The separated flow over a wall-mounted bump geometry under harmonic oscillations of the inflow stream is investigated with direct numerical simulations. The bump geometry gives rise to streamwise pressure gradients similar to those encountered on the suction side of low-pressure turbine (LPT) blades. Under steady inflow conditions, the separated-flow laminar-to-turbulent transition is initiated by self-sustained vortex shedding due to Kelvin-Helmholtz (KH) instability. In LPTs the dynamics are further complicated by the passage of the wakes shed by the previous stage of blades. The wake-passing effect is modeled here by introducing a harmonic variation of the inflow conditions. Three inflow oscillation frequencies and three amplitudes are considered. The frequencies are comparable to the wake-passing frequencies in practical LPTs. The amplitudes range from 1% to 10% of the inflow total pressure. The dynamics of the separated flow are studied by isolating the flow components that are respectively coherent with and uncorrelated to the inflow oscillation. Three scenarios are identified. The first one is analogous to the steady inflow case. In the second one, the KH vortex shedding is replaced during a part of the inflow period by the formation and release of a large vortex cluster. The third scenario consists solely of the periodic formation and release of the vortex cluster; it leads to a consistent reduction of the separated flow length over the entire period compared to the steady inflow case and would be the most desirable flow condition in a practical application.

The viscous fingering instability, which forms when a less-viscous fluid invades a more-viscous one within a confined geometry, is an iconic system for studying pattern formation. For both miscible and immiscible fluid pairs the growth dynamics change after the initial instability onset and the global structures, typical of late-time growth, are governed by the viscosity ratio. Here we introduce an experimental technique to measure flow throughout the inner and outer fluids. This probes the existence of a new length scale associated with the local pressure gradients around the interface and allows us to compare our results to the predictions of a previously proposed model for late-time finger growth.

The dead-end pore is a geometry common to studies of diffusiophoresis. In most works on diffusiophoresis in dead-end pores, the solute concentration at the pore inlet is quickly changed between two extreme values, yielding a steplike change in solute concentration. We explore—noting diffusiophoresis is inherently nonlinear and other boundary conditions are largely unexplored—the influence of a time-variable boundary solute concentration. We first define metrics for the efficiency of diffusiophoretic injection and withdrawal and characterize the steplike boundary condition. We then introduce a linear change in solute concentration over a variable timescale and comment on changes in efficiency. We find particle migration becomes linear in the limit of slow transitions relative to the timescale for solute diffusion and define an asymptotic efficiency. We further characterize oscillatory changes in the boundary solute concentration and the implications of the oscillation frequency, from slow (yielding linear particle migration) to fast (yielding nonlinear paricle migration) oscillation. The particle dynamics are distinct and can be tuned by adjusting the timescale for oscillation. Our findings are relevant to processes both in the laboratory, where they could inform the choice of timescale or oscillation frequency for changes in solute concentration, and in nature, where various events cause solute concentrations to change over distinct and disparate timescales.

We provide an experimental framework to measure the flow rate–pressure drop relation for Newtonian and shear-thinning fluids in two common deformable configurations: (i) a rectangular channel and (ii) an axisymmetric tube. Using the Carreau model to describe the shear-dependent viscosity, we identify the key dimensionless rheological number $\mathrm{Cu}$, which characterizes shear thinning, and we show that our experiments lie within the power-law regime of shear rates. To rationalize the experimental data, we derive the flow rate–pressure drop relation taking into account the two-way-coupled fluid-structure interaction between the flow and its compliant confining boundaries. We thus identify the second key dimensionless number $\alpha$, which characterizes the compliance of the conduit. We then compare the theoretical flow rate–pressure drop relation to our experimental measurements, finding excellent agreement between the two. We further contrast our results for shear-thinning and Newtonian fluids to highlight the influence of $\mathrm{Cu}$ on the flow rate–pressure drop relation. Finally, we delineate four distinct physical regimes of flow and deformation by mapping our experimental flow rate–pressure drop data for Newtonian and shear-thinning fluids into a $\mathrm{Cu}-\alpha$ plane.

