Numerical simulations have unexplored potential in the study of droplet impact on nonuniform wettability surfaces. In this paper, we compare numerical and experimental results to investigate the application potential of a volume-of-fluid method utilized in OpenFOAM. The approach implements the Kistler model for the dynamic contact angle of impacting droplets. We begin with an investigation into the influence of the most important solver parameters to optimize the computational setup and reach the best compromise between computational cost and solution errors, as assessed in comparison to experimental results. Next, we verify the accuracy of the predictions for droplet impact on uniformly hydrophilic or superhydrophobic surfaces. Benchmarking the maximal spreading factor, contact, and spreading times, as well as contact-line behavior, we show strong agreement between the present numerical results and the models of Pasandideh-Fard et al., Phys. Fluids 8, 650 (1996) and Clanét et al., J. Fluid Mech. 517, 199 (2004). Lastly, we demonstrate the capability of the model to accurately predict outcome behaviors of droplets striking distributed-wettability surfaces, which introduce 3D outcome characteristics, even in orthogonal impact. The model successfully predicts droplet splitting and vectoring, as reported in the experiments of Schutzius et al., Sci. Rep. 4, 7029 (2014). Finally, we demonstrate a configuration wherein a droplet centrally strikes a circular disk of different wettability than its surrounding domain. The main contribution of the present paper is a numerical model capable of accurately simulating droplet impact on spatially nonuniform wettability patterns of any foreseeable design.

We investigate the formation of a liquid jet due to an impact. The fluid contained in a completely wettable tube undergoes a constant acceleration-deceleration motion with the acceleration time being much smaller than the deceleration time duration. During the impact, the fluid near the wall rises up. For a small deceleration time and liquid viscosity, the velocity of the contact line between the liquid and the wall approximates the tube velocity. Later, the tube deceleration causes the flow to focus at the center of the tube, forming a liquid jet. The velocity of the liquid jet is mainly characterized by five dimensionless numbers: the Weber number (We), the Ohnesorge number (Oh), the Bond number (Bo), the dimensionless acceleration (${\tau }_a$), and the deceleration time (${\tau }_d$). For zero Bond numbers and small acceleration time, our numerical simulations show that the jet velocity $V_j$ scales with ${\text{Oh}}^{-1/4}{\text{We}}^{1/8}{\tau }_d^{-2/3}$ for large $\text{Oh}$. For a wide range of Bond numbers, the kinetic energy reduction due to viscous dissipation in the jet tip $[1-V_j^2/V_{j,0}^2]$ scales with ${\text{Oh}}^{2/3}f{(\text{We},\text{Bo})}^{2/3}$ for small Oh, where $V_{j,0}$ is the inviscid jet velocity, and $f(\text{We},\text{Bo})$ is an empirical function of We and Bo obtained from a least-squares fit of numerical results. At small Bo, the jet forms due to the focusing flow and the jet velocity decreases with surface tension. On the other hand, at large Bo, when the initial interface is flatter, focusing of surface waves enhances the jet formation and jet velocity increases with surface tension. For the Bond number in experiments, we also investigate the breakup criteria for the liquid jets. By denoting the critical Weber number for breakup as ${\text{We}}_c$, we find that $f{({\text{We}}_c,\text{Bo})}^{-2/3}$ linearly increases with ${\text{Oh}}^{2/3}$ for a wide range of $\text{Oh}$, and has a nonmonotonic dependence on ${\tau }_d$.

We consider a steady, homogeneous, shearing flow of identical, rigid, frictionless, inelastic spheres. We adopt nonlinear stress relations that include anisotropy in the velocity fluctuations and, in the balance equations for the second moment of the velocity fluctuations, we incorporate velocity correlations in the expressions for the collisional production. We use the resulting solutions of the balance equations in existing expressions for the dimensionless pressure, shear stress, and the normal stress difference to determine their behavior with volume fraction. The first normal stress difference remains near zero, the pressure, shear stress and second normal stress difference increase monotonically, becoming singular at random close packing with powers 5/2, 5/2, and 7/4, respectively.

