This Letter presents nontrivial stochastic identities for random isotropic second-rank tensor fields. They can be considered as markers of statistical isotropy in turbulent flows of any nature. The case of axial symmetry is also considered. We confirm the validity of the identities using different direct numerical simulations of turbulent flows.

We revisit the mesoscopic hydrodynamic description of the dynamics of sessile partially wetting compound drops, i.e., of drops that consist of two immiscible nonvolatile partially wetting liquids and are situated on a smooth rigid solid substrate. We briefly discuss and complete existing dynamic models employing a gradient dynamics approach. Thereby, the underlying energy features capillarity and wettability contributions for all relevant interfaces in full-curvature formulation. Establishing transparent consistency relations between macroscopic and mesoscopic parameters, we obtain mesoscopic Neumann and Young laws that are also fully consistent with the macroscopic ones. In particular, we discuss the minimal requirements for the wetting energy that ensure the full spectrum of macroscopic parameters for partially wetting cases is addressed by the mesoscopic model. Subsequently, we distinguish long-wave and full-curvature variants of the dynamical model based on properties of the energy, and employ the latter to illustrate the usage of the mesoscopic model. As examples, we chose the spreading of individual compound drops on one-dimensional horizontal substrates, sliding compound drops on one-dimensional inclined substrates, and the coarsening of drop ensembles on one- and two-dimensional horizontal substrates. In each case, the discussion emphasizes occurring qualitative changes in the drop configurations.

We study the three-dimensional shear layer response of an overexpanded rectangular jet to small-perturbation-based control and associated impact on its noise field using linear analysis and implicit large-eddy simulations (ILES). Using the most receptive frequency, the rectangular shear layer is forced to excite specific circumferential vortical structures by gradually increasing the phase difference between consecutive actuators, thereby augmenting the three-dimensional characteristics of the shear layer. Upon adopting this active control strategy, the jet exhibits increased shear-layer spreading rate, shortened potential core, and smaller shock-expansion cells. While downstream noise reduction is achieved, the resulting tonal response of the overexpanded jet is higher than a perfectly expanded jet particularly in the upstream direction, due to additional shock-vortex interactions. Turbulent and acoustic signatures reveal that forcing at the third azimuthal mode of the corresponding circular jet, termed M3, has the most desirable noise impact, consistent with prior experimental observations. As identified from linear global modes and ILES, M3 forcing minimizes the tonal response of actuation, while concurrently reducing the radiative efficiency of the jet by attenuating acoustic energy in the supersonic phase-speed regime, and turbulent kinetic energy levels in the shear layer. Further, M3 forcing weakens the coherent-structure/shock interactions and curtails upstream propagating guided acoustic modes and plume flapping, thus effectively mitigating shock-associated noise and screech, respectively. The study highlights the control authority of small-perturbation actuation on the hydrodynamic and acoustic components of shocked jets, while incurring a relatively small thrust penalty of approximately one percent.

In turbulent flows, the fluid element gets deformed by chaotic motion due to the formation of sharp velocity gradients. A direct connection between the element of fluid stresses and the energy balance still remains elusive. In this Letter, an exact identity of incompressible turbulence is derived linking the velocity gradient norm across the scales with the mean kinetic energy. In the context of three-dimensional (3D) homogeneous turbulence, this relation can be specialized obtaining the expression of the mean kinetic energy decomposed either in terms of deformations due to strain motion or via the vorticity norm of the fluid element. Applied to data from direct numerical simulations (DNS) describing homogeneous and isotropic turbulence, the decomposition reveals that, beyond the scales dominated by the external forcing, extensional and contractile deformations account approximately for $40\%$ and $55\%$ of the kinetic energy of the associated scale while less than the remaining $5\%$ is carried by the indefinite-type stresses. From these two identities, one can derive an exact expression for the kinetic energy spectrum which is based solely on real space quantities providing a characterization of the Kolmogorov constant as well. Numerical evidences show that this formulation of the energy spectrum is consistent with the Kolmogorov power-law spectral scaling.

Fluid-rock reactions are of great interest in many engineered geological storage and disposal systems where the long term integrity of the system is key, and where fluid seepage through a permeable rock may lead to reaction and convective transport of material through the formation. If an unsaturated fluid displaces formation fluid in equilibrium with a reactive porous medium, a reaction front develops, across which the invading fluid becomes saturated with the soluble matrix material. Depending on the composition of the invading fluid, it may initially be less dense than the formation fluid, but following reaction it may become denser than the formation fluid. If the invading fluid displaces the formation fluid downwards through the porous layer, the reaction front may then be stabilized by buoyancy, but a Rayleigh-Taylor type instability can develop at the interface between the reacted fluid and the original formation fluid ahead of the reaction front. We present a series of new analog experiments of this process by injecting aqueous sugar solutions into a porous layer containing saturated salt solution, salt powder, and glass ballotini. As an analog of a reaction front, a dissolution front develops as the aqueous sugar solution dissolves the salt powder and becomes denser than the saturated salt solution. The buoyancy instability then leads to a growing finger interface. If the buoyancy speed of the fluid, $u_B$, is smaller than $u_F-u_R$, where the speed of the advancing fluid-fluid front is $u_F$ and the speed of the dissolution front is $u_R$ then the instability grows as if the system were unconfined. However, if $u_B>u_F-u_R$, then the supply of fluid at the dissolution front limits the growth of the instability. We present an idealised model for the speed of the non-linear buoyancy-driven fingers, and we consider the implications of our results for the long term integrity of a number of geological storage systems.

