Fluid-structure simulations of slender inextensible filaments in a viscous fluid are often plagued by numerical stiffness. Recent coarse-graining studies have reduced the computational requirements of simulating such systems, though they have thus far been limited to the motion of planar filaments. In this paper we extend such frameworks to filament motion in three dimensions, identifying and circumventing coordinate-system singularities introduced by filament parametrization via repeated changes of basis. The resulting methodology enables efficient and rapid study of the motion of flexible filaments in three dimensions, and is readily extensible to a wide range of problems, including filament motion in confined geometries, large-scale active matter simulations, and the motility of mammalian spermatozoa.

Small spatial perturbations grow into fingers along the unstable interface of a fluid displacing a more viscous fluid in a porous medium or a Hele-Shaw cell. Mitigating this Saffman-Taylor instability increases the efficiency of fluid displacement applications (e.g., oil recovery), whereas amplifying these perturbations is desirable in, e.g., mixing applications. In this work, we investigate the Saffman-Taylor instability through analysis and experiments in which air injected with an oscillatory flow rate outwardly displaces silicone oil in a radial Hele-Shaw cell. A solution for linear instability growth that shows the competing effects of radial growth and surface tension, including wetting effects, is defined given an arbitrary reference condition. We use this solution to define a condition for stability relative to the constant flow rate case and make initial numerical predictions of instability growth by wave number for a variety of oscillations. These solutions are then modified by incorporating reference conditions from experimental data. The morphological evolution of the interface is tracked as the air bubble expands and displaces oil between the plates. Using the resulting images, we analyze and compare the linear growth of perturbations about the mean interfacial radius for constant injection rates with and without superimposed oscillations. Three distinct types of flow rate oscillations are found to modulate experimental linear growth over a constant phase-averaged rate of fluid displacement. In particular, instability growth at the interface is mildly mitigated by adding to the base flow rate provided by a peristaltic pump a second flow with low-frequency oscillations of small magnitude and, to a lesser extent, high-frequency oscillations of large amplitude. In both cases, the increased stability results from the selective suppression of the growth of large wave numbers in the linear regime. Contrarily, intermediate oscillations consistently destabilize the interface and significantly amplify the growth of the most unstable wave numbers of the constant flow rate case. Numerical predictions of low-frequency oscillations of opposite sign (initially decreasing) show promise of even greater mitigation of linear instability growth than that observed in this investigation. Looking forward, proper characterization of the unsteady, wetting, and nonlinear dynamics of instability growth will give further insight into the efficacy of oscillatory injection rates.

Homogeneous shear turbulence (HST) is an idealized version of the shear turbulence observed in practical free shear flows, and can be simulated using simple computational domains. One of the numerically efficient configurations to simulate turbulent flows is to use triply periodic domains. However, owing to the mean streamwise velocity being nonhomogeneous, periodic boundary conditions cannot be used along one of the directions. Several studies included shear periodic boundary conditions in the cross-stream direction. However, in these simulations, the turbulence statistics grew exponentially with time, whereas the turbulence observed in free shear flows is statistically stationary. In Dhandapani et al. [Phys. Rev. Fluids 4, 084606 (2019)], the authors fixed this problem by focusing on the velocity fluctuations, performing HST simulations with only shear production and neglecting shear convection. The current study improves upon the previous simulations by including shear convection, by introducing an inflow/outflow in the cross-stream direction. To reduce the impact of the boundary conditions, an elongated domain is used. The simulation results show that the aspect ratio has very little effect on both isotropic and shear turbulence. When convection is included, the turbulence statistics still reach a statistically stationary state. The Reynolds shear stress and the anisotropy values agree very well with the results from experiments and simulations of mixing layers, planar jets, and round jets.

