We experimentally examine the formation of viscous fluid threads in hydrodynamic focusing sections using both miscible and immiscible fluid pairs at relatively low flow rates. A systematic comparative study is conducted between diffusive and capillary regimes using a viscous oil and a variety of polar organic solvents in a simple microflow geometry. Silicone oil and various low molecular weight alcohols are used as model fluids to investigate the dynamics of viscous multiphase flows at ultralow interfacial tension and with partially miscible systems. An original methodology based on analysis of thread width and detachment length in the viscous regime is developed to quantify various interfacial destabilization processes over a wide range of injection flow rates. For miscible fluid pairs, we investigate several regimes of thread swelling and, for immiscible fluid pairs, we discuss diverse modes of droplet formation and wetting dynamics. This work provides a comprehensive general classification of immiscible and miscible fluid dynamics with large viscosity contrasts in microchannels together with a unifying phenomenological description of thread behavior based on simple functional relationships to better delineate the role of flow parameters and fluid properties on viscous microflow processes.

We report experimental measurements of the onset of grain motion in fully submerged erodible beds containing grains of two sizes driven by a turbulent shear flow. Although we find that a traditional Shields-number framework successfully accounts for grain-size effects in beds composed of grains of only a single size, our results show that bimodal beds are distinct in a way that cannot be captured by a Shields-number rescaling. In particular, we find that large grains in a bimodal bed are mobilized into bedload transport by stresses that would normally be subcritical for them but that the behavior of small grains is less significantly affected. By analyzing higher-order statistics, we reveal the key role played by the granular contact and force networks in the bed near onset and clarify the impact of grain-size polydispersity on the transition from a static to an eroding bed. Our results have implications for modeling sediment transport in natural systems where polydispersity is unavoidable.

Modeling realistic fluid and plasma flows is computationally intensive, motivating the use of reduced-order models for a variety of scientific and engineering tasks. However, it is challenging to characterize, much less guarantee, the global stability (i.e., long-time boundedness) of these models. Previous work provided a theorem outlining necessary and sufficient conditions to ensure global stability in systems with energy-preserving, quadratic nonlinearities, with the goal of evaluating the stability of projection-based models. In this work, we incorporate this theorem into modern data-driven models obtained via machine learning. First, we propose that this theorem should be a standard diagnostic for the stability of projection-based and data-driven models, examining the conditions under which it holds. Second, we illustrate how to modify the objective function in machine learning algorithms to promote globally stable models, with implications for the modeling of fluid and plasma flows. Specifically, we introduce a modified “trapping SINDy” algorithm based on the sparse identification of nonlinear dynamics (SINDy) method. This method enables the identification of models that, by construction, only produce bounded trajectories. The effectiveness and accuracy of this approach are demonstrated on a broad set of examples of varying model complexity and physical origin, including the vortex shedding in the wake of a circular cylinder.

Particles transported in fluid flows, such as cells, polymers, or nanorods, are rarely spherical. In this study, we numerically and theoretically investigate the dispersion of an initially localized patch of passive elongated Brownian particles in a two-dimensional Poiseuille flow, demonstrating that elongated particles exhibit an enhanced longitudinal dispersion. In a shear flow, the rods translate due to advection and diffusion and rotate due to rotational diffusion and their classical Jeffery's orbit. The magnitude of the enhanced dispersion depends on the particle's aspect ratio and the relative importance of its shear-induced rotational advection and rotational diffusivity. When rotational diffusion dominates, we recover the classical Taylor dispersion result for the longitudinal spreading rate using an orientationally averaged translational diffusivity for the rods. However, in the high-shear limit, the rods tend to align with the flow and ultimately disperse more due to their anisotropic diffusivities. Results from our Monte Carlo simulations of the particle dispersion are captured remarkably well by a simple theory inspired by Taylor's original work. For long times and large Péclet numbers, an effective one-dimensional transport equation is derived with integral expressions for the particles' longitudinal transport speed and dispersion coefficient. The enhanced dispersion coefficient can be collapsed along a single curve for particles of high aspect ratio, representing a simple correction factor that extends Taylor's original prediction to elongated particles.

