High-fidelity numerical simulations of an impinging shock interacting with a turbulent boundary layer at free-stream Mach number ${\text{Ma}}_{\infty }=5.0$ are performed for three shock angles and a weakly cooled wall condition (wall-to-recovery temperature ratio of $T_w/T_r=0.8)$, matching the experimental conditions of Schülein [AIAA J. 44, 1732 (2006)]. Additional simulations are carried out with a heated wall $\left(T_w/T_r=1.9\right)$ to investigate the impact of the wall thermal condition on shock/boundary-layer interactions in the hypersonic regime. The free interaction theory is found to remain valid in the hypersonic regime even at different wall thermal conditions. The interaction length scaling proposed by Jaunet et al. [AIAA J. 52, 2524 (2014)] previously validated only at supersonic Mach numbers, is found to remain viable at higher Mach numbers only if the model coefficient is adjusted, thus showing that this coefficient is not universal.

We numerically study the energy transfer in a multicomponent two-dimensional film made of an active polar gel and a passive isotropic fluid in presence of surfactant favoring emulsification. We show that by confining the active behavior into the localized component, the typical scale where chemical energy is transformed in mechanical energy can be substantially controlled. Quantitative analysis of kinetic energy spectra and fluxes shows the presence of a multiscale dynamics due to the existence of a flux induced by the active stress only, without the presence of a turbulent cascade. An increase in the intensity of active doping induces drag reduction due to the competition of elastic and dissipative stresses against active forces. Furthermore we show that a nonhomogeneous activity pattern induces localized response, including a modulation of the slip length, opening the way toward the control of active flows by external variation of the actvity level.

Synchrotron x-ray microtomography combined with sensitive pressure differential measurements were used to study flow during steady-state injection of equal volume fractions of two immiscible fluids of similar viscosity through a 57-mm-long porous sandstone sample for a wide range of flow rates. We found three flow regimes. (1) At low capillary numbers, Ca, representing the balance of viscous to capillary forces, the pressure gradient, $\mathbf{\nabla }P$, across the sample was stable and proportional to the flow rate (total Darcy flux) $q_t$ (and hence capillary number), confirming the traditional conceptual picture of fixed multiphase flow pathways in porous media. (2) Beyond ${\text{Ca}}^{*}\approx {10}^{-6}$, pressure fluctuations were observed, while retaining a linear dependence between flow rate and pressure gradient for the same fractional flow. (3) Above a critical value $\text{Ca}>{\text{Ca}}^i\approx {10}^{-5}$ we observed a power-law dependence with $\mathbf{\nabla }P\sim q_t^a$ with $a\approx 0.6$ associated with rapid fluctuations of the pressure differential of a magnitude equal to the capillary pressure. At the pore scale a transient or intermittent occupancy of portions of the pore space was captured, where locally flow paths were opened to increase the conductivity of the phases. We quantify the amount of this intermittent flow and identify the onset of rapid pore-space rearrangements as the point when the Darcy law becomes nonlinear. We suggest an empirical form of the multiphase Darcy law applicable for all flow rates, consistent with the experimental results.

We present the experimental evidence of prompt splashing due to surface roughness at drop impact on a dry smooth surface, by suppressing corona splashing due to the surrounding gas. Prompt splashing occurs during a very early stage of the impact process, and it cannot be suppressed by reducing the gas pressure even to 0.8 kPa. We evaluate the conditions under which corona splashing hides prompt splashing at atmospheric conditions. We also demonstrate the importance of the distinction of two events, i.e., prompt splashing occurs and it can be clearly distinguished.

We consider the flow of a thixotropic fluid in a uniform cylindrical pipe, driven by an oscillating pressure gradient or a body force. For a variety of rheological models, solutions can be obtained by integrating ordinary rather than partial differential equations: We illustrate this approach for the thixoviscoplastic Houška model and the thixoviscous simplified Moore–Mewis–Wagner model. We present asymptotic results in the limits of small and large Deborah numbers and numerical results for intermediate Deborah numbers. Under asymmetrical “sawtooth” forcing, thixotropy leads to the net transport of fluid along the pipe, even when there would be no net transport of the corresponding generalized-Newtonian fluid. We propose the name “thixotropic pumping” for this transport mechanism.

At finite Reynolds numbers, particles migrate across flow streamlines to their equilibrium positions in microchannels. Such a migration is attributed to an inertial lift force, and it is well known that the equilibrium location of neutrally buoyant particles is determined only by their size and the Reynolds number. Here we demonstrate that the decoration of a bottom wall of the channel by superhydrophobic grooves provides additional possibilities for manipulation of neutrally buoyant particles. It is shown that the effective anisotropic hydrodynamic slip of such a bottom wall can be readily used to alter the equilibrium positions of particles and to generate their motion transverse to the pressure gradient. These results may guide the design of novel inertial microfluidic devices for efficient sorting of neutrally buoyant microparticles by their size.