A combination of time-resolved particle image velocimetry (PIV) and tomographic PIV was used to study the instantaneous three-dimensional vortex shedding as well as mean velocities and turbulent stresses in the near wake of a smooth and a rough sphere. Sphere roughness was modeled by spiraling grooves found in nature on pine cones. The measurements extended up to five sphere diameters $D$, downstream of the sphere, and were performed across a Reynolds number range of $226<{\mathrm{Re}}_D<$ 5067, spanning several vortex shedding regimes. Our results showed that the main effect of the sphere roughness on the near-wake flow was to lower ${\mathrm{Re}}_D$ for which the clear, temporally averaged recirculating wake pattern observed at low ${\mathrm{Re}}_D$ disappeared. Furthermore, mean velocities and root-mean-square (rms) values of fluctuating velocities scaled best with the mean recirculating wake length, ${\overline{L}}_w$, instead of $D$ that is commonly used in the far wake. Normalized, maximum rms values of velocity fluctuations measured in a horizontal equatorial plane increased with increasing ${\mathrm{Re}}_D$ and were well fitted by a logarithmic function. The mean velocity defect recovery was well described by a power law with exponents decreasing from $-1$ to $-3$ at ${\mathrm{Re}}_D\approx$ 2000, and subsequently increasing to $-2.3$ at ${\mathrm{Re}}_D\approx$ 5000. Most surprisingly, our results showed that ${\overline{L}}_w/D$ was locally minimum at ${\mathrm{Re}}_D\approx 900$. At these ${\mathrm{Re}}_D$, the wake transitioned from a well-organized laminar wake, characterized by a single vortex shedding frequency, to one exhibiting high and low shedding frequency branches. By analyzing the instantaneous centroid positions of the velocity defect in a transverse plane, we showed that the local minimum value of ${\overline{L}}_w/D$ was the result of increased wake “meandering” that resulted in enhanced mixing at this ${\mathrm{Re}}_D$. Moreover, at the transition, the wake alternated between the organized shedding pattern observed at low ${\mathrm{Re}}_D$ and the one lacking any preferred orientation at higher ${\mathrm{Re}}_D$.

The plane wall jet (PWJ) was used as a model flow field to study the linear and nonlinear mechanisms within complex wall-bounded flows. Large-scale, large-amplitude forcing was used to introduce a “tracer” flow scale into the unforced base flow and the resulting embedded mechanisms were studied. The PWJ had a nominal Reynolds number ${\text{Re}}_j=b{V}_j/\nu =5965$ and was forced acoustically at a Strouhal number $\text{St}=f_{f}b/V_j=3.4\times {10}^{-3}$ and the resulting flow field was characterized at various downstream locations ($x/b\le 162$) using hot-wire anemometry. Here, $b$ is the PWJ exit slot width, $V_j$ is the nominal PWJ exit centerline velocity, $\nu$ is the kinematic viscosity, and $f_f$ is the forcing frequency. The forcing increased the outer length scale $\delta$ (increased spreading rate of the PWJ) along with a decrease in the outer velocity scale $U_m$ and an increase in the local Reynolds number. The self-similarity of the mean streamwise velocity profile of the forced and unforced flow, respectively, was unaltered by the forcing, but the momentum in the wall region and the friction velocity were reduced along with a large increase in the streamwise turbulence in the wall region. The linear response of the PWJ to the forcing resulted in flow structures that have strong similarities to the naturally occurring structures of the unforced flow, both in the inner boundary layer and in the outer free-shear layer. A comparison of the energy spectra of the forced and unforced flow showed that the recipient scales, of the excess energy from forcing, were primarily the large scales in the wall region, with the specific scale of these recipient structures being that of the outer free-shear structures. At the upstream locations this energy transfer was primarily in the form of a forward cascade, while at downstream locations the transfer was in the manner of an inverse cascade. The nonlinear interaction between the large scales in the flow and finer scales was also found to be enhanced by the forcing. The spectra also suggested that the forcing isolated the energy transfer mechanism within the flow where the input energy was supplied at the forcing frequency. These observations led to the interpretation that the natural energy transfer mechanism within a PWJ is to transfer energy from the boundary layer coherent structures to the larger outer free-shear layer structures. The implications of these observations to modeling such complex wall-bounded flow fields, particularly considering the on-going work on the linear dynamics of the Navier-Stokes equation, were also discussed.

