In order to understand the rotational motion of a microswimmer in a Newtonian fluid, we model it as an infinite cylinder with a helical, propagating surface wave. Using the method of series expansion, we calculate the linear and angular velocities of the cylinder, assuming that the wave amplitude is much smaller than the wavelength. To the first order in the wave amplitude, for the first mode of a purely azimuthal wave (that is, when the wavelength equals the cylinder's circumference), the cylinder moves along a circular path in the plane normal to its axis. Otherwise, the first-order velocities of the cylinder are zero, like the Taylor sheet. The time-averaged motion of the cylinder is determined by calculating the second-order velocities; the axial component of the wave vector leads to the linear motion of the cylinder along its axis and the azimuthal component to the angular motion around the axis. With the same stroke, the cylinder is always slower and less efficient than the Taylor sheet.

A bluff body advancing through the water surface at high Froude number produces intricate two-phase flow patterns. One intuitive feature is an entrapped air cavity which subsequently breaks apart into a mass of droplets and bubbles. The bluff-induced cavity partially accounts for the appearance of bubble clouds in the wake. However, few experimental or numerical studies have been devoted to this phenomenon. To clarify this mechanism, high-fidelity simulations are performed to emphasize the evolution of the aerated cavity generated by a surface-piercing rectangular plate. First, the mesh independency study is performed to validate the trend of the convergence of the time-averaged wave profile, the bubble size distribution, the bubble number density, and the entrapped bubble volume. Then the formation and development of the aerated cavity induced by a surface-piercing plate with various yaw angles (${\alpha }_E\in \left[{10}^{\circ },{50}^{\circ }\right]$) are investigated. Numerical simulations show that the air pocket is entrapped and develops with stabilized rotational motion, and the subsequent breakup of the air pocket constitutes the leading cause of the bubbly wake. The geometrical characteristics of the aerated rotation cavity are summarized as a function of yaw angles. Moreover, with the adaptive mesh strategy and high-resolution schemes, all the bubbles of equivalent radius $r\ge 2\mathrm{mm}$ are captured and tracked, so the spatial and size distribution laws of the varying-sized bubbles pinching off from the air cavity in the wake are summed up. In addition, large-scale coherent structures wrapped around the cavity and the effects on air entrainment are discussed.

We perform an experimental study on the turbulent flow around a square-back Ahmed body of height, $h$, at varying $Re=u_{\infty }h/\nu \in [0.5,1]\times {10}^5$, where $u_{\infty }$ is the free-stream velocity and $\nu$ is the incoming flow kinematic viscosity, under different yaw angles $\beta =(0^{\circ },-5^{\circ },-{10}^{\circ })$, to analyze the use of rear flexibly hinged parallel plates as a control strategy to reduce the drag in a self-adaptive manner under changing flow conditions. The model implements rear parallel rigid flaps of depth $d=0.5h$, which are mounted with torsional joints through embedded flexible foils of calibrated thickness. This holding system restricts the motion of the plates to a rotary displacement, $\theta$. The fluid-structure dynamics is characterized by the reduced velocity, defined as $U^{*}=u_{\infty }/f_{n}h$, where $f_n$ is the natural frequency of rotary oscillations of the hinged plates, measured in free-decay tests of flaps. In fact, we have explored the range of reduced velocity, $U^{*}=[0,65]$, varying $u_{\infty }$ and consequently Re. We perform force and pressure measurements to quantify the variations of the drag and the base pressure coefficients while laser displacement sensors are used to obtain the angular flaps motion. Results show that the hinged plates decrease the drag coefficient of the original body by nearly $4.4\%$ for flow conditions aligned with the body axis. Under cross-flow conditions, their efficiency is even larger, attaining relative reductions drag of nearly 9.1% at $\beta =-{10}^{\circ }$ (13.5% in comparison with a body with fixed rigid plates of the same depth). Such variations are shown to be associated with a passive reconfiguration process of rear flaps. Additionally, hinged flaps are shown to interact with the reflectional-symmetry-breaking (RSB) modes, typically present in the wake of three-dimensional bodies. At aligned conditions, the interaction with the RSB modes is characterized by two regimes, in such a way that the hinged flaps manage to partially stabilize the RSB modes, and consequently to inhibit the bistable behavior at low values of $U^{*}$ (in a similar manner to rigid flaps), while at high values of $U^{*}$, they respond dynamically to switches between the opposite wake deflections of the RSB modes, deviating themselves accordingly.

