Wenzel surfaces with the Wenzel-to-Cassie dewetting transition and bouncing boundaries separating them; the 1NB, 2NB, 1B, and 2B regimes occur on monostable Cassie surfaces, distinguished by the Cassie-to-Wenzel wetting transition and bouncing boundaries. By establishing criteria of all boundaries, a universal phase diagram of impacting nanodroplets on pillared surfaces is constructed. Besides, to understand the altered spreading dynamics by the liquid intrusion effect, ${\beta }_{\max }$ is modeled. The bulk droplet above pillared surfaces is found to have the same spreading dynamics as a nanodroplet on flat surfaces, which decouples the effects of the bulk droplet and the liquid intruding into pillar gaps. Subsequently, two intrusion regimes are classified based on different intrusion morphology of the liquid front, and the scalings for intrusion volume in different intrusion regimes are obtained with the corresponding transition criterion being proposed. Eventually, scaling laws of ${\beta }_{\max }$ for impacting nanodroplets on pillared surfaces are established by incorporating the volume term of the bulk droplet, and are in good agreement with all available MD data of ${\beta }_{\max }$, showing their strong robustness and universality.

Injection of liquid foam through soils is increasingly used in applications such as soil remediation or soil improvement, where it is also crucial to control the liquid relative permeability through the foam-filled soil. We have measured the time dependence of the liquid permeability of granular packings initially filled with liquid foam for different values of the liquid saturation. It is shown that, systematically, permeability increases significantly over time before reaching saturation. We have demonstrated that this evolution is directly related to the coarsening of the liquid foam confined in the pore space. We have shown how the evolution of the liquid permeability can be predicted from the knowledge of the bubble size evolution.

The dynamic model is one of the most successful inventions in subgrid-scale (SGS) modeling as it alleviates many drawbacks of the static coefficient SGS stress models. The model coefficient is often calculated dynamically through the minimization of the Germano-identity error (GIE). However, the driving mechanism behind the dynamic model's success is still not well understood. In wall-bounded flows, we postulate that the principal directions of the resolved rate-of-strain tensor play an important role in the dynamic models. Specifically, we find that minimization of the GIE along only the three principal directions (or less), in lieu of the nine components in its original formulation, produces equally comparable results as the original model when examined in canonical turbulent channel flows, a three-dimensional turbulent boundary layer, and a separating flow over periodic hills. This suggests that not all components of the Germano identity are equally important for the success of the dynamic model, and that there might be dynamically more important directions for modeling the subgrid dynamics.

The viscoelastic relaxation time of a polymer solution is often measured using capillary breakup extensional rheometry (CaBER) where a droplet is placed between two plates which are pulled apart to form a thinning filament. For a slow plate retraction protocol, required to avoid inertio-capillary oscillations for low-viscosity liquids, we show experimentally that the CaBER relaxation time ${\tau }_e$ inferred from the exponential thinning regime is in fact an apparent relaxation time that may increase significantly when increasing the plate diameter and the droplet volume. Similarly, we observe that ${\tau }_e$ increases with the plate diameter for the classical step-strain plate separation protocol of a commercial (Haake) CaBER device and increases with the nozzle diameter for a dripping-onto-substrate (DoS) method. This dependence on the flow history before the formation of the viscoelastic filament contradicts polymer models such as Oldroyd-B that predict a filament thinning rate $1/3\tau$ ($\tau$ being the model's relaxation time), which is a material property independent of geometrical factors. We show that this is not due to artifacts such as solvent evaporation or polymer degradation and that it can be rationalized by finite extensibility effects (FENE-P model) only for a dilute polymer solution in a viscous solvent, but not for semidilute solutions in a low-viscosity solvent.