We investigate the flow of quasi-2D liquid foams, composed of a single monolayer of bubbles in close contact and confined between two glass plates in a Hele-Shaw cell, with a specific emphasis on understanding how bubble shapes evolve in response to varying flow speeds. Utilizing an experimental setup capable of displacing a substantial number of bubbles in the spanwise direction, while the bubble shapes remain stationary as the bubbles themselves are advected in a plug flow, we reveal an average bubble anisotropy characterized by elongated bubbles in the streamwise direction and curved bubble edges in a preferential orientation. Notably, these effects intensify with increasing flow speeds. While the bubble anisotropy is created at the entrance of the cell, our study establishes a clear connection between bubble edge curvature and orientation, confinement thickness, frictional forces with the plates, and the inherent anisotropy of the bubbles. We introduce a model that not only aligns with these observations but also demonstrates quantitative agreement with experimental data.

The coupling between mass transfer and hydrodynamic phenomena in two-phase flow is not straightforward due to the different effects that can be encountered. Its description is complex and requires particular efforts, especially in the modeling of the interface between phases. Here, we consider the case of a two-component droplet (one miscible and one immiscible in water) released in a 2D rectangular domain filled with water. Mass transfer occurs between the miscible element and the surrounding water, which leads to a density inversion that directly affects the droplet trajectory through buoyancy. We perform simulations using a ternary Cahn-Hilliard model to capture such coupled phenomena. The Boussinesq approximation for a multicomponent system is used to define the density law and an analytical chemical potential is proposed for the thermodynamic landscape. The effect of the mobility parameter on the flow is highlighted, the solutal Marangoni effect is discussed, and the results are found in good agreement with the dynamics described from an experimental study of the literature.

It is known that in an unbounded fluid, the inline configuration of a freely rising bubble pair is often unstable with respect to lateral disturbances. This work numerically examines the stability of this configuration in the presence of a nearby vertical wall. The focus is on moderately inertial regimes, where two bubbles rising initially in line typically separate laterally from each other under unbounded conditions. In the presence of the wall, our results indicate that while the path of the bubble pair predominantly separates laterally, the plane of separation largely depends on the wall-bubble interaction. This interaction involves a competition between two distinct effects, with the dominance determined by the ratios of buoyancy-to-viscous and buoyancy-to-capillary forces, which define the Galilei $\left(\text{Ga}\right)$ and Bond $\left(\text{Bo}\right)$ numbers, respectively. When $\text{Bo}$ is below a critical $\text{Ga}$-dependent threshold, irrotational effects dominate, initially stabilizing both bubbles near the wall until horizontal separation among them occurs in the wall-parallel plane. Conversely, at higher $\text{Bo}$, vortical effects dominate such that both bubbles migrate away from the wall. During the departure, asymmetric interactions cause the wall-normal velocities of the two bubbles to differ, leading to horizontal separation in the wall-normal plane. These two separation motions, both newly identified in the present study, are found to result from two distinct mechanisms: one associated with the shear flow generated in the gap separating the wall and the leading bubble, which attracts the trailing bubble toward the wall, and the other linked to vortex shedding from the leading bubble, which promotes the trailing bubble's faster escape from the wall. A slight angular deviation favors separation in the wall-parallel plane, promoting the formation of a near-wall, bubble-rich layer as observed in prior investigations of buoyancy-driven, bubble-laden flows.

The “fluid-mechanical sewing machine” creates periodic patterns through the coiling nature of a viscous fluid falling onto a moving surface. At relatively moderate heights, the reported patterns are translated coiling, alternating loops, W pattern, and meander. A simplified theoretical model based on the geometry and local bending of the contact point can predict these patterns. We experimentally explore the patterns in this region by collecting data to compare with the model. Our review of the model's bifurcation diagram reveals additional patterns beyond the ones reported, although current experiments have not shown their existence. The W pattern, previously omitted in regime diagrams because of its small region, is now shown explicitly. We report on the consistent appearance of a period-doubled version of the W pattern, as well as rare appearances of resonant patterns. Comparing the theoretical model to experimental data, we find that the predicted phase diagram and the meander variation deviate from observations. These deviations hint at an unaccounted dynamics that merits further study.

This paper presents a comprehensive framework for addressing the challenges associated with turbulence linear forcing in incompressible two-phase flows. By examining existing literature on linear forcing techniques for single-phase flows, which typically yield constant turbulent production, kinetic energy, or dissipation rates, we derive a general method based on constant energetics. This method ensures that any constant power of kinetic energy multiplied by any constant power of dissipation rate remains unchanged over time. A linear stability analysis of this forcing method is performed, demonstrating its relevance and suitability in practical scenarios. Then, we investigate the linear forcing of turbulence in two-phase flows. Removing the mean contribution of the capillary forces prevents the exponential growth of kinetic energy reported in previous works. The paper also explores the impact of capillary forces on the energetics budgets and their implications for turbulent forcing. While the capillary power does not contribute significantly to the budget of kinetic energy, the capillary-related term prevails in the budget of dissipation rate. Including this term in the constant-energetics forcing method improves the control of the dissipation rate in the simulations. A further improvement is proposed by removing discretization errors in the computation of the energetics budgets, which provides a perfect control of the turbulent quantities. Turbulent modulation of the energy spectrum is also discussed showing that the proposed linear forcing method allows us to recover the expected modulation of the dispersed phase on the turbulent cascade. Indeed, the energy spectra compare well with previous works on turbulent emulsions, bubbly flows, and droplet/particle-laden flows.

We investigate the transition from pure Couette flow to Poiseuille flow at $\text{Re}\approx 2250$ with a focus on the observed disappearance of single-circle coherent structures occupying the whole channel height. According to the DNS study by Gandía-Barberá et al. [Phys. Fluids 30, 041702 (2018)], these are accompanied by a change of sign in the Reynolds stress tensor at sufficiently large pressure gradients, although from a deeper theoretical point of view the actual mechanisms for the disappearance of these structures remained completely uncovered