The cooling process associated with the flow induced by a spark plasma discharge generated between a pair of electrodes is measured using stereoscopic particle image velocimetry (S-PIV) and background oriented schlieren (BOS). Density measurements show that the hot gas kernel initially cools fast by convective cooling, which is followed by a slower cooling process. The cooling rates during the fast regime range from 2 to 10 times those in the slower regime. An analytical model is developed to relate the cooling observed in the fast regime using BOS to the total entrainment of cold ambient fluid per unit volume of the hot gas kernel, measured using S-PIV. The model calculates the cooling ratio to characterize the cooling process and shows that the cooling ratios estimated from the density measurements are in close agreement with those calculated from the entrainment. These measurements represent quantitative density and velocity measurements of the flow induced by a spark discharge and reveal the role of entrainment in the cooling of the hot gas kernel. These results underscore that convective cooling of the hot gas kernel, in the fast regime, leads to approximately 50% of the cooling and occurs within the first millisecond of the induced flow.

The stretching of viscoelastic polymer solutions close to breakup can create attached drops on a filament, whose properties and dynamics are little understood. The stretching of capillary bridges and the consecutive filament, until its breakup, can be quantified using diameter-space-time diagrams, which demonstrate hierarchy, as well as asymmetry of satellite drops around a big central drop. All drops experience migration, oscillation, and merging. In addition, the position of the minimum diameter on the filament is determined, along with the number of drops, their positions, the diameters of drops and the filament breakup time. The maximum number of drops on the filament can be predicted using the Deborah number. The diagrams also quantify the large Hencky strains in the filaments before pinch-off. The obtained minimum diameter is used to measure the extensional viscosity, which indicates the effect of polymer concentration and direction of filament thinning.

Settling experiments were conducted in a turbulence column to investigate the effect of turbulence on the effective fall velocity of solid particles slightly denser than the fluid $({\rho }_p\gtrsim {\rho }_f)$. Five types of particles of different materials and shapes were tested, their size ranging between $o\left(1\right)\eta$ and $o\left(10\right)\eta$, where $\eta$ is the Kolmogorov viscous length scale. Thus, the particles were of finite size with an unknown analytical form for the fluid-particle forces. The density ratio ranged as $({\rho }_p-{\rho }_f)/{\rho }_f=\{0.13:1.6\}$, and the still-fluid particle Reynolds number as ${\text{Re}}_p^0=\{75:981\}$. The turbulence levels characterized with the integral-scale Reynolds number ranged as ${\text{Re}}_L=\{34:510\}$. Two-dimensional (2D) particle image velocimetry was used to obtain flow statistics, the residual mean circulation, and the turbulence statistics, while 2D particle tracking was performed to measure particle settling velocities. For all types of particles tested, settling retardation is observed as the turbulence intensity is increased. It is found that if both the effective fall velocity $W_s$ and the turbulent fluid velocity $W_{f,\text{rms}}$ are nondimensionalized by the still-fluid particle terminal velocity $W_0$, the settling retardation can be described by a unique relation independent of the particle type, $W_s/W_0=f(W_{f,\text{rms}}/W_0)$, for the given range of flow regimes. Using analytical descriptions of the loitering and nonlinear drag effects, this scaling is shown to have a solid physical basis.

We investigate the streamwise evolutions of energy and pressure spectra along the shear-layer region of very near-field grid-generated turbulence. The energy and pressure spectra evolve significantly in this near-field. The shear-layer and vortex-shedding frequencies appear immediately in different spectra but the shear-layer's spectral signature is very soon replaced by a broad power-law spectrum on both sides of that frequency. The spectra evolve further by filling the gap between the vortex shedding and the shear-layer frequencies eventually leading to near $-5/3$ power-law energy spectra at the point on the shear-layer region where the turbulence intensity reaches a maximum. The pressure spectrum reaches a $-7/3$ power-law shape significantly further downstream. These spectral scalings cover a range between the vortex-shedding frequency and frequencies larger than the shear-layer frequency. They are discussed in relation to turbulent coherent structures of various sizes, obtained by using Gaussian low-pass filtering of instantaneous turbulent flow fields. High enstrophy small-scale structures originate from the shear-layer instability whereas low enstrophy large-scale structures originate from the vortex shedding. The generation of near-field $-5/3$ energy and $-7/3$ pressure spectra involves cooperative interactions between these two different size structures.