Turbulent signals are known to exhibit burstlike activities, which affect the turbulence statistics at both large and small scales of the flow. In our study, we pursue this problem from the perspective of an event-based framework, where bursting events are studied across multiple scales in terms of both their size and duration. To illustrate our method and assess any dependence on the Reynolds number ($\mathrm{Re}$), we use two data sets: from the Melbourne wind tunnel ($\mathrm{Re}\approx 14750$) and from SLTEST, an atmospheric surface layer experiment ($\mathrm{Re}\approx {10}^6$). We show that an index, namely, the “burstiness index,” can be used successfully to describe the multiscale nature of turbulent bursting while accounting for the small-scale intermittency effects. With this index, we demonstrate that irrespective of $\mathrm{Re}$, the presence of large amplitude fluctuations in the instantaneous velocity variance and momentum flux signals are governed by the coherent structures in the flow. For small-scale turbulence, a $\mathrm{Re}$ dependence is noted while studying the scalewise evolution of the burstiness features of second-order streamwise velocity increments (${\left(\mathrm{\Delta }u\right)}^2$). Specific to the wind-tunnel data set, the burstiness index of the ${\left(\mathrm{\Delta }u\right)}^2$ signal displays a strong dependence on height and decreases as the scales increase with the maximum being obtained at scales comparable to the dissipative structures. However, such features are nearly absent in the atmospheric flows. To conclude, this research paves a way to evaluate the effect of bursts on the turbulence statistics at any specified scale of the flow.

Pore-size gradients are often used in the design of membrane filters to increase filter lifetime and ensure fuller use of the initial membrane pore volume. In this work, we impose pore-size gradients in the setting of a membrane filter with an internal network of interconnected tubelike pores. We model the flow and foulant transport through the filter using the Hagen-Poiseuille framework coupled with advection equations via conservation of fluid and particle flux, with adsorption as the sole fouling mechanism. We study the influence of pore-size gradient on performance measures such as total filtrate throughput and accumulated contaminant concentration at the membrane downstream pore outlets. Within the limitations of our modeling assumptions we find that there is an optimal pore-radius gradient that maximizes filter efficiency independent of maximum pore length (an input parameter that influences the structure of the pore network), and that filters with longer characteristic pore length perform better.

The evolution of turbulence kinetic and internal energy plays a critical role in aerodynamics and thermodynamics. Following the previous study on the framework of energy exchange in compressible turbulent flows [Fan et al., Phys. Rev. Fluids 7, L092601 (2022)], we rigorously derive the spectral transport equations of turbulence kinetic and internal energy in terms of the two-point correlations of velocity and a sound-speed-like variable, respectively. With the equations, the spectral distributions of the budget terms, including production, dissipation, pressure strain, heat-conduction action, spatial and interscale transfer, are comprehensively examined in the hypersonic turbulent boundary layers at Mach number 5.86 and friction Reynolds number 420. Special attention is paid to the effect of wall cooling. The results enlighten the scale dependence of the energy transport across space and scales, and among components, helping us to clarify the evolution of turbulence kinetic and internal energy in high-speed turbulent flows.

We investigate experimentally the unsteady draining flow from a rotating tank. The fluid in the tank is first set in solid rotation, before the draining hole is opened. We show that the draining may be drastically reduced by the rotation, as the vortex circulation increases together with the surface deformation. We demonstrate that the usual Torricelli's draining law has to be modified with the surface deformation and that the draining time is mainly governed by a nondimensional parameter corresponding to the ratio of the size of the outlet to the thickness of the Ekman boundary layer.