A self-aligning particle (SAP) attains a permanent orientation without application of external torques in a low Reynolds number simple shear flow in contrast with the continuous rotation exhibited by most rigid bodies including thin fibers and disks. SAPs align close to the fluid lamellae, and we characterize the robustness of this flow alignment to secondary disturbances such as perturbation to the shear flow, Brownian motion, interparticle interactions, or the presence of a wall using dynamic simulations of representative SAP geometries. The robustness of the flow alignment of SAPs at all concentrations generates highly aligned microstructures inaccessible to traditional particle suspensions.

The low-Reynolds-number Stokes flow driven by rotation of two parallel cylinders of equal unit radius is investigated by both analytical and numerical techniques. In Part I, the case of counterrotating cylinders is considered. A numerical (finite-element) solution is obtained by enclosing the system in an outer cylinder of radius $R_0\gg 1$, on which the no-slip condition is imposed. A model problem with the same symmetries is first solved exactly, and the limit of validity of the Stokes approximation is determined; this model has some relevance for ciliary propulsion. For the two-cylinder problem, attention is focused on the small-gap situation $\varepsilon \ll 1$. An exact analytic solution is obtained in the contact limit $\varepsilon =0$, and a net force $F_c$ acting on the pair of cylinders in this contact limit is identified; this contributes to the torque that each cylinder experiences about its axis. The far-field torque doublet (“torquelet”) is also identified. Part II treats the case of corotating cylinders, for which again a finite-element numerical solution is obtained for $R_0\gg 1$. The theory of Watson [Mathematika 42, 105 (1995)] is elucidated and shown to agree well with the numerical solution. In contrast to the counterrotating case, inertia effects are negligible throughout the fluid domain, however large, provided Re $\ll 1$. In the concluding section, the main results for both cases are summarized, and the situation when the fluid is unbounded ($R_0=\infty$) is discussed. If the cylinders are free to move (while rotating about their axes), in the counterrotating case they will then translate relative to the fluid at infinity with constant velocity, the drag force exactly compensating the self-induced force due to the counterrotation. In the corotating case, if the cylinders are free to move, then they will rotate as a pair relative to the fluid at infinity and the net torque on the cylinder pair is zero; the flow relative to the fluid at infinity is identified as a “radial quadrupole.” If, however, the cylinder axes are held fixed, then the Stokes flow in the counterrotating case extends only for a distance $r\sim {\mathrm{Re}}^{-1}log\left[{\mathrm{Re}}^{-1}\right]$ from the cylinders, and it is argued that the cylinders then experience a (dimensionless) force ${\widehat{F}}_y\sim 1/log[{\mathrm{Re}}^{-1}log\left[{\mathrm{Re}}^{-1}\right]]$; in the corotating case, the cylinder pair experiences a (dimensionless) torque $\widehat{\mathcal{T}}$, which tends to 17.2587 as $\varepsilon \downarrow 0$; this torque is associated with a vortex-type flow $\sim r^{-1}$ that is established in the far field. Situations that can be described by the condition $\varepsilon <0$ are treated for both counter- and corotating cases in the Supplemental Material.

We investigate experimentally the dissolution of an almost spherical butyramide particle during its sedimentation, in the low Reynolds high Péclet regime. The particle sediments in a quiescent aqueous solution, and its shape and position are measured simultaneously by a camera attached to a translation stage. The particle is tracked in real time, and the translation stage moves accordingly to keep the particle in the field of the camera. The measurements from the particle image show that the radius shrinking rate is constant with time, and independent of the initial radius of the particle. We explain this with a simple model, based on the sedimentation law in the Stokes' regime and the mass transfer rate at low Reynolds and high Péclet numbers. The theoretical and experimental results are consistent within $20\%$. We introduce two correction factors to take into account the nonsphericity of the particle and the inclusions of air bubbles inside the particle, and reach quantitative agreement. With these corrections, the indirect measurement of the radius shrinking rate deduced from the position measurement is also in agreement with the model. We discuss other correction factors, and explain why they are negligible in the present experiment. We also compute the effective Sherwood number as a function of an effective Péclet number.