In this work, numerical simulations of the Navier-Stokes, Nernst-Planck, and the Poisson equations are employed to describe the transport processes in an aqueous electrolyte in a parallel-plate nanochannel, where surface-acoustic waves (SAWs) are standing or traveling along (piezo-active) channel walls. It is found that—in addition to the conventional acoustic streaming flow—a time-averaged electroosmotic flow is induced. Employing the stream function–vorticity formulation, it is shown that the Maxwell stress term causes an electroosmotic propulsion that is qualitatively identical to the one discussed in the context of alternating current (AC) electroosmosis (EOF). Differences arise mainly due to the high actuation frequencies of SAWs, which are in the MHz range rather than in the kHz regime typical for ACEOF. Moreover, the instantaneous spatial periodicity of the EOF in the travel direction of the SAW is intrinsically linked to the dispersion relation of the latter rather than a free geometric parameter. This leads to a specific frequency band where an EOF of sizable magnitude can be found. On the low-frequency end, the ratio between the electric double layer (EDL) thickness and the SAW wavelength becomes extremely small so that the net force leading to a nonvanishing time-averaged EOF becomes equally small. On the high-frequency end, the RC time of the EDL is much larger than the inverse of the SAW frequency. This leads to both a vanishing effective charge density of the EDL as well as to inertial effects at the boundary between the EDL and the bulk of the electrolyte. For a parallel-plate channel, the EOF can be maximized by using two SAWs on both channel walls that have the same frequency but are phase shifted by ${180}^{\circ }$. This maximizes the electric field and the corresponding electric current across the channel that drives the mechanical imbalance of the ion cloud in the EDL. For instance, at 10 MHz, $9\text{nm}$ (nominal) EDL thickness, and a plate separation of $480\text{nm}$, a (time-averaged) plug-like EOF with peak velocity of $O\left({10}^{-1}\right)\text{mm}{\text{s}}^{-1}$ is found. Although reliable information about the acoustic streaming velocity under such confinement is scarce, it appears that the SAW-EOF is larger than that and therefore the dominant pumping mechanism for such a scenario. The proposed actuation might be a viable alternative for driving liquid electrolytes through narrow ducts and channels, without the need for electric interconnects and electrodes.

The rupture of a liquid film due to coflowing turbulent shear flows in the gas phase is studied using a volume-of-fluid method. To simulate this multiphase problem, we use a simplified numerical setup where the liquid film is “sandwiched” between two fully developed boundary layers from a turbulent channel simulation. The film deforms and eventually ruptures within the shear zone created by the coflows. This efficient setup allows systematic variation of physical parameters to gauge their role in the aerodynamically driven deformation and rupture of a liquid film under fully developed sheared turbulence. This work presents a detailed study of the developing pressure field over the deforming film and related aerodynamic effects, as previously suggested by other authors, in particular the role of the inviscid lift and drag forces. A cumulative lift force is introduced to capture the effect of the alternating pressure minima and maxima forming over the film, which amplify and eventually rupture the film. A velocity scale derived from the lift-induced drag force reflects the state of the turbulent boundary layer over the film and collapses the temporal development of this cumulative lift force as well as the amplitude of film deformation with some success for the different film thicknesses and Reynolds numbers.

We report the rheology of a dilute ferrofluid droplet suspension under simple shear flow, using the three-dimensional lattice-Boltzmann simulation and the phase-field model. In our simulation, we utilize 12M computational grids to fully resolve the droplet deformation, and GPU parallelization is used to speed up the computation. The droplet deformation is determined by both the background shear flow and the external magnetic field effects. The ferrofluid droplet has a character to elongate in the direction of the external field, and a uniform static magnetic field is applied to the system to control the droplet shape. By changing the external field strength and direction, we found that the suspension rheologies can be drastically modified. The viscosity increase (decrease) with the external field when the external field is applied to the velocity gradient direction (velocity direction). Just by imposing the external magnetic field, the specific viscosity becomes $12\sim 620\%$ of the viscosity under no external magnetic field. The magnetic force is also practical to control the normal stresses, since the normal stress in $i\mathrm{th}$ direction decreases when the magnetic field is applied to the $i\mathrm{th}$ direction. Therefore, in order to increase (decrease) the first normal stress difference $N_1$, the external magnetic field should be applied to the velocity direction (velocity gradient direction). To increase (decrease) the second normal stress difference $N_2$, the external magnetic field should be applied to the velocity gradient direction (vorticity direction). By applying the magnetic field, we also show that the normal stresses $N_1,$ $N_2$ even show opposite sign from the normal droplet solution $(N_1>0,$ $N_2<0)$ under small-Reynolds-number conditions. Our work suggests that the ferrofluid droplet would be a practical complex fluid to control the suspension properties, just by changing the external magnetic field strength and directions.