The behavior of flagellated bacteria swimming in non-Newtonian media remains an area with contradictory and conflicting results. We report on the behavior of wild-type and smooth-swimming E. coli in Newtonian, shear-thinning, and viscoelastic media, measuring their trajectories and swimming speed using a three-dimensional real-time tracking microscope. We conclude that the speed enhancement in Methocel solution at higher concentrations is due to shear thinning and an analytical model is used to support our experimental result. We argue that shear-induced normal stresses reduce wobbling behavior during cell swimming but do not significantly affect swimming speed. However, the normal stresses play an important role in decreasing the flagellar bundling time, which changes the swimming-speed distribution. A dimensionless number, the “strangulation number” (Str) is proposed and used to characterize this effect.

We numerically study the retraction of an axisymmetric viscous filament in a passive surrounding fluid. The analysis focuses on the evolution of the tip velocity, from the early stage of the filament retraction until it reaches its final equilibrium spherical shape. The problem is governed by two control parameters: the Ohnesorge number, Oh, which measures the relative importance of viscous and surface tension effects, and the initial aspect ratio of the filament, $\mathcal{A}$. We investigate the influence of Oh over a wide range of aspect ratios. The small-Oh regime is characterized by the occurrence of a spherical blob at the extremity of the filament. This feature has a key impact on the tip dynamics, which moves with an oscillating velocity whose mean value is close to the Taylor-Culick prediction. The oscillatory behavior of the tip velocity is explained through a simple mass-spring model. This regime is also characterized by the presence of capillary waves, with a phase velocity slightly larger than the Taylor-Culick velocity. Surface oscillations are also observed when the filament reaches its final spherical shape; the corresponding period agrees well with predictions of the linear theory. At intermediate Oh and large $\mathcal{A}$, the tip velocity reaches a value close to the Taylor-Culick prediction. However, for smaller aspect ratios, the maximum tip velocity is much smaller than this prediction, and does not exhibit any oscillation. The recoil dynamics is qualitatively and quantitatively different at high Oh. In this case, the radius of the filament grows uniformly over time and no blob forms, making the tip velocity decrease after a short transient. A self-similar solution is found to closely match the numerical results in this regime.

We exploit the deformation of drops spinning in a denser background fluid to investigate the effective interfacial tension (EIT) between miscible molecular fluids. We find that, for sufficiently low interfacial tension, spinning drops develop dumbbell shapes, with two large heads connected by a thinner central body. We show that this shape depends not only on the density and viscosity contrast between the drop and background fluids, but also on the fluid molecular structure, and hence on the stresses developing at their interface due to a different molecular interaction. We systematically investigate the dynamics of dumbbell-shaped drops of water-glycerol mixtures spinning in a pure glycerol reservoir. By developing a model for the deformation based on the balance of the shear stress opposing the deformation, the imposed normal stress on the drop, and an effective interfacial tension, we exploit the time evolution of the drop shape to measure the EIT. Our results show that the EIT in water-glycerol systems is orders of magnitude lower than that reported in previous experimental measurements, and in excellent agreement with values calculated via the phase field model proposed by Truzzolillo et al. [Phys. Rev. X 6, 041057 (2016)].