The structure of liquid foams follows simple geometric rules formulated by Plateau 150 years ago. By placing such foam on a microtextured hydrophilic surface, we show that the bubble footprint exhibits a morphological transition. This transition concerns the liquid channels, also called pseudo-Plateau borders, which are straight between vertices on a smooth surface. We demonstrate experimentally that for a sufficiently large roughness size compared to the width of the liquid channels, the footprint adopts a zigzag shape. This transition is associated with the absence of a wetting film between the pillars caused by capillary suction of the foam, observed by confocal microscopy. We rationalize the number of zigzag segments by a geometric distribution describing the observations made with the footprint perimeter and the mesh size of the asperities.

We perform a direct comparison between experiment and simulation of density-driven convective mixing in three-dimensional (3D) porous media. We find excellent agreement between the experiment and the model in terms of both the convection fingering pattern and the average rate of fluid mixing. In particular, the experiment exhibits dynamic self-organization of columnar plumes into a reticular pattern, which, until now, had only been observed in 3D simulations. We also report good quantitative agreement between the experiment and simulation in the evolution of the state of mixing by comparing, over time, (i) the average concentration at depth, (ii) the variance of the concentration field, (iii) the scalar dissipation rate, and (iv) the dissolution flux. We derive a relation between the scalar dissipation rate and the dissolution flux in a closed system, and we show that the flux in a 3D system is approximately $\sim 30\%$ higher than in a 2D system, confirming previous numerical estimates.

We investigate the stability of the steady vertical path and the emerging trajectories of a buoyancy-driven annular disk as the diameter of its central hole is varied. The steady and axisymmetric wake associated with the steady vertical path of the disk, for small hole diameters, behaves similarly to the one past a permeable disk, with the detachment of the vortex ring due to the bleeding flow through the hole. However, as the hole diameter increases, a second recirculating vortex ring of opposite vorticity forms at the internal edge of the annulus. A further increase in the hole size leads to the shrinking of these recirculating regions until they disappear. The flow modifications induced by the hole influence the stability features of the steady and axisymmetric flow associated with the steady vertical path. The fluid-solid coupled problem shows a nonmonotonic behavior of the critical Reynolds number for the destabilization of the steady vertical path, for low values of the disk's moment of inertia. However, for very large holes, with dimension approximately more than half of the external diameter, a marked increase of the neutral stability threshold is observed. The nature of the primary instability changes as the hole size increases, with large (small) amplitude oscillations of the trajectory at intermediate (very small and large) internal diameters. We then illustrate results obtained with fully nonlinear simulations of the time-dependent dynamics, together with a comparison of the linear stability analysis results. Falling styles, typically described as steady, hula-hoop, fluttering, chaotic, and tumbling, are shown to emerge as attractors for the nonlinear dynamics of the coupled fluid-structure system. The presence of a central hole does not always reduce the falling Reynolds number, and it may cause the transition from tumbling towards fluttering, from fluttering to hula-hoop, and from hula-hoop to steady, hence promoting trajectories with smaller lateral deviations from the vertical path. The observed trajectories and patterns agree well with linear stability analysis results, in the vicinity of the threshold of instability.

Understanding the solidification dynamics of impacted water droplets is fundamental and crucial for applications, especially with the presence of frost and salt. Here, we experimentally investigate the spreading and freezing dynamics of saline droplets upon impact on a cold, frosty surface. Our findings demonstrate that the frost and salt can lead to an extended spreading of impacted droplets under specific conditions. In addition to the well-known 1/2 inertial spreading scaling law for droplets impact on a cold substrate, we observe a distinct transition to a 1/10 scaling law dominated by the capillary-viscous relation at low impacting velocities. We formulate the onset criterion for this extended spreading regime and derive a scaling dependence that captures the droplet's arrested diameter over various supercooling temperatures, by incorporating the effect of impact inertia, partial-wetting behavior, and salinity. Based on the analysis, a unified model is proposed for predicting the droplet arrested diameter over a wide range of impact velocity and salinity.