Uncertainties in the explosive-specific parameters of the Jones-Wilkins-Lee (JWL) equation of state (EOS) are carefully considered in hydrodynamic simulations of an explosive experiment to minimize the error in the flow prediction. Experimental data of the leading shock position in the transverse direction over time serves as the prediction metric for quantifying simulation prediction error. The uncertainty quantification technique, global sensitivity analysis, is utilized to determine the JWL parameters to which the transverse shock propagation is most sensitive. A polynomial response surface (PRS) is constructed in the space of the most influential JWL parameters, and the point of minimum error between the experimental data and the PRS yields calibrated JWL parameters for the experimental flow. The simulation results following the parameter calibration show good agreement with the experimental data. It was found that two significant parameters, the heat release per unit mass of reactant $Q$ and JWL model exponent $R_1$ are strongly related, which makes it difficult to identify accurate values.

Using the Chebyshev spectral method, the effect of high frequency (HF) vibrations on a cubic cell heated from the side and containing a liquid metal is investigated. This study extends the numerical and theoretical two-dimensional results presented in the authors’ past work [Phys. Fluids 31, 043605 (2019)] about the influence of HF vibration direction on the flow structure in a rectangular crucible filled with a liquid metal. The vibration direction can now be three dimensional, and not limited to the main flow plane. In practice, the study considers that the vibration vector is contained in one of the three principal planes of the cavity $(xz,xy$, and $yz$ planes). Two different cases, i.e., under weightlessness and gravity conditions, are considered for each type of vibration to better understand the separate effect of both vibration and buoyancy forces and also their combined effects. Each type of vibration has its own features and affects the flow intensity and patterns differently.

We study the propulsive performance of a naturally cosinusoidal-shaped filament actuated at one end in viscous fluids. In the limit of small actuation amplitudes, the propulsive force generated by the filament is derived asymptotically. Nonlinear numerical simulations confirm the theoretical results and examine the cases of largely deformed filaments. Exploiting the intrinsic curvature and structural elasticity enables the curved filament to produce considerable negative propulsion, as well as bidirectional propulsion subject to a varying actuation frequency. These features are elucidated by a reduced-order model of one or two degrees of freedom. Our findings might inspire the design of microrobots endowed with better maneuverability and soft material systems responsive to the changing environment.

The preferential concentration of heavy inertial point particles in homogeneous isotropic turbulence is investigated with direct numerical simulations. The particle clustering is measured by the standard deviation of normalized Voronoï volumes. With the particle number, large-scale time and length fixed, it is found that the degree of particle clustering is reduced with the increase of Taylor Reynolds number $\left(R_{\lambda }\right)$ for $52\le R_{\lambda }\le 139$ when the Stokes number (St) is small (e.g., St $<2.0)$, where St is the ratio of particle response time $\left({\tau }_p\right)$ to the Kolmogorov timescale $\left({\tau }_{\eta }\right)$. On the contrary, the clustering of high-St particles tends to become stronger with the increase of $R_{\lambda }$ in the same $R_{\lambda }$ range. Quantities invoked for low-St particle clustering include ${\tau }_{\eta }$, the characteristic time $\left({\tau }_f\right)$ of particles being trapped by “shear structures” and the strength of “shear structures” quantified by the second invariant of velocity gradient tensor $\left(Q=S_{ij}{S}_{ij}-{\mathrm{\Omega }}_{ij}{\mathrm{\Omega }}_{ij}\right)$. While the increase of $Q$ with Reynolds number enhances preferential concentration, ${\tau }_{\eta }$ and ${\tau }_f$ both decrease as Reynolds number increases, which could moderate the level of particle clustering. Then the observable reduction in the clustering of low-St particles with increasing $R_{\lambda }$ emerges as the dominance of ${\tau }_{\eta }$ and ${\tau }_f$ over $Q$ effects. In addition, we find that the strain rate cannot directly affect the spatial inhomogeneous distribution of low-St particles, but instead it impacts low-St particle clustering indirectly due to its correlation with the rotation rate. Unlike low-St particles dominated by small-scale eddies, the clustering of high-St particles is mainly influenced by large-scale eddies due to the “resonant” effect between particles and eddies.