Motivated by the laboratory experiments of Rodenborn et al. [Phys. Fluids 23, 026601 (2011)], a weakly nonlinear model is developed that accounts for viscous dissipation in the reflection of a finite-width internal wave beam from a uniform slope. Asymptotically, at high Reynolds number, viscous effects come into play predominantly in the immediate vicinity of the critical slope angle equal to the propagation angle to the horizontal of the incident wave beam. However, in the experiments of Rodenborn et al. where the Reynolds number is moderately large, it turns out that viscosity is important throughout the slope range considered, which explains the overall poor agreement of their observations with earlier inviscid models. The predictions of the proposed model, by contrast, are in good qualitative, and in some respects quantitative, agreement with these experiments, and they also compare favorably against numerical Navier-Stokes simulations.

We investigate the long-time evolution of flow structures and the kinetic-potential energy exchange in rotating stratified turbulence, which is of great significance in geophysical flows. Numerical simulations of forced three-dimensional homogeneous rotating stratified turbulence in transient state with different Froude numbers are performed. Numerous small vortices spread in the flow, besides a cyclone and an anticyclone that fill up the domain after a very long time. Cyclonic vortices, though being less numerous than anticyclonic vortices, grow faster, thus becoming comparable to the domain scale at an earlier time. When the strength of stratification is varied, we find that in the case with weak stratification, the intensity of global kinetic-potential energy exchange is nearly constant in earlier times, while it oscillates in time at later times. Moreover, for the simulation with weak stratification, the areas of intense kinetic-potential energy exchange tend to concentrate in segmented cylinders. In contrasts, when the strength of stratification is comparable to that of rotation, the areas of intense kinetic-potential energy exchange populate the flow as quadrupoles. For both simulations with stratification, the intense kinetic-potential energy exchange is found to be associated with the cyclonic structures. A possible relation between the sign of ${\omega }_z$ and the spatial distribution of the density field $\theta$ is proposed, and the conditional average $\langle \partial \theta /\partial z|{\omega }_z\rangle$ is found to be almost time-invariant throughout most of the domain.

We derive a generalized induced-charge electrokinetic (ICEK) velocity around a conducting object placed in an arbitrary multimodal electric field. The generalized model allows consideration of asymmetric rectified electric fields (AREFs), which have recently been established to occur in liquids where the ions present have unequal mobilities. Including the AREF yields fluid velocities in which both the direction and the magnitude depend sensitively on the applied potential, frequency, ionic type and strength, and even the exact placement of the object between parallel electrodes. The results provide an explanation for the long-standing question of flow reversals observed in ICEK systems.

A theoretical investigation is presented for a linear viscoelastic flow induced by an oscillatory colloidal particle in nonadsorbing polymer solutions. At small-amplitude oscillations, the polymer distribution is assumed to be at equilibrium and forms a depletion zone around the particle based on the mean-field approximation. The goal of the theoretical approach is to predict the apparent complex viscosity sensed by the particle and compare this with the actual viscosity of the bulk fluid. Due to the local inhomogeneity, substantial deviation between the apparent and true viscosity in the bulk needs to be corrected quantitatively. The resulting apparent complex viscosity or friction coefficient in the Fourier domain will help to interpret active and passive microrheological measurements of colloid-polymer mixtures that take polymer depletion into account.

This experimental study explored the dynamics of lock-in phenomena associated with upstream shear layer (USL) instabilities for an equidensity gaseous jet in crossflow (JICF). Axisymmetric sinusoidal forcing of the jet fluid at different forcing amplitudes and frequencies was used to explore lock-in under flow conditions corresponding to naturally occurring absolutely/globally unstable and convectively/locally unstable shear layers, at relatively low and high jet-to-crossflow momentum flux ratios $J$, respectively. Dynamical phenomena were quantified via hotwire anemometry, which not only documented differences in spectral characteristics but also in Poincaré maps obtained via time-delay embedding in the temporal data. The experiments provided evidence of unconditional lock-in as well as quasiperiodicity in response to forcing, reflective of marginal lock-in phenomena; these phenomena were observed for both globally unstable and convectively/locally unstable shear layers in the absence of forcing. The free jet limit in the absence of crossflow also exhibited unconditional lock-in, with some characteristics similar to those for the JICF at applied forcing frequencies above the fundamental mode. For the globally unstable JICF, a simple van der Pol nonlinear oscillator model used to represent the dynamics of the USL showed consistency with experimental findings and thus provided additional insights into the nature of shear layer dynamics.