While the degrees of freedom needed to represent the dynamics of high Reynolds number turbulence are extremely large, we show using well-resolved direct numerical simulations that one can capture essential physics with only a fraction of modes obeying the Navier-Stokes equations; the other modes can be modeled with very simple dynamics. This result suggests that the attractor for the dynamics of fully developed turbulence is robust to modeling errors and the strongly nonlinear dynamics may reside on fewer degrees of freedom than traditionally thought. The proposed approach is validated in terms of dissipation rate, skewness of velocity gradients, the energy and transfer spectrum, and structure functions. The mixed-dynamics model explored here, which may open different venues for turbulence modeling, may also be applicable to a broader set of physical phenomena governed by nonlinear complex dynamics with a wide range of scales.

Electrocapillary driven two-phase flows in a confined configuration of a classical experiment of Melcher and Taylor are studied. The computed streamlines of the flow of the heavier dielectric liquid (corn oil) qualitatively represent the corresponding experimental image. With the increase of electrocapillary forcing, the flow pattern changes, so that the main circulation localizes near a boundary with a larger electric potential. When a dielectric liquid is replaced by a poorly conducting one, the system becomes nonisothermal owing to the Joule heating. Then the flow is driven also by buoyancy and thermocapillary convection, whose effect becomes noticeably stronger than the electrocapillary one. With the increase of electric conductivity, the electrocapillary effect is further weakened compared to the two others, while the electrocapillary and thermocapillary forces remain comparable at the central part of the interface. The results show that consideration of the two-phase model is mandatory for obtaining correct flow patterns in the lower, heavier fluid. The Lippmann equation, connecting electrically induced surface tension with nonuniform surface electric potential, is numerically verified for both isothermal and nonisothermal formulations and is found to hold in both of them.

The presence of a dispersed phase substantially modifies small-scale turbulence. However, there has not been a comprehensive mechanistically based understanding to predict turbulence modulation. Based on the energy flux balance, we propose a theoretical model to predict the turbulent kinetic energy modulation in isotropic turbulence due to the dispersed phase. The comparison between model predictions and results from prior particle-resolved simulations and existing high-fidelity experiments supports the performance of the model over a range of turbulence and particle parameters. The model is then used to explore turbulence modulation characteristics over a wider parameter space formed by five independent system-controlling parameters, showing rather complicated dependence on the particle size and particle-to-fluid density ratio.

Acoustic fields are widely used to manipulate suspended particles, by rectifying the inertia of rapid oscillations into steady transport. We develop an analytic theory of this particle motion, systematically unifying inviscid acoustophoresis with viscous streaming effects. By applying the Lorentz reciprocal theorem, we obtain a Faxén-like relationship that relates particle motion to a generalized version of the secondary radiation force that depends on the thickness of the oscillatory Stokes layer around the particle, and the density and compressibility contrast between the particle and the fluid. The theory identifies a reversal of particle motion when inertial and viscous forces are comparable, which we validate quantitatively with numerical solutions of the timescale-separated hydrodynamics. We discuss the implications of our findings for practical applications seeking to sort or focus particles by size or material properties.

In stars and planets natural processes heat convective flows in the bulk of a convective region rather than at hard boundaries. By characterizing how convective dynamics are determined by the strength of an internal heating source we can gain insight into the processes driving astrophysical convection. Internally heated convection has been studied extensively in incompressible fluids, but the effects of stratification and compressibility have not been examined in detail. In this work, we study fully compressible convection driven by a spatially uniform heating source in two-dimensional (2D) and 3D Cartesian, hydrodynamic simulations. We use a fixed temperature upper boundary condition which results in a system that is internally heated in the bulk and cooled at the top. We find that the flow speed, as measured by the Mach number, and turbulence, as measured by the Reynolds number, can be independently controlled by separately varying the characteristic temperature gradient from internal heating and the diffusivities. Two-dimensional simulations at a fixed Mach number (flow speed) demonstrate consistent power at low wave number as diffusivities are decreased. We observe convection where the velocity distribution is skewed towards cold, fast downflows and that the flow speed is related to the length scale and entropy gradient of the upper boundary where the downflows are driven. We additionally find a heat transport scaling law which is consistent with prior incompressible work.