The attached-eddy model (AEM) is one of the most successful coherent-structure-based phenomenological models in wall turbulence. In the classical AEM, the probability density of eddy $p_e$ is assumed to follow an inverse law with the eddy size $h_e$, i.e., $p_e\propto h_e^{-1}$, to satisfy a constant Reynolds-shear-stress distribution in the inertial layer of canonical wall-bounded turbulent flows. In this paper, we first extend the AEM to general attached eddies with $p_e\propto h_e^{-\alpha }$, where $\alpha$ is an arbitrary positive real number. Scaling laws for velocity covariance (Reynolds stress) by general attached eddies are derived. Preliminary evidence for the validity of the model is provided from adverse-pressure-gradient turbulent boundary layer and turbulent wing boundary layer flows. Second, considering that the eddy cascade self-similarity is manifested by generalized power laws for probability density $p_e$, population density $M_e$, area coverage $C_e$, and volume fraction $V_e$ of eddies, i.e., $p_e\propto h_e^{-\alpha }, M_e\propto h_e^{-\beta }, C_e\propto h_e^{-\gamma }$, and $V_e\propto h_e^{-\zeta }$, we directly connect the exponents with the fractal dimension $D_e$ of the general attached eddies in a simple and clear way. The present paper highlights that the scaling laws of velocity covariance in the inertial layer of wall-bounded turbulent flows can be directly linked to the characteristics of the cascade self-similarity of the general attached eddies. We believe that the scaling laws derived here and the generalized power-law relationships are useful for a deeper understanding of the connection between coherent structures and turbulence statistics.

A flexibly mounted cylinder placed in a Newtonian flow undergoes vortex-induced induced vibrations (VIV) during which the shedding frequency and the oscillation frequency are synchronized. In Newtonian fluids, VIV occurs at Reynolds numbers as low as $\mathrm{Re}=19$. Here, we show that the expected VIV response of the cylinder can be greatly affected if the viscosity of the fluid is shear thinning, by conducting VIV experiments in a series of fluids of xanthan gum solutions of increasing concentration and increasing shear-thinning intensity. While the VIV response of the weakly shear-thinning fluid closely resembles the VIV response of Newtonian fluids, we show that by increasing concentration and shear thinning, the critical Reynolds number at which VIV occurs increases, while the reduced velocity at which lock-in begins, the width of the lock-in range, and the oscillation amplitude decrease. Beyond a critical concentration, VIV is completely suppressed over the entire range of Reynolds numbers studied here. The increase in critical Reynolds number and the reduction in the width of the lock-in range and the amplitude are likely caused by the increased viscosity and increased momentum diffusion of the shed vortices in the cylinder's wake, where the shear rate is small and the viscosity is large as it has recovered back toward its zero-shear-rate limit. The reduction in the critical reduced velocity is caused by an increase in the vortex shedding frequency as the fluid becomes more shear thinning. For the most shear-thinning fluid tested where VIV is completely suppressed, the vortices are shed very far from the cylinder and do not cause any oscillations.

The breakup of a liquid jet by a surrounding gas jet is studied in a coaxial configuration using high-speed back-lit imaging. This work focuses on the time dynamics and the statistics of the length of the liquid jet. The inlet velocities are varied for both fluids to obtain a wide range of gas and liquid Reynolds numbers and equivalently a wide range of gas-to-liquid dynamic pressure ratio $M$ and Weber number. The variety of scales exhibited throughout this range, exploring two breakup regimes, is covered by adapting the spatial and temporal resolutions as well as the field of view of the imaging system. An in-depth study of the distributions of the length of the liquid jet is presented, with the associated scalings for the evolution of the first three statistical moments with the relevant dimensionless parameters, fully describing the statistics through a unique function. The first two moments of the distributions are shown to be power laws of $M$ and their ratio is observed to be constant. The temporal dynamics are studied using autocorrelation functions of the length of the liquid jet. The correlation times are shown to be controlled by the gas jet, with a secondary influence of the liquid Reynolds number through a change of behavior that appears to be related to the onset of liquid turbulence. In addition, a transition between two regimes highlighted by a change of shape of both the probability density and autocorrelation functions of the liquid core length is introduced and its link to the turbulence characteristics of the gas jet and the underlying breakup mechanisms is discussed.