Two micron-sized water droplets approaching each other do not always coalesce due to the cushioning effect of the air between them. When the droplets do not carry any electrical charges, one needs to consider the breakdown of hydrodynamics at very small scales to decide whether the droplets collide and coalesce or not. In contrast, two approaching droplets that are oppositely charged always coalesce if the charges are large enough. To find the charge for which the transition to charge-dominated collisions occurs, we computed the collision efficiency of charged, hydrodynamically interacting droplets settling in quiescent air, including the noncontinuum regime at small interfacial distances. For oppositely charged droplets, we find that the transition occurs when a saddle point of the relative droplet dynamics exits the region within which the continuum hydrodynamics breaks down. For cloud droplets with radii 16 and $20\mu \mathrm{m}$, we observe that the transition occurs at $\sim {10}^3$ elementary charges $e$. For charges smaller than this, we predict that the coalescence rate depends primarily upon the Knudsen number ($\mathrm{Kn}$, the ratio of the mean-free-path of air to the mean droplet radius), whereas coalescence for much larger charges does not depend upon $\mathrm{Kn}$. For droplets charged with the same polarity, we find the critical charge to be substantially larger ($\sim {10}^{4}e$ for the above radii) for reasons that we discuss.

Most of the studies on pressure fluctuations in wall-bounded turbulent flows aim at obtaining statistics as power spectra and scaling laws, especially at the walls. In the present study we study energetic coherent pressure structures of turbulent channel flows, aiming at a characterization of dominant coherent structures throughout the channel. Coherent structures are detected using spectral proper orthogonal decomposition (SPOD) and modeled using resolvent analysis, similarly to related works dealing with velocity fluctuations but this time using pressure fluctuations as the output of interest. The resolvent operator was considered with and without the Cess eddy-viscosity model. Direct numerical simulations (DNSs) of incompressible turbulent channel flows at friction Reynolds numbers of approximately 180 and 550 were employed as databases in this study. Three representative dominant structures emerged from a preliminary spectral analysis: near-wall, large-scale, and spanwise-coherent structures. For frequency–wave number combinations corresponding to these three representative structures, SPOD results show a strong dominance of the leading mode, highlighting low-rank behavior of pressure fluctuations. The leading resolvent mode closely agrees with the first SPOD mode, providing support to studies that showed better performance of resolvent-based estimators when predicting pressure fluctuations compared to velocity fluctuations [Amaral et al., J. Fluid Mech. 927, A17 (2021)]. The dominant mechanisms of the analyzed modes are seen to be the generation of quasistreamwise vortices with pressure fluctuations appearing close to vortex centers. A study on the individual contributions of the nonlinear terms (treated as forcing in resolvent analysis) to the pressure output reveals that each forcing component plays a constructive role to the input-output formulation, which also helps understanding the weaker role of forcing “color” in driving pressure fluctuations.

The computation of the second-order mean wave drift loads on a body with thin perforated shells is fundamental and relevant to a wide range of applications in marine engineering, marine aquaculture, offshore renewable energy, etc. In this work, formulations involving a control surface at a distance from the body are proposed to compute drift loads on structures composed of an impermeable hull and a perforated surface accurately and efficiently. Applications of mathematical identities and conservation of fluid momentum are proved to yield identical formulations. Due to the presence of perforated shells, an integral caused by the dissipation through perforated surfaces is included in the formulation. The present formulation cannot only give all six components of the mean wave drift force and moment, but also determine the drift loads on each individual body of a multibody system. The developed formulations are applied to a series of structures, including single-body and multibody systems. It is found that the perforated surface integral plays a secondary role in the computation of drift loads. Besides, perforating body surfaces can mitigate the near-trapped wave motion in a multibody system. Compared to a fixed system, the mean wave drift loads can be amplified around the resonance frequencies of body motions. The dissipation through the perforated shell can enhance the damping effect and suppress the excessive motion response, resulting in a reduction in the amplified drift loads.

Capillary imbibition underpins many processes of fundamental and applied relevance in fluid mechanics. A limitation to the flow is the coupling to the confining solid, which induces friction forces. Here we study the effect of coating the solid with a liquid lubricant layer. Using a theoretical framework, we show that for sufficiently small lubricant viscosity, dissipation entirely occurs in the lubricant layer, resulting in a linear growth of the advancing front. We extend our study to forced imbibition, where the same mechanism gives rise to an exponential front growth. This new ability to control multiphase flows in confinement opens new opportunities for flow control in micro and nanofluidic devices.