Scale-resolving simulations (SRS) of spatially evolving turbulent flows require specification of physically meaningful inflow fields for optimal outcome. SRS methods that employ two-equation subgrid closures must ensure that the inflow unresolved-field velocity-scale (kinetic energy) and length-scale (dissipation or frequency) distributions are compatible with the inflow resolved fields. This work aims to develop accurate inflow turbulent boundary layer description by (i) adapting the recycling-rescaling technique for the resolved field and (ii) deriving unresolved flow-field statistics that are consistent with the resolved-flow profile using the equilibrium boundary layer analysis. The proposed scheme is employed to simulate a spatially evolving zero pressure gradient flat plate boundary layer over a computational domain of $650<{\mathrm{Re}}_{\theta }<1434$. The SRS results are evaluated in the following categories: wall coefficients, mean-flow profiles, second- and higher-order moments, and multipoint correlations. The agreement with established direct numerical simulation data is shown to be good. Equally importantly, it is demonstrated that the prescribed degree of flow resolution is maintained quite precisely. Overall, the results indicate that the proposed approach can improve the computational efficiency of two-equation SRS closure methods in a wide range of spatially developing turbulent flows.

Dispensing, transporting, and manipulating minute liquid volumes is important to a wide range of scientific and application areas, spanning from biology and medicine to chemistry and materials. Although digital microfluidics are emerging as a popular methodology in the lab-on-a-chip field, important obstacles to its broad adoption, such as those related to reusability, reconfigurability, and susceptibility to fouling, persist. In addition, as liquid volumes decrease in size, their sustenance in an open atmosphere becomes practically impossible due to high volatility, leading rapidly to complete evaporation. Here we introduce and demonstrate a microfluidic platform based on the coalescence-induced self-propulsion of sessile microdroplets on unpatterned substrates. We employ controlled dropwise liquid ejection by electrohydrodynamic printing to create, actively sustain (despite high volatility), and freely translate femtoliter-sized droplets (∼2–5 μm radius) under open-atmosphere conditions. The omnidirectional planar movement of the droplets is achieved by a precisely controlled, on-demand sequence of coalescence events, where the directed motion of an already deposited droplet is dictated by the positioning of the subsequent droplet printed adjacent to it. We studied the transport mechanism experimentally and theoretically and found that, for short time scales (relative to the substrate translation and droplet evaporation), the radial growth of the new smaller droplet being printed can greatly exceed the retraction of the neighboring, already deposited droplet. This rapid growth is exploited to create a liquid meniscus bridging the so generated droplet doublet, and merging it into a single droplet by the action of capillary pressure differences. Evaporative losses ensure that the moving droplets are kept at a constant size after merging, in each coalescence cycle. We observe this coalescence whenever the interspacing between two sequentially printed droplets is below a critical value, and show that we can control this with the underlying substrate velocity. Armed with this transport mechanism, we then demonstrate the utility of this approach by tasking the coalescing self-propelled droplet doublet to perform microfluidic operations such as collecting, transporting, and merging solid residues on a surface, in an on-demand, Pac-Man type motion, exemplifying capabilities for digital microfluidic applications.