In this Letter, we derive the Korteweg–de Vries (KdV) equation corresponding to the surface dynamics of a shallow depth ($h$) two-dimensional fluid with odd viscosity (${\nu }_o$) subject to gravity ($g$) in the long-wavelength weakly nonlinear limit. In the long-wavelength limit, the odd viscosity term plays the role of surface tension albeit with opposite signs for the right and left movers. We show that there exist two regimes with a sharp transition point within the applicability of the KdV dynamics, which we refer to as weak $\left(\right|{\nu }_o|<\sqrt{g{h}^3}/6)$ and strong $\left(\right|{\nu }_o|>\sqrt{g{h}^3}/6)$ parity-breaking regimes. While the “weak” parity-breaking regime results in minor qualitative differences in the soliton amplitude and velocity between the right and left movers, the “strong” parity-breaking regime on the contrary results in solitons of depression (negative amplitude) in one of the chiral sectors.

In view of the mechanism of the enhanced cavitation erosion of hydraulic machinery operating in sand-laden water, we carry out a systematic investigation on the interaction between a laser-induced cavitation bubble and a free-settling spherical particle near a rigid boundary. We document different types of particle-bubble interactions and experimentally discover two important phenomena where the particle ends up impacting on the boundary at a relatively high velocity, driven by the explosive growth of the bubble and the microjet of the nonspherical bubble collapse respectively. By combining numerical and analytical analyses with experiments, we identify two limiting conditions of the particle-bubble bounce and the particle-boundary impact respectively in terms of the initial relative distance between the particle and the bubble, and the stand-off distance of the bubble against the boundary. These results provide guidance in controlling the particle-bubble dynamics in applications, such as alleviating cavitation erosions in sand-laden water, improving the efficiency of surface cleaning and drug delivery by cavitation and other means.

Using molecular dynamics (MD) simulations, this study investigates the splash of water nanodroplets on hydrophilic to hydrophobic surfaces with static contact angles ranging from 30 ° to 105 ° in the ranges of $\mathrm{We}=24.76-525$ and Re = 18.43–65.51. Here, We is the Weber number, describing the ratio of inertial to capillary forces, and Re is the Reynolds number, defined as the ratio of inertial to viscous forces. Two splash patterns, internal breakup and prompt splash, are observed under normal conditions. The mechanisms behind these two patterns are found to be different from those of macroscale impacting droplets. The internal rupture of macroscale droplets is attributed to initial air holes on solid surfaces, whereas it arises from the vibration of a nanometer-thick spreading film for nanodroplets. The internal breakup of nanodroplets relies heavily on surface wettability because the attenuation of vibration is much more drastic on hydrophilic surfaces than hydrophobic surfaces owing to larger viscous dissipation rates. A damped harmonic vibration model is developed to characterize the vibration, which verifies the dependence of internal rupture on surface wettability. The prompt splash of macroscale droplets is initiated by air bubbles under the spreading lamella; however, the Rayleigh-Taylor instability of ejected rims caused by a rapidly decelerated spreading lamella gives rise to the prompt splash of nanodroplets. This mechanism is further verified by comparing the number of fingers predicted by the Rayleigh-Taylor instability theory with that obtained by MD simulations. Corona splash has been observed for macroscale droplets at standard atmospheric pressure conditions, but the present simulations show that an extremely high pressure of 1900 kPa is required to trigger it for nanodroplets.

We report on the experimental behavior of oil drops suspended in water and passing in a constricted capillary tube under an imposed pressure gradient. The surfaces of the droplets are covered either by colloidal solid particles or soluble surfactants. We investigate the coupling between the flow behavior and the concentration gradient in adsorbed species that are induced by surface expansion when a water lubrication film persists between the drop and the capillary walls. For both particle-laden and surfactant-laden drops, we evidence the formation of strong concentration gradients resulting in surface tension gradients. We show how local values of surface tension can be monitored using flow rate measurements. In the case of particle-laden drops, we demonstrate that the surface tension gradient is balanced by viscous friction in the lubrication film. In the case of surfactant-laden drops, we suggest a Marangoni flow opposes the decrease of surfactant concentration at the front of the drop, up to a threshold value of the surface expansion rate. Finally, we discuss how these effects increase the passage time of surfactant-laden drops in the constriction.