Designing locomotory gaits for synthetic microswimmers has been a challenge due to stringent constraints on self-propulsion at low Reynolds numbers (Re). Here, we introduce a new theoretical approach of designing a class of self-learning, adaptive (or “smart”) microswimmers via reinforcement learning. Diverging from the traditional paradigm of specifying locomotory gaits a priori, here a self-learning swimmer can develop and adapt its propulsion strategy based on its interactions with the surrounding medium. We illustrate this new approach using a minimal but representative model swimmer consisting of an assembly of spheres connected by extensible rods. Without requiring any prior knowledge of low Re locomotion, we demonstrate that this self-learning swimmer can recover a previously known propulsion strategy, identify more effective locomotory gaits, and adapt its locomotory gaits in different media. This approach opens an alternative avenue to designing the next generation of smart microrobots with robust locomotive capabilities.

The dynamics of droplets impacting on solid surfaces are directly related to a variety of engineering applications. As some industrial processes have been refined to the nanoscale, research interest in nanodroplets impact is growing. In this work, molecular dynamics (MD) is employed to investigate the impact processes of nanodroplets on superhydrophobic surfaces decorated with triangular nanoridges. We confirm that the decorated nanoridges can significantly promote the bouncing performance of nanodroplets, including enlarging the bounce domain, reducing the contact time, and enhancing the bounce velocity. We identify five distinct bounce modes for nanodroplets on the nanoridged surfaces, and the variation laws of contact time and bounce velocity of nanodroplets are determined by the characteristics of these bounce modes. Configuration of nanoridges can influence the variation laws of contact time and bounce velocity through changing the bounce modes of nanodroplets. The restitution coefficient can be piecewise fitted as the power functions of the impact Weber number of nanodroplets, regardless of the droplet diameters and ridge configurations. This work elucidates the characteristics and mechanism of nanodroplets impacting on the nanoridged surfaces, which is conducive to the design of nanostructured surfaces for related applications.

The effects of a pipe axial rotation on buoyant miscible exchange flows are studied experimentally and numerically. The pipe is inclined at intermediate angles, where buoyant and inertial effects are present. The pipe inclination angle and the common viscosity of the fluids are found to have negligible effects on the dynamics of the flow. On the other hand, the pipe rotation speed and the density difference are important flow parameters. The flow is shown to be mainly governed by a balance between the characteristic inertial-buoyant (${\widehat{V}}_i$) and rotational (${\widehat{V}}_{\omega }$) velocities. By increasing the pipe rotation speed ($\widehat{\omega }$), the penetration velocity of the heavy fluid into the light one (${\widehat{V}}_f$) decreases and, eventually, the penetration stops at a propagation distance ($\widehat{L}$) within a propagation time period ($\widehat{T}$). It is found that ${\widehat{V}}_f, \widehat{L}$, and $\widehat{T}$ decrease nonlinearly with $\widehat{\omega }$, and empirical correlations are proposed to predict them versus ${\widehat{V}}_{\omega }$ and ${\widehat{V}}_i$.

Locomotion of self-propelled particles such as motile bacteria or phoretic swimmers often takes place in the presence of applied flows and confining boundaries. Interactions of these active swimmers with the flow environment are important for the understanding of many biological processes, including infection by motile bacteria and the formation of biofilms. Recent experimental and theoretical works have shown that active particles in a Poiseuille flow exhibit interesting dynamics including accumulation at the wall and upstream swimming. Compared to the well-studied Taylor dispersion of passive Brownian particles, a theoretical understanding of the transport of active Brownian particles (ABPs) in a pressure-driven flow is relatively less developed. In this paper, employing a small wave-number expansion of the Smoluchowski equation describing the particle distribution, we explicitly derive an effective advection-diffusion equation for the cross-sectional average of the particle number density in Fourier space. We characterize the average drift (specifically upstream swimming) and effective longitudinal dispersion coefficient of active particles in relation to the flow speed, the intrinsic swimming speed of the active particles, their Brownian diffusion, and the degree of confinement. In contrast to passive Brownian particles, both the average drift and the longitudinal dispersivity of ABPs exhibit a nonmonotonic variation as a function of the flow speed. In particular, the dispersion of ABPs includes the classical shear-enhanced (Taylor) dispersion and an active contribution called the swim diffusivity. In the absence of translational diffusion, the classical Taylor dispersion is absent and we observe a giant longitudinal dispersion in the strong flow limit. Our continuum theory is corroborated by a direct Brownian dynamics simulation of the Langevin equations governing the motion of each ABP.