We explore the spatial-temporal structure functions of Burgers turbulence driven by a temporal Ornstein-Uhlenbeck (OU) process, where the characteristic time scale of the OU process is much larger than that of the energy flux across spatial scales. Based on the Kármán-Howarth-Monin equation and the temporal scale separation, we postulate an expression for the third-order spatial-temporal structure function away from the dissipation scale. This expression combines Kolmogorov's exact result of spatial structure function and the exponential temporal decay of the external force. We numerically justify this expression and find that the high-order structure functions also decay exponentially; however, the dependence of decay rates on order is different for the odd- and even-order structure functions. Comparing the OU-driven Burgers turbulence with that driven by temporal white noise, their spatial structure functions are identical when the energy injection rates are the same, which justifies Kolmogorov's theory, but these two systems' temporal structure functions differ. Also, the velocity probability density function in the OU-driven Burgers turbulence shows a bimodal distribution, contradicting the near-Gaussian distribution in white-noise-driven turbulence. Even though we lack a rigorous and general deviation of the dependence of the third-order structure function on the temporal statistics of the driving force, our results imply that one can obtain forcing temporal statistics using measured temporal data. However, inferring energy flux across spatial scales solely based on temporal information seems impossible.

Recent experimental work in a guinea pig model has established that influenza A virus is transmissible through the air via aerosolized fomites, which are microscopic dust and dander particulates contaminated with infectious virus [S. Asadi et al., Nat. Commun. 11, 4062 (2020)]. Here we report that influenza A transmits efficiently from intranasally inoculated animals to downwind susceptible animals over a wide range of ventilation airspeeds with no statistically significant change in transmission probability despite increasing the airspeed by a factor of ten. We demonstrate that this finding is inconsistent with a transmission mechanism predicated entirely on emission of virus-laden expiratory particles from the inoculated animal, since the resulting airborne viral concentrations should be greatly diluted at larger airspeeds. Instead, the results suggest that the overall rate of virus aerosolization increases with the ventilation airspeed, in accord with a transmission mechanism predicated on aerosolized fomites in which their generation rate is proportional to the airspeed.

The motion of flexible fibers through structured fluidic environments is ubiquitous in nature and industrial applications. Most often, their dynamics results from the complex interplay between internal elastic stresses, contact forces, and hydrodynamic interactions with the walls and obstacles. By means of numerical simulations, experiments, and analytical predictions, we investigate the dynamics of flexible fibers settling in a viscous fluid embedded with obstacles of arbitrary shapes. We identify and characterize two types of events, trapping and gliding, for which we detail the mechanisms at play. We observe nontrivial trapping conformations on sharp obstacles that result from a subtle balance between elasticity, gravity, and friction. In the gliding case, a flexible fiber reorients and drifts sideways after sliding along the obstacle. The subsequent lateral displacement is large compared with the fiber length and strongly depends on its mechanical and geometrical properties. We show how these effects can be leveraged to propose a strategy to sort particles based on their size and/or elasticity. This approach has the major advantage of being simple to implement and fully passive, since no external source of energy is needed.

Miscible displacement of nondilute fluid pairs in subsurface porous media plays a key role in ${\mathrm{CO}}_2$ subsurface sequestration and many other applications. We conduct microfluidic experiments in a near-fracture porous geometry so that nondilute effects are isolated from other disruptive behaviors. We show that although Darcy-Fickian coupling works well for dilute fluid systems, it completely fails to predict nondilute fluid-fluid displacement. Compared to that predicted by Darcy-Fickian models, nondilute fluid-fluid displacement demonstrates much faster and “diffusive” mixing, an unexpected wedgelike mixing front, and abnormal convection perpendicular to the major concentration. Simply correcting Fick's law cannot reproduce these phenomena. Maxwell-Stefan drifting and Korteweg stress may rationalize experimental observations, but major challenges emerge in microscopic modeling and upscaling. We provide this work as a benchmark and call for future study to incorporate appropriate nondilute effect terms at different scales into the modeling of ${\mathrm{CO}}_2$ sequestration and other relevant applications.