We report experimental results on the dynamics of large bubbles in a Hele-Shaw cell subject to various inclination angles with respect to gravity. Low Reynolds number cases are studied by injecting bubbles in a stagnant water/UCON mixture in three different Hele-Shaw cell geometry. The leading order rise speed $v_b$ follows the Taylor-Saffman limit which is inversely proportional to the viscosity $\eta$, but directly proportional to the square of the cell gap $h$ and the effective gravity, accounting for cell tilt angle $\theta$. However, when the cell is increasingly inclined, the bubble buoyancy in the cell gap leads to a substantial decrease in the rise speed, as compared to the Taylor-Saffman speed. Buoyancy pushes the bubble toward the top channel wall, whereby a difference between the lubrication film thickness on top of and underneath the rising bubble occurs. We attribute these observations to the loss of symmetry in the channel gap, due to cell inclination. Nonetheless, the top lubrication film is observed to follow the Bretherton scaling, namely, ${(\eta v_b/\sigma )}^{2/3}$, where $\sigma$ is the liquid surface tension while the bottom film does not exhibit such a scaling. Finally, we illustrate that a model incorporating a friction term to the power balance between buoyancy and viscous dissipation matches well with all experimental data.

The electrochemical separation of charged species is becoming increasingly relevant for industry. A developing set of promising technologies in this space centers around the utilization of deionization shocks in porous, charged materials. To date, primarily homogeneous media have been investigated; however, heterogeneities are present in many porous structures and have been hypothesized to improve performance. Throughout this study, we demonstrate that heterogeneity in the porous structure area density and surface charge density of a crossflow shock electrodialysis cell leads to substantial vortex formation in the depletion zone. Vortices are dependent on the extent of alternating high and low permeabilities, in addition to the expanse of the depletion zone, greatly affecting performance. Heterogeneities in the geometry of the media may lead to an increased selectivity at lower energy input and also exert a strong influence when hierarchical structures are present.

Biofilament-motor protein complexes are ubiquitous in biology and drive the transport of cargo vital for many fundamental life processes at the cellular level. As they move, motor proteins exert compressive forces on the filaments to which they are attached. If the filament is clamped or tethered in some way, this force leads to buckling and a subsequent range of dynamics. The follower force model, in which a single compressive force is imposed at the filament tip, is a simple filament model that is becoming widely used to describe an elastic filament, such as a microtubule, compressed by a motor protein. Depending on the force value, one can observe different states including whirling, beating, and writhing, though the bifurcations giving rise to these states are not completely understood. In this paper, we utilize techniques from computational dynamical systems to determine and characterize these bifurcations. We track emerging time-periodic branches and identify quasiperiodic states. We investigate the effect of filament slenderness on the bifurcations and, in doing so, present a comprehensive overview of the dynamics which emerge in the follower force model.

We experimentally investigate the buoyant miscible injection of a heavy viscoplastic fluid with moderate yield stresses into a lighter Newtonian fluid, via an eccentric inner pipe inside an inclined closed-end outer pipe. To capture the flow dynamics, we employ nonintrusive methods, including camera imaging and ultrasound Doppler velocimetry. Our analysis reveals that the flow behavior is governed by a set of dimensionless flow parameters: Reynolds number, Froude number, inclination angle, Bingham number, and viscosity ratio. Using a dimensionless plane that elegantly combines the aforementioned dimensionless numbers, we successfully identify and categorize various flow regimes, such as stable and unstable slumping, separation, and diffusive and nondiffusive mixing. We analyze these flow regimes and quantify their transition boundaries. Our analysis also considers the distinct characteristics of these flow regimes, focusing on interfacial velocities, including the heavy fluid front velocity, the separated piece velocity, and the backflow front velocity, and examines the flow velocity field and mixing index.