In this paper, we experimentally explore the formation, evolution, and breakup of the Armstrong liquid bridge. The extremely complicated evolution stage is revealed, which involves many coupled processes including the morphology change, current variation, heat transfer, and water evaporation. By focusing on the final fate of this liquid bridge, we observe that the breakup occurs once an effective length ($\tilde{L}$) is reached. This effective length increases linearly with the applied voltage, implying a threshold electric field to sustain the liquid bridge. Moreover, by an introduced external flow, the lifetime of the liquid bridge can be controlled, while the effective length associated with the breakup is independent of the external flow rate. Hence, these findings remarkably demonstrate that the breakup of the liquid bridge is directly correlated with the effective length. In order to understand this correlation, a simplified model of an electrified jet is employed to take the electric field into account. By the linear stability analysis, the attained phase diagram agrees with the experiments well. Although a more comprehensive theory is required to consider other factors such as the surface charges, these results might provide a fresh perspective on the “century-old” Armstrong liquid bridge to further elucidate its underlying physical mechanism.

We study the effect of gas rarefaction on the propagation of vibroacoustic sound in a two-dimensional setup of a gas confined by a planar oscillating wall. Focusing on small-amplitude harmonic excitations imposed to only part of the surface, the problem is analyzed in the entire range of gas rarefaction rates, governed by the ratio between the gas mean free path and wavelength of a prescribed wall signal. Analytical solutions are obtained in the free-molecular and continuum limits, consisting of the gas response to a delta function and other locally confined wall actuations. The analysis is supplemented by direct simulation Monte Carlo calculations in the intermediate range of gas rarefaction rates. Remarkably, distinct differences are observed between sound propagation characteristics in the two limits. At continuum-limit conditions, the acoustic signal propagates isotropically in a monopole-type pattern, and decays inversely to the square root distance from the source. In contrast, the signal in the collisionless flow regime is exponentially decaying away from the source and follows a “nearly dipole-type” directivity field, where the acoustic pressure vanishes in the direction normal to the source axis of motion. The differences in results, stemming from the fundamentally distinct continuum and ballistic flow models, are discussed and rationalized in terms of the analytical limit-case descriptions.

A local artificial neural network (LANN) framework is developed for turbulence modeling. The Reynolds-averaged Navier-Stokes (RANS) unclosed terms are reconstructed by the artificial neural network based on the local coordinate system which is orthogonal to the curved walls. We verify the proposed model in the flows over periodic hills. The correlation coefficients of the RANS unclosed terms predicted by the LANN model can be made larger than 0.96 in an a priori analysis, and the relative error of the unclosed terms can be made smaller than $18\%$. In an a posteriori analysis, detailed comparisons are made on the results of RANS simulations using the LANN, global artificial neural network (GANN), Spalart-Allmaras (SA), and shear stress transport (SST) $k\text{−}\omega$ models. It is shown that the LANN model performs better than the GANN, SA, and SST $k\text{−}\omega$ models in the prediction of the average velocity, wall-shear stress, and average pressure, which gives the results that are essentially indistinguishable from the direct numerical simulation data. The LANN model trained at low Reynolds number, $\text{Re}=2800$, can be directly applied to the cases of high Reynolds numbers, $\text{Re}=5600$, 10 595, 19 000, and 37 000, with accurate predictions. Furthermore, the LANN model is verified for flows over periodic hills with varying slopes. These results suggest that the LANN framework has a great potential to be applied to complex turbulent flows with curved walls.

The vaporization and combustion of clusters of aluminum particles in shocked flows is studied through interface-resolved 2D numerical simulations. These mesoscale simulations elucidate, for the first time, aspects of vaporization and burning in molten aluminum $\left(\mathrm{Al}\right)$ particle clusters that are markedly different from an isolated burning $\mathrm{Al}$ particle. Unsteadiness due to shock-generated baroclinic vorticity (inviscid mechanisms) and interactions between the wakes of molten $\mathrm{Al}$ particles (viscous mechanisms) are found to have significant effects; vortical mixing facilitates kinetically limited combustion of the particles located upstream in the cluster. Whereas, for particles located downstream in the cluster, the interaction with the low-speed, oxygen-lean wake of the upstream particles leads to diffusion-limited combustion. Results show that particles in a cluster have lower rates of vaporization and combustion than isolated particles under the same overall flow conditions. To isolate inviscid and viscous effects, the flame structure and vaporization rate for particles in a cluster are quantified in terms of local flow conditions, i.e., the local Mach number, Reynolds number, location of a particle in the cluster, and volume fraction. The results obtained in this study will be useful in understanding and modeling the mesoscale physics of shock-induced burning of explosively dispersed reactive aluminum particles.