The interaction between particles and turbulent flow is investigated by simultaneous measurement of the time-resolved three-dimensional (3D) velocity of particles and the carrier liquid phase. The investigation is conducted in a horizontal channel flow at a Reynolds number, Re, of 20 000, based on the average velocity and full channel height. The particle-laden suspension is produced by nearly neutrally buoyant beads with a density of $1.05\mathrm{g}/\mathrm{c}{\mathrm{m}}^3$ and a mean diameter of 370 μm at a volumetric concentration of $0.1\%$. The liquid phase is seeded with 2 μm tracers, the images of which are digitally separated from the larger beads using a medina filter, and processed using time-resolved 3D particle tracking velocimetry. Conditional sampling of the beads and their surrounding fluid, based on the beads’ wall-normal motion, showed that ascending beads were mostly located within ejection motions of the fluid. However, the descending beads did not indicate any correlation with the streamwise fluid velocity; the beads were surrounded by wallward fluid motions with both positive and negative streamwise velocity fluctuations. For both ascending and descending beads, the surrounding fluid motion had a strong spanwise velocity component. Inspection of the 3D beads’ pathlines showed a spiral motion of beads around a streamwise axis. At $y/h<0.2$, the descending beads showed a stronger correlation with their surrounding fluid, while ascending beads demonstrated a stronger correlation with their surrounding flow farther away from the wall. Conditional sampling of the beads and their surrounding flow was also performed based on the streamwise acceleration of the beads. The results showed that, in the near-wall region of $y/h<0.2$, slip velocity and the resultant drag force were not in the same direction as the bead acceleration. Therefore, for this near-wall region, the drag force is not sufficient to model the dynamics of the large nearly buoyant beads.

We present spatially resolved measurements of the columnar vortex structures in rotating Rayleigh-Benard convection. The scaled radial profiles of the azimuthal velocity $u_{\varphi }\left(r\right)$ and vertical vorticity $\omega \left(r\right)$ of the vortices are analyzed and compared with the predictions of the asymptotic theory. The results reveal that the asymptotic theory predicts accurately $u_{\varphi }\left(r\right)$ and $\omega \left(r\right)$ in the geostrophic convection regime. In the weak rotation regime, it is found that the experimental data deviate from the theoretical predictions. Our measurements of the mean velocity, vorticity of the vortices, and the strength of the vortex shield structure all indicate a flow transition from weakly rotating convection to geostrophic convection. Results of the parameter values for the transition are supportive of the scaling relationship obtained from previous heat-transfer measurements.

Experiments are conducted exploring the flow of Carbopol past obstacles in a narrow slot and compared with predictions of a model based on the Herschel-Bulkley constitutive law and the conventional Hele-Shaw approximation. Although Carbopol is often assumed to be a relatively simple yield-stress fluid, the flow pattern around an obstacle markedly lacks the fore-aft symmetry expected theoretically. Such asymmetry has been observed previously for viscoplastic flows past obstacles in unconfined geometries, but the narrowness of the Hele-Shaw cell ensures that the stress state is very different, placing further constraints on the underlying origin. The asymmetry is robust, as demonstrated by varying the shape and number of the obstacles, the surfaces of the cell walls, and the steadiness of the flow rate. The results suggest that rheological hysteresis near the yield point may be the cause of the asymmetry.

We study the dynamics of a pair of initially spherical drops rising side by side in a surrounding, denser, fluid. Our primary focus is on liquid-liquid systems, and a range of viscosity and density ratios is explored by three-dimensional numerical simulations. Interesting dynamics are reported, which cannot be extrapolated from previously known dynamics of gas-liquid systems. Similar to two air bubbles though, we find that two liquid drops move away from each other as they rise, in cases where a single drop would rise vertically. A pair of light drops always remains in two-dimensional motion, and higher drop viscosity increases the tendency of wobbling. This is in contrast with the dynamics of a single drop that follows a highly three-dimensional trajectory at very low drop viscosity, but is restricted to two-dimensional motion at higher drop viscosity. On the other hand, a pair of heavier drops displays three-dimensional behavior at low drop viscosity and two-dimensional behavior at high viscosity. We find that a pair of drops is far less sensitive to viscosity contrast than a single drop is, in our parameter range. In contrast to gas-liquid systems, where the shape change of the bubble was tied to nonlinear dynamics of the trajectory, we find in liquid-liquid systems that interesting drop trajectories can occur without corresponding large shape changes. It is found that the separation distance between the drops exhibits a nonmonotonic trend with an increase in the density ratio. The physical reason for this nonmonotonic trend is simple and explained by inspecting the velocity components.

The transient growth in thermocapillary liquid layers is examined by nonmodal stability theory. Two kinds of thermocapillary liquid layers including linear flow and return flow are considered. The transient growth is measured by a growth function, which depends on both the velocity and temperature. It was found that rather large transient growth occurs in subcritical flows at small Prandtl numbers (Pr), while the temperature field on the surface has a negative effect on the transient growth. In particular, the transient growth function increases significantly with the Reynolds number, but decreases with Pr. The most amplified perturbation is characterized by counter-rotating vortices and streaks, which are both nearly streamwise. Energy analysis shows that the energy of transient growth mainly comes from the basic flow, while the work done by Marangoni forces on the surface is negligible.