We report on an instability arising in subsurface, laterally sheared geostrophic flows. When the lateral shear of a horizontal flow in geostrophic balance has a sign opposite to the Coriolis parameter and exceeds it in magnitude, embedded perturbations are subjected to inertial instability, albeit modified by viscosity. When the perturbation arises from the surface of the fluid, the initial response is akin to a Stokes problem, with an initial flow aligned with the initial perturbation. The perturbation then grows quasi-inertially, rotation deflecting the velocity vector, which adopts a well-defined angle with the mean flow, and viscous stresses, transferring horizonal momentum downward. The combination of rotational and viscous effects in the dynamics of inertial instability prompts us to call this process “Ekman-inertial instability.” While the perturbation initially grows superinertially, the growth rate then becomes subinertial, eventually tending back to the inertial value. The same process repeats downward as time progresses. Ekman-inertial transport aligns with the asymptotic orientation of the flow and grows exactly inertially with time once the initial disturbance has passed. Because of the strongly superinertial initial growth rate, this instability might compete favorably against other instabilities arising in ocean fronts.

The one-degree-of-freedom vortex-induced vibrations (VIVs) of a low mass-damping circular cylinder forced to vibrate periodically have been investigated experimentally. A specially designed cylinder model allowed us to generate rotational oscillations while the system was responding to VIVs. Variations in the amplitude and frequency response have been studied, together with the excitation on the system. For dimensionless frequencies smaller than those of the response, rotations had little effect on the dynamics of the system. Otherwise, the dynamic response of the cylinder was in general reduced if compared to the nonrotating case, especially when forcing frequencies were larger than the VIV responding frequency under locked-in conditions. The very minor changes observed in the wake structures indicated that the VIV motion dominated the vortex formation process instead of the periodic forcing.

Most motile bacteria swim in viscous fluids by rotating multiple helical flagellar filaments. These semirigid filaments repeatedly join (“bundle”) and separate (“unbundle”), resulting in a two-gait random-walk-like motion of the cell. In this process, hydrodynamic interactions between the filaments are known to play an important role and can be categorized into two distinct types: direct interactions mediated through flows that are generated through the actuation of the filaments themselves, and indirect interactions mediated through the motion of the cell body (i.e., flows induced in the swimming frame that result from propulsion). To understand the relative importance of these two types of interactions, we study a minimal singularity model of flagellar bundling. Using hydrodynamic images, we solve for the flow analytically and compute both direct and indirect interactions exactly as a function of the length of the flagellar filaments and their angular separation. We show (i) that the generation of thrust by flagella alone is sufficient to drive the system towards a bundled state through both types of interaction in the entire geometric parameter range; (ii) that for both thrust- and rotation-induced flows indirect advection dominates for long filaments and at wide separation, i.e., primarily during the early stages of the bundling process; and (iii) that, in contrast, direct interactions dominate when flagellar filaments are in each other's wake, which we characterize mathematically. We further introduce a numerical elastohydrodynamic model that allows us to compute the dynamics of the helical axes of each flagellar filament while analyzing direct and indirect interactions separately. With this we show (iv) that the shift in balance between direct and indirect interactions is nonmonotonic during the bundling process, with a peak in direct dominance, and that different sections of the flagella are affected by these changes to different extents.

Shock wave trains in liquid jets were previously generated only by ablation with femtosecond x-ray lasers. Here we show that shock trains in water microjets can be also generated using nanosecond green laser pulses with 1- to 10-mJ energy. The ablation of 15-, 20-, 30-, and 70-$\mu \mathrm{m}$ water microjets opened a gap in the jets and launched an initial shock wave. Fully developed shock trains were observed in the 30- and 70-$\mu \mathrm{m}$ jets up to 250-ns delays, and these trains were also transmitted inside the nozzles. A few tens of nanoseconds after the pulse, the shock dynamics and its pressure became similar to the ones generated by x-ray lasers, with a more rapid pressure decay in thinner jets. At time delays exceeding 100 ns in the 30-$\mu \mathrm{m}$ jets, the leading shock pressure stabilized to an approximately constant pressure of 40 MPa. The energy density deposited in the jets was estimated at 30 MJ/${\mathrm{cm}}^3$ by comparing the jet gaps in the green and x-ray laser experiments, and matched previous estimates for optical ablation in water. The pressure decay in the 30-$\mu \mathrm{m}$ jets was modeled based on the pressure decay observed in x-ray laser experiments.