Since industrial fluidized-bed reactors typically operate with polydispersed particles, the ability to approximate such reactors as the superposition of corresponding monodispersed fluidized beds would greatly simplify their design and operation. To evaluate the validity of superposition of monodispersed reactor behavior, we evaluate the effects of bidispersity by comparing three-dimensional liquid-solid monodispersed and segregated bidipsersed fluidized beds. Simulations were conducted using the immersed boundary method with direct forcing in a periodic domain and with particle Reynolds numbers of 20–70 based on the largest particle diameter. We show that the volume fraction, kinematic wave speed, particle velocity fluctuations, and collisional and hydrodynamic stresses in the segregated layers of a bidispersed fluidized bed can be well approximated by the corresponding properties of a monodispersed fluidized bed. In the transition region between the layers, only the volume fraction and collision stresses monotonically decrease with height. At low Reynolds numbers, particle velocity fluctuations in the upper layers are the largest. As the particle Reynolds number increases, particle velocity fluctuations in the transition and lower layers become the largest sequentially. At intermediate particle Reynolds numbers, the hydrodynamic stresses in the transition region are greater than those in the upper and lower layers. As the particle Reynolds number increases, the difference between the hydrodynamic stresses in the transition layer and the two layers become more significant. This paper demonstrates that, despite the clear segregation into layers that behave, such as monodispersed beds, the transition region is governed by complex bidispersed mechanisms that cannot be explained in terms of the particle behavior in the segregated layers. Overall, particle dynamics of the segregated layers in the bidispersed fluidized bed can be approximated with the corresponding monodispersed layers. The result implies that industrial applications, such as wastewater treatment performance in bidispersed or polydispersed fluidized beds can be predicted with results from past numerical or experimental studies of monodispersed fluidized beds.

Spherical particles at a liquid interface attract each other and aggregate. The capillary forces at play are well described for a pair of objects, but as soon as many particles interact, no direct calculation is possible and only a statistical approach can account for the global dynamics. Here, we focus on the statistics of clustering of such a system with a long-range interaction which varies during the aggregation process. We measure experimentally and numerically the distribution of sizes as a function of time and exhibit a self-similar clustering mechanism subdivided into two aggregating regimes, with a well-defined transition that we characterize.

This study concerns conformal invariance of certain statistics in $2d$ turbulence. Namely, there exists numerical evidence by Bernard et al. [Nature Phys. 2, 124 (2006)], that the zero-vorticity isolines $\mathit{x}(l,t)$ for the $2d$ Euler equation with an external force and a uniform friction belong to the class of conformally invariant random curves. Based on this evidence, the CG invariance was formally proven by Grebenev et al. [J. Phys. A: Math. Theor. 50, 435502 (2017)] by a Lie group analysis for the 1-point probability density function (PDF) governed by the inviscid Lundgren-Monin-Novikov (LMN) equations for $2d$ vorticity fields under the zero external force field. In this work we consider the first equation from the LMN chain for $2d$ scalar fields under Gaussian white-in-time forcing and large-scale friction. With this, the flow can be kept in a statistically steady state and the analysis is performed for the stationary LMN. Specifically, for the inviscid case we prove the CG invariance of the 1-point statistics of the zero-isolines $\mathit{x}\left(l\right)$ of a scalar field, i.e., the CG invariance of the probability $f_1(\mathit{x}\left(l\right),\varphi )d\varphi$ that a random curve $\mathit{x}\left(l\right)$ passes through the point $\mathit{x}$ with $\varphi =0$ for $l=l_1$. We show an example, where the proposed transformations represent a change between PDF's describing homogeneous and nonhomogeneous fields. Possible implications of this result are discussed.

We study the relation between large-scale structures in the concentration field with those in the velocity field in a dye-seeded turbulent jet. The scalar concentration in a plane is measured using laser-induced fluorescence. Uniform concentration zones of an advected scalar are indentified using cluster analysis. We simultaneously measure the two-dimensional velocity field using particle image velocimetry. The structures in the velocity field are characterized by finite-time Lyapunov exponents. The measurement of the scalar- and velocity fields moves with the mean flow. In this moving frame, turbulent structures remain in focus long enough to observe well-defined ridges of the finite-time Lyapunov field. This field gauges the rate of point separation along Lagrangian trajectories; it was measured both for future and past times since the instant of observation. The edges of uniform concentration zones are correlated with the ridges of the past-time Lyapunov field, but not with those of the future-time Lyapunov field. We quantify this relation using both conditional averages and the ordinary correlation function.