We consider the effect of stratification on systematic large-scale flows generated in anelastic convection. We present results from three-dimensional numerical simulations of convection in a rotating plane layer in which the angle between the axis of rotation and gravity is allowed to vary. This model is representative of different latitudes of a spherical body. We consider two distinct parameter regimes: (i) weakly rotating and (ii) rapidly rotating. In each case, we examine the effect of stratification on the flow structure and heat transport properties focusing on the difference between Boussinesq and anelastic convection. Furthermore, we show that regimes (i) and (ii) generate very different large-scale flows and we investigate the role stratification has in modifying these flows. The stratified flows possess a net helicity not present in the Boussinesq cases which we suggest, when combined with the self-generated shear flows, could be important for dynamo action.

Regions with shearing motions are investigated in isotropic turbulence with the triple decomposition, by which a velocity gradient tensor is decomposed into three components representing an irrotational straining motion, a rotating motion, and a shearing motion. A mean flow around the shearing motions shows that a thin shear layer is sustained by a biaxial strain, which is consistent with Burgers' vortex layer. The thickness of each shear layer is well predicted by Burgers' vortex layer. A comparison between genuine turbulence and a random velocity field confirms that the biaxial strain acting on the shear is a dynamical consequence from the Navier-Stokes equations rather than from a kinematic relation. The interplay between the shear and biaxial strain causes enstrophy production and strain self-amplification. For a wide range of Reynolds number, the shear is strong enough for the instability to cause a roll-up of the shear layer, where the perturbation grows much faster than large-scale turbulent motions.

The dynamic evolution of a highly underexpanded transient supersonic jet at the exit of a pulse detonation engine is investigated via high-resolution time-resolved schlieren and numerical simulations. Experimental evidence is provided for the presence of a second triple shock configuration along with a shocklet between the reflected shock and the slipstream, which has no analog in a steady-state underexpanded jet. A pseudo-steady model is developed, which allows for the determination of the postshock flow condition for a transient propagating oblique shock. This model is applied to the numerical simulations to reveal the mechanism leading to the formation of the second triple point. Accordingly, the formation of the triple point is initiated by the transient motion of the reflected shock, which is induced by the convection of the vortex ring. While the vortex ring embedded shock move essentially as a translating strong oblique shock, the reflected shock is rotating towards its steady-state position. This results in a pressure discontinuity that must be resolved by the formation of a shocklet.

Since the early work of Johnston [Johnston, Halleent, and Lezius, J. Fluid Mech. 56, 533 (1972)], the mean flow scaling in a spanwise rotating channel has received much attention. While it is known that the mean velocity near the pressure, turbulent side follows a linear scaling $U=2\mathrm{\Omega }y+C$ at high rotation speeds, the functional dependence of $C$ on the Reynolds number and the rotation number has been an open question. Here, $U$ is the mean velocity, $\mathrm{\Omega }$ is the constant rotating speed in the spanwise direction, and $C$ is a constant. In this work, we show that $C^{+}=log\left(l_{\mathrm{\Omega }}^{+}\right)/K$, where the superscript $+$ denotes normalization using wall units at the pressure side; $l_{\mathrm{\Omega }}=u_{\tau ,p}/2\mathrm{\Omega }$ is a rotation-induced length scale; $K$ is a constant and $K\approx \kappa$, where $\kappa$ is the von Kármán constant; and $u_{\tau ,p}$ is the wall friction velocity at the pressure side.