Surfactants can have a detrimental effect on the drag reduction in shear flow over superhydrophobic surfaces in Cassie state. While surfactant-free gas-liquid interfaces are often well approximated as shear-free, surfactants can impede the flow by stacking up in front of obstacles. We study shear-flow along an array of narrow gas-filled grooves of finite length embedded in an otherwise planar surface, with the gas-liquid interface protruding slightly above or below the plane. Assuming immiscible surfactants forming an incompressible, inviscid surfactant phase at the gas-liquid interfaces we employ a recently proposed model [J. Fluid Mech. 949, A34 (2022)] for addressing this situation. Using a domain perturbation technique together with the Lorentz reciprocal theorem we obtain the slip length characterizing the flow over such surfaces to second order in the maximal interface deflection as a small parameter. We find that within the range of moderate interface deflections studied, the slip length for flow over such surfaces is negative (positive) for surfaces protruding above (below) the surface and is much smaller than for flow over a corresponding surfactant-free interface. Thus, contrary to expectations of reduced drag in flow over superhydrophobic surfaces in Cassie state, surfactant covered interfaces can even be detrimental for drag reduction in the limit where surfactants act as an effectively incompressible surface-fluid. This has important implications for the appropriate design of superhydrophobic surfaces for reducing flow resistance.

The dynamics of a shock wave impinging on a transitional high-enthalpy boundary layer out of thermochemical equilibrium is investigated by means of a direct numerical simulation. The freestream Mach number is equal to 9, and the oblique shock impinges with a cooled flat-plate boundary layer with an angle of ${10}^{\circ }$, generating a reversal flow region. In conjunction with freestream disturbances, the shock impingement triggers a transition to a fully turbulent regime shortly downstream of the interaction region. Accordingly, wall properties emphasize the presence of a laminar region, a recirculation bubble, a transitional zone, and a fully turbulent region. In the entire transitional process, the recognized mechanisms are representative of the second mode instability combined with stationary streaky structures, their destabilization being eventually promoted by shock impinging. The breakdown to turbulence is characterized by large increases of skin friction and wall heat flux, due to the particular shock pattern. At the considered thermodynamic conditions the flow is found to be in a state of thermal nonequilibrium throughout the computational domain. Overall, the dynamics of the interaction is little affected by thermal nonequilibrium effects; on the contrary, the latter are enhanced and sustained by the shock-induced laminar/turbulent transition, while chemical activity is almost negligible due to wall cooling. In the interaction region, relaxation towards thermal equilibrium is delayed, and the fluctuating values of the rotranslational and the vibrational temperatures strongly differ, despite the wall cooling. The fully turbulent portion exhibits evolutions of streamwise velocity, Reynolds stresses, and turbulent Mach number in good accordance with previous results for highly compressible cooled-wall boundary layers in thermal nonequilibrium, with turbulent motions sustaining thermal nonequilibrium. Nevertheless, the vibrational energy is found to contribute minimally to the total wall heat flux.

Using experiments and numerical simulations, we investigate the spontaneous spreading of droplets of aqueous glycerol (Newtonian) and aqueous polymer (shear-thinning) solutions on smooth surfaces. We find that in the first millisecond the spreading of the shear-thinning solutions is identical to the spreading of water, regardless of the polymer concentration. In contrast, aqueous glycerol solutions show a different behavior, namely, a significantly slower spreading rate than water. In the initial rapid spreading phase, the dominating forces that can resist the wetting are inertial forces and contact-line friction. For the glycerol solutions, an increase in glycerol concentration effectively increases the contact-line friction, resulting in increased resistance to wetting. For the polymeric solutions, however, an increase in polymer concentration does not modify contact-line friction. As a consequence, the energy dissipation at the contact line cannot be controlled by varying the amount of additives for shear-thinning fluids. The reduction of the spreading rate of shear-thinning fluids on smooth surfaces in the rapid-wetting regime can only be achieved by increasing solvent viscosity. Our results have implications for phase-change applications where the control of the rapid spreading rate is central, such as anti-icing and soldering.