In this paper, we present a Lagrangian method for searching initial disturbances which maximize their total energy growth after a certain time horizon for linearized fluid-structure interaction problems. We illustrate this approach for the channel flow case with compliant walls. The walls are represented as thin spring-backed plates, the so-called Kramer-type walls. For nearly critical values of the control parameters (reduced velocity $V_R$ and Reynolds number $\text{Re}$), analyses for sinuous or varicose perturbations show that the fluid-structure system can sustain two types of oscillatory motions of large amplitude. The first motion is associated with two-dimensional perturbations that are invariant in the spanwise direction. For that case and a certain range of streamwise wavenumbers, the short-time dynamics of sinuous perturbations is driven by the nonmodal interaction between the Tollmien-Schlichting and the traveling-wave flutter (TWF) modes. The amplitude of the oscillation is found to increase with the reduced velocity, and the optimal gain exhibits larger values than its counterpart computed for a channel flow between rigid walls. For perturbations of varicose symmetry, the transient energy is rapidly governed by the unstable TWF mode without a clear low-frequency oscillation. The second type of motion concerns streamwise-invariant and spanwise-periodic perturbations. In that situation, it is found that perturbations of sinuous symmetry exhibit the largest amplification factors. For moderate values of the reduced velocity, $V_R=\mathcal{O}\left(1\right)$, the dynamics is the result of a simple superposition of a standing wave, due to traveling-wave flutter modes propagating downstream and upstream, and the roll-streak dynamics. The variations of these oscillations with the reduced velocity, spanwise wavenumber, and Reynolds number are then investigated in detail for the sinuous case.

The linear temporal stability of the fully developed pulsatile flow in a torus with high curvature is investigated using Floquet theory. The baseflow is computed via a Newton-Raphson iteration in frequency space to obtain basic states at supercritical Reynolds numbers in the steady case for two curvatures, $\delta =0.1$ and 0.3, exhibiting structurally different linear instabilities for the steady flow. The addition of a pulsatile component is found to be overall stabilizing over a wide range of pulsation amplitudes, in particular for high values of curvature. The pulsatile flows are found to be at most transiently stable with large intracyclic growth rate variations even at small pulsation amplitudes. While these growth rates are likely insufficient to trigger an abrupt transition at the parameters in this work, the trends indicate that this is indeed likely for higher pulsation amplitudes, similar to pulsatile flow in straight pipes. At the edge of the considered parameter range, subharmonic eigenvalue orbits in the local spectrum of the time-periodic operator, recently found in pulsating channel flow, have been confirmed also for pulsatile flow in toroidal pipes, underlining the generality of this phenomenon.

We investigate transport of dense fluid flow through nanoporous membranes in the limit of steric exclusion using molecular dynamics (MD) and finite element simulations. Simulation results suggest that, for simple fluids, deviations from Sampson flow are a consequence of the competition between slip and finite atomic size effects. The latter manifest themselves by introducing an effective pore size, as well as an effective membrane thickness. We propose an analytical model for the membrane permeance that accounts for all these factors. We also show how this model can be modified to describe transport of low molecular weight aromatic hydrocarbons across these membranes in the steric limit. Extensive validation of this model is conducted through MD simulations of Lennard-Jones fluids permeating single- and multilayer graphene membranes, as well as low molecular weight organic liquids permeating single-layer graphene membranes.

Recent work has demonstrated that Lagrangian chaos can arise at the Darcy scale in even simple poroelastic media, relevant across geophysical, biophysical, and industrial domains. Key factors controlling the onset of chaotic advection in poroelastic media flow include medium heterogeneity, compressibility, and transient forcing. Here we focus on how the range of Lagrangian coherent structures (LCSs) present in poroelastic flows influences the transport of diffusive solutes. We use a minimal two-dimensional sinusoidally forced poroelastic computational model to show that LCS interactions impact the dispersion of solute plumes via the establishment of minimum flux manifolds, leading to strongly anomalous plume moments and solute residence time distributions. We interpret these results with fluid element stretching distributions and local Lyapunov exponents. Anomalous features persist even at low Péclet number. Our data show that solute dispersion in poroelastic systems subject to transient forcing can only be understood by resolving the LCSs of these complex flows.