Spermatozoa self-propel by propagating bending waves along a predominantly active elastic flagellum. The organized structure of the $9+2$ axoneme is lost in the most-distal few microns of the flagellum, and therefore this region is unlikely to have the ability to generate active bending; as such it has been largely neglected in biophysical studies. Through elastohydrodynamic modeling of humanlike sperm we show that an inactive distal region confers significant advantages, in both propulsive thrust and swimming efficiency, when compared with a fully active flagellum of the same total length. The beneficial effect of the inactive end piece on these statistics can be as small as a few percent but can be above 430%. The optimal inactive length, between 2% and 18% of the total length, depends on both wave number and viscous-elastic ratio, and therefore is likely to vary in different species. Potential implications in evolutionary biology and clinical assessment are discussed.

The wall-resolved large-eddy simulation (WRLES) database of the flow around the A-airfoil at the near-stall condition [K. Asada and S. Kawai, Phys. Fluids 30, 085103 (2018)] is analyzed to understand the mechanism of the boundary layer development and to examine the predictability of the trailing-edge stall phenomena using the wall-modeled LES (WMLES). The analysis based on the integral relation for the boundary layer indicates that the skin friction has dominant effects on the boundary layer development in the mild-adverse pressure gradient region ($x/c>0.6$). The effects of the skin friction accumulate along the airfoil upper surface, which determines the growth of the momentum thickness in the downstream and the consequent flow separation near the trailing edge. Therefore, this analysis indicates that the wall modeling in $x/c<0.6$ is important for the prediction of the stall phenomena, while that near and downstream of the separation location little affects the stall phenomena. Also, the budget analysis reveals that the eddy viscosity in the mild-adverse pressure gradient regions increases compared to that of the equilibrium boundary layer, which should be incorporated properly in the wall model. The same flowfield is simulated using the WMLES, and the results show an overall good agreement with the WRLES. The analysis based on the integral relation indicates that the WMLES can predict the stall phenomena with reasonable accuracy because the outer layer turbulence, whose effects are dominant near the separation point, is directly resolved in the WMLES. Despite the overall agreement with the WRLES, the WMLES results also suggest that potential issues remain in the underresolution near the leading edge and the eddy viscosity modeling of the wall model for flows with adverse pressure gradient.

Soluto-inertial (SI) suspension interactions involve nonequilibrium colloidal migration over millimeters, driven by “beacons” that establish long-lasting chemical gradients. Previous demonstrations of the SI concept were restricted to fixed, cylindrical beacons that would sustain solute fluxes in controlled two-dimensional geometries. Here we examine soluto-inertial interactions established by a spherical beacon that sediments through a suspension. The sedimenting beacon leaves a trailing solute wake, the flux from which drives the motion of neighboring suspended objects. Experiments reveal wakes that can attract or repel particles, depending on the solute-colloid pair, creating local regions in the suspension that are enriched in or devoid of particles. Theoretical descriptions accurately capture experimental observations and provide predictive ability to gauge the strength of these interactions in terms of the design parameters. We anticipate that long-range, bulk suspension interactions driven by “drop-in” beacon additives will enable on-demand flocculation of dilute suspensions and separation of colloidal mixtures.

We compute, model, and predict drag reduction of an actuated turbulent boundary layer at a momentum-thickness-based Reynolds number of $R{e}_{\theta }=1000$. The actuation is performed using spanwise traveling transversal surface waves parametrized by wavelength, amplitude, and period. The drag reduction for the set of actuation parameters is modeled using 71 large-eddy simulations (LESs). This drag model allows us to extrapolate outside the actuation domain for larger wavelengths and amplitudes. The modeling novelty is based on combining support vector regression for interpolation, a parametrized ridgeline leading out of the data domain, a scaling for the drag reduction, and a discovered self-similar structure of the actuation effect. The model yields high prediction accuracy outside the training data range.