The natural frequency of an interface between a bilayer of immiscible fluids is shown to depend on the morphology of the bottom wall in addition to the density difference of the fluids, the interfacial tension, the fluid depths, and the disturbance wave number. To take into account deep wall-wave amplitudes and the viscosities of the fluids, a reduced-order method is employed that assumes the thickness of the bilayer to be small in comparison to the container width. A key result is that the wavy wall is shown to lower the natural frequencies unless the number of waves of the wall pattern is twice that of the number of waves at the interface. In addition, there are no restrictions on the types of interfacial modes that can be obtained. These theoretical findings carry over to the resonant frequency determined by parametric excitation, i.e., Faraday excitation. The theoretical results are qualitatively validated by physical experiments that use Faraday excitation over frequency ranges to obtain different interfacial modes under conditions that approximate slippery sidewalls. As a result of the shift in the resonant frequency there is a shift in the instability regions when fluid layers are subject to Faraday excitation.

Through boundary integral simulations, we investigate, in the creeping flow limit and in the absence of Brownian noise, the effects of Navier slip on the orientational dynamics and effective shear viscosity of a semidilute suspension of two-dimensional particles with either circular or elongated (platelike) shape, interacting only via hydrodynamic and contact forces. We have recently shown that it is theoretically possible for a dilute system of slip platelike particles to display an effective shear viscosity smaller than the viscosity of the suspending fluid. This large viscosity reduction is primarily due to the suppression of the tumbling motion predicted for a no-slip particle and the attainment of a stable orientation. In this paper, we show that the effect of particle-particle interaction at semidilute concentrations is to cause the particles to fluctuate about the stable orientation and, above a threshold solid fraction $c_{\text{crt}}$, to tumble. As a consequence, a sharp increase in the effective shear viscosity with solid fraction $c$ occurs for $c>c_{\text{crt}}$. Our results suggest that, for a given particle aspect ratio, there is a value of $c$ that maximizes the reduction in the effective shear viscosity of the suspension.

The presence of interparticle cohesion can drastically change the behavior of granular materials. For instance, powders are challenging to handle, and one can make a sandcastle using wet grains. In this study, we report experimental results for columns of model cohesive grains collapsing under their own weight in air and spreading on a rough horizontal surface. The effects of two different sources of interparticle cohesion on two collapse geometries are compared and characterized in a common framework. Grains are made cohesive by adding a small amount of water, such that they are in the pendular state, or by applying a polymer coating. The effects of cohesion are reported for a cylindrical column that spreads unconfined axisymmetrically and a confined rectangular column that flows in a single direction. A dimensionless number, comparing macroscopic cohesive strength to particle weight, is shown to capture the effects of cohesion on the final morphology. To this end, a characterization of the cohesive strength of the granular materials is obtained, independent of the physical source of cohesion at the particle scale. Such a framework allows for a common description of cohesive granular materials with different sources of cohesion.

Gravity currents are ubiquitous in polar regions and marginal seas and play a crucial role in the formation of deep waters in the ocean. They contribute to the vorticity and energy transfers towards the ocean interior. We present results from an experimental study on downslope intruding gravity currents into an initially two-layer stably stratified ambient on a rotating platform at high buoyancy Reynolds numbers. We identify a turbulent process for the downslope transport, intermittent and localized, which takes the form of cascading. This process is intrinsic to rotating gravity currents, i.e., it arises without any external tuning, and the related transport does not exhibit any characteristic length scale, suggesting self-organized criticality. The cascading intrusion mechanism reveal to be the main contributor to the vorticity and turbulence in the ambient interior, with a dependence on the Coriolis parameter $f$ and the density anomaly to the surrounding ambient. Two mechanisms for vorticity production are recognized: first, the spreading of the intrusion from cascading into the interior and, second, the meandering and breakup of the deep boundary current (formed from downward Ekman transport) induced by intrusion from cascading. When the intrusion spreads at the pycnocline only, anticyclonic eddies are formed in the intrusion and top layers, whereas for intrusions spreading through the full bottom layer, vortices of both signs are generated due to bottom friction. The turbulence in the receiving ambient reveals to be horizontally isotropic, nonstationary, and nonhomogeneous. Energy is injected through the intrusion issued by cascading at the penetration length scale $L_p$ and forces the turbulence in the intrusion area close to the slope. The central area far from the boundaries is characterised, instead, by freely evolving two-dimensional turbulence, forced at large scales. These results suggest a complementary way to interpret oceanic observations of gravity currents spreading in the ocean interior.