We investigate the cleaning mechanism of an oil-impregnated porous surface by utilizing a method of vortex ring interaction. The kinetic energy of a vortex ring is exploited to expunge the trapped oil from the spherical-bead-based porous surface. Qualitative and quantitative measurements were made using high-speed shadowgraphy imaging, planar laser-induced fluorescence (PLIF) imaging, and particle image velocimetry (PIV) techniques. The interaction phenomenon is explored from the perspective of vortex ring dynamics followed by oil sheet dynamics. Five different strengths of a vortex ring [characterized by the circulation ($\mathrm{\Gamma }$) -based Reynolds number (${\mathrm{Re}}_{\mathrm{\Gamma }}=2550$–14 260: ${\mathrm{Re}}_{\mathrm{\Gamma }}=\mathrm{\Gamma }/\nu$, where $\nu$ is the kinematic viscosity)] and two types of surface porosity ($\varphi$) (open area ratio, 0.21 and 0.41) are considered for parametric analysis. The interaction process with oil is divided into three regimes: (i) penetration, (ii) bag formation, and (iii) bag breakup. Depending on the strength of the vortex ring, it is observed that surface cleaning takes place from both upstream and downstream regions of the porous surface. The vortex rings with higher ${\mathrm{Re}}_{\mathrm{\Gamma }}$ can expunge more oil through a complicated interaction process involving Rayleigh-Taylor- and Rayleigh-Plateau-type instabilities. However, along with ${\mathrm{Re}}_{\mathrm{\Gamma }}$, the interaction dynamics depend strongly on the shape and $\varphi$ value. The interaction process is characterized by vorticity cancellation, Kelvin-Helmholtz (KH) instabilities, and three-dimensional interactions.

A systematic experimental investigation of the dynamics of a Newtonian drop in microscopic cross-slot of a shear thinning and inelastic fluid (aqueous solutions of xanthan) is presented. The flows are driven at large Reynolds numbers and are relevant to efficient high-throughput emulsification in microchannels. Depending on the initial size of the drop, the driving flow rates and the rheological behavior of the continuous phase, two fundamental dynamic modes are observed. The first dynamic mode relates to the trapping of the drop. By time-resolved tracking of both the positions and the deformations of the drop over 100 distinct drops a comprehensive statistical description of the trapping events is provided. The probability of trapping when xanthan solutions are used as a continuous phase follow a common trend when the effective strength of the swirling flow motion within the impingement region is gradually increased by tuning both the flow rates and the polymer concentration, suggesting that the trapping events emerge via an imperfect bifurcation. A second phenomenon that is of particular relevance to the emulsification process relates to the breakup of drops. The dynamics of the breakup process are quantitatively described in terms of the characteristic breakup times, number of emerging daughter droplets, and drop morphology are equally dependent on both the driving flow rates and the polymer concentration. Further physical insights into the intricate coupling between the flow conditions, the shear thinning rheology of the continuous phase, and the single-drop dynamics are obtained in terms of a quantitative description of the kinematics of drop deformation. This analysis was performed using a novel tool that allows one to assess the velocity distributions along the drop contours and extract the rates of deformation, the strains corresponding to the breakup process, and the kinematic print of the flow (shear or extension). Finally, a full diagram mapping all the modes of the single-droplet dynamics is presented.

Partitions are an essential part of industrial reactors and thermal management devices whose primary purpose is to increase transport rates by obstructing flow in one direction and promoting in the other via secondary and small-scale motions. Inspired by such applications, we have investigated thermal convection in a two-dimensional square enclosure heated at the bottom and cooled at the top, with four additional thin vertical partitions arranged parallel to facilitate organized plume motions in the range of Rayleigh numbers ${10}^6$ to ${10}^9$. The large-scale classical circulation observed in thermal convection breaks down into many roll configurations based on the constriction gap ($\mathcal{S}$) between the partitions and the conduction walls. Due to their arrangement, we observed increased plume ejection, impact, and shear near the conduction walls when the partitions disturb the thermal boundary layers. The plume ejection and impact on either end of the constriction gap sets a pressure-driven forced convection on the conduction wall, thus increasing overall heat transport by at least an order of magnitude. We found the maximum heat transport when $0.2{\delta }_{\text{RB}}<\mathcal{S}<0.4{\delta }_{\text{RB}}$, where ${\delta }_{\text{RB}}$ is the time-averaged thermal boundary layer thickness in classical thermal convection. Using both the numerical simulations and a simple control volume-based analysis, we have estimated that the heat transport increases as ${\mathcal{S}}^3$ for small constriction gaps and as an inverse power of $\mathcal{S}$ for the large gap limit. With the help of energy dissipation, we have concluded that increasing plume intensity near the conduction walls leads to the observed high heat transport.