Swimming eukaryotic microorganisms such as spermatozoa, algae, and ciliates self-propel in viscous fluids using traveling wavelike deformations of slender appendages called flagella. Waves are predominant because Purcell's scallop theorem precludes time-reversible kinematics for locomotion. Using the calculus of variations on a periodic long-wavelength model of flagellar swimming, we show that the planar flagellar kinematics maximizing the time-averaged propulsive force for a fixed amount of energy dissipated in the surrounding fluid correspond for all times to waves traveling with constant speed, potentially on a curved centerline, with propulsion always in the direction opposite to the wave.

Antibubbles are fluid entities with the inverse phase of regular bubbles. While the structure and stability of antibubbles have been studied, a fundamental understanding of antibubble formation remains limited. We report a theoretical and experimental study of antibubble formation. In the experiment, pairs of surfactant-laden water drops impinged successively on the surface of the same liquid reservoir to create antibubbles. We propose four criteria for antibubble formation from a scaling analysis. Two dimensionless groups prescribe the likelihood of antibubble formation, the summative Weber number and the ratio of timescales between the capillarity driven pinch-off and the viscous drainage of air.

Viscous fingering patterns form in confined geometries at the interface between two fluids as the lower-viscosity fluid displaces the one with higher viscosity. Previous studies have examined the most unstable wavelength of the patterns that form using both linear-stability analysis and the dynamics of finger growth in the nonlinear regime. Interesting differences in dynamics have been seen between rectilinear and radial geometries as well as between fluid pairs that are immiscible (with interfacial tension) or miscible (with negligible interfacial tension). This paper reports measurements of how all of these systems transition from the linearly unstable regime to their late time, nonlinear dynamics. In all four cases there is a region of stable or slow growth characterized by an onset length scale before fingers enter the late-time regime. For immiscible fluids in a rectilinear geometry this onset length is consistent with linear-stability analyses. All other cases are not adequately described by existing theory. In radial geometries, the onset length predicted from theory is an order of magnitude smaller than what is experimentally observed and has the incorrect scaling with dimensionless numbers. For miscible fluids in a rectilinear geometry the onset length is related to the development of steady-state structures within the confining dimension and cannot be explained by quasi-two-dimensional theories. By combining the onset length with the finger growth rate measured after onset, the global patterns that form well into the late-time dynamics can be predicted.

Microplastics are an increasingly significant problem in the world's oceans. They are transported by various ocean phenomena, one of the most fundamental of which is surface gravity waves. Since microplastics are irregularly shaped and are not typically neutrally buoyant, understanding the settling of negatively buoyant, nonspherical plastic particles under surface gravity waves is important for accurately predicting the fate of microplastics in the ocean. Here we experimentally investigate the settling of plastic rods, disks, and spheres in wavy flows. We find that the average vertical velocities of the particles can both increase and decrease in waves, relative to the particle settling velocity in quiescent flow. This variation is a function of the flow inertia at the length scale of the particle, which we characterize with a particle Reynolds number, ${\mathrm{Re}}_p$, and is also a function of particle shape. We further examine the average vertical particle velocities by looking at two factors contributing to their behavior: The relative velocities between the particles and the flow and the manner in which the particles sample the flow. We find that the average relative velocities between the particles and the flow remain constant with ${\mathrm{Re}}_p$, even though the variation of the relative velocities of the rods with orientation increases with increasing ${\mathrm{Re}}_p$. The observed variation of the average vertical particle velocities with ${\mathrm{Re}}_p$ can be explained instead by how the particles sample the flow, as each of the particle shapes nonuniformly sample the flow as a function of ${\mathrm{Re}}_p$. Accounting for the variation of particle settling velocities with shape and inertia in models is necessary to improve the accuracy of predictions of the transport of microplastics in the ocean.