The verification of whether small-scale turbulence is isotropic remains a grand challenge. The difficulty arises because the presence of small-scale anisotropy is tied to the dissipation tensor, whose components require the full three-dimensional information of the flow field in both high spatial and temporal resolution, a condition rarely satisfied in turbulence experiments, especially during field scale measurement of atmospheric turbulence. To circumvent this issue, an intermittency-anisotropy framework is proposed through which we successfully extract the features of small-scale anisotropy from single-point measurements of turbulent time series by exploiting the properties of small-scale intermittency. Specifically, this framework quantifies anisotropy by studying the contrasting effects of burstlike activities on the scalewise production of turbulence kinetic energy between the horizontal and vertical directions. The veracity of this approach is tested by applying it over a range of datasets covering an unprecedented range in the Reynolds numbers $(\mathrm{Re}\approx {10}^3–{10}^6)$, sampling frequencies (10 kHz to 10 Hz), surface conditions (aerodynamically smooth surfaces to typical grasslands to forest canopies), and flow types (channel flows, boundary-layer flows, atmospheric flows, and flows over forest canopies). For these diverse datasets, the findings indicate that the effects of small-scale anisotropy persists up to the integral scales of the streamwise velocity fluctuations and there exists a universal relationship to predict this anisotropy from the two-component state of the Reynolds stress tensor. This relationship is important towards the development of next-generation closure models of wall turbulence by incorporating the effects of anisotropy at smaller scales of the flow.

The dynamics and energy-harvesting capacity of fixed-free plates covered with piezoelectric materials in oscillatory cross flows are investigated numerically by using a coupled fluid-structure-electric model. The focus is on the effect of hydrodynamic interaction within a formation of such plates. Through systematic simulations, it was discovered that at certain combinations of parameters (e.g., plate stiffness, distance between neighboring plates, and Keulegan-Carpenter number), the group-averaged values of plate deformation and power extraction in an array of plates surpass those of a single stand-alone plate. For example, in an array of five plates the group-averaged deformation and power extraction can be increased by 43% and 110% in comparison with a single plate, respectively. Further investigation shows that this phenomenon is determined by the competition between two mechanisms: the shielding mechanism and the wake energy recovery mechanism. Constructive interaction occurs when the latter one outweighs the former one. Parametric studies have also been conducted to identify the region within the parametric space in which constructive interaction can be achieved.

In turbulent Rayleigh-Bénard convection, it is generally acknowledged that the thermal boundary layer (BL) governs heat transfer, although its scaling with the Rayleigh number is still debated. Various methods have been developed to measure the characteristic thickness of the BL, which are mostly employed in a time-averaged manner. Among them, only the slope method can be applied in an instant of time, being therefore capable of time-resolved analysis; however, it provides no further insight when the Nusselt number is known. Accordingly, the average properties of the BL are thoroughly studied, mainly in the context of heat transfer; its time-dependent structural dynamics and roughness remain largely unexplored. Here, we propose a Lagrangian method to characterize both the time-averaged and the spatio-temporal evolution of the BL, that marks the edge of the BL where convective and diffusive transports overlap. The characteristic thickness of the BL, that is defined by this method, is not a trivial function of the Nusselt number and can be considered a potential tool to analyze the BL structure while varying the Nusselt number. It is also demonstrated using 3D direct numerical simulations, that the injection of heat is extremely inhomogeneous in space and time; the vast majority of heat accumulates in narrow domains, that is governed by the local plume dynamics.