We study the mechanically driven flows of non-Newtonian fluids in narrow and confined configurations. Using the Lorentz reciprocal theorem, we derive a closed-form expression for the flow rate–pressure drop relation of complex fluids in such geometries, which holds for a wide class of non-Newtonian constitutive models. For the weakly non-Newtonian limit, our theory provides the first-order non-Newtonian correction for the flow rate–pressure drop relation solely using the corresponding Newtonian solution, eliminating the need to solve the non-Newtonian flow problem. In particular, for the flow-rate-controlled situation, we find that the first-order non-Newtonian pressure drop correction may increase, decrease, or not change the total pressure drop for a viscoelastic second-order fluid, depending on the geometry, but always decreases it for a shear-thinning Carreau fluid.

The effect of background stable temperature stratification in the developing stage of horizontal convection is studied by conducting laboratory experiments. By imposing horizontally differential heating at the top of a layer of low-temperature water, both vertical and horizontal temperature differences are explicitly defined. In developing horizontal convection of the present study, the flow structures are driven only by the baroclinic torque produced by the horizontal temperature difference, and braked by the restoring force of stable temperature stratification. We thus defined a nondimensional stratification parameter, which represents the balance of the braking force and the baroclinic torque, in addition to the Rayleigh number. Various features of the flow structures, maximum velocity, stream function, roll thickness, circulation of the roll, total kinetic energy, and Reynolds number, which are quantified via particle-tracking velocimetry, are summarized in spaces of the two nondimensional parameters. In the developing horizontal convection, the quantified flow features are well organized by power laws of the nondimensional parameters. The finite domain of the fluid container augments the effect of the apparent braking force, and the bulk quantities of the roll structures are suppressed by the stable temperature stratification. These results are the evidences for the significance of the nondimensional stratification parameter in the developing horizontal convection, unlike thermally equilibrated horizontal convection conventionally considering destabilizing thermal buoyancy as the primary driving force.

In this paper the dynamics of the simultaneously filling and emptying of a box is studied theoretically and experimentally. Both situations, consisting of negatively buoyant (fountains) and positively buoyant (plumes) discharges, are considered. For the sake of generality, no assumption is made about the value of the density deficit (between the release and the ambient fluid), so this study deals with the so-called non-Boussinesq general case. Experiments are carried out with buoyant air-helium mixtures continuously released from the top (fountain) or bottom (plume) into air in a cylindrical tank with an open bottom boundary and a top vent of variable areas. At steady state, for both fountain and plume configurations, a buoyant layer of constant thickness and density forms under the tank ceiling. Based on mass and buoyancy conservation equations applied on the buoyant layer, theoretical models are proposed to estimate its depth and density at steady state. The theoretical models compare favorably with the experimental data. Subsequently, these models allow us to compare the plume and the fountain configurations for identical source conditions, box size, and vent area. Even if, in the majority of situations, the plume configuration allows a better mixing of the buoyant fluid with the environment, it is found that beyond a certain value of the fountain height, the fountain configuration becomes more efficient than the plume configuration for mixing phenomena.

To obtain insights into dynamics of developed plane Couette turbulence, this paper considers the bifurcation structure of unstable periodic orbits (UPOs) in the large-eddy-simulation (LES) system with the Smagorinsky-type eddy viscosity model. Treating the Smagorinsky constant as a bifurcation parameter, we detect the bifurcation points connecting two known UPOs which were separately discovered in the Navier-Stokes system [G. Kawahara and S. Kida, J. Fluid Mech. 449, 291 (2001)]. At the moderately high Reynolds number, the LES UPO of the present study possesses the spanwise vortices, which seem to be caused by the streak instability and appear in the central region of the channel. We note that to our knowledge a spanwise vortex has not been reported through the UPO analysis of wall flows. The stretched spanwise vortices of the LES UPO enhance transfer of the streamwise turbulent momentum as in developed near-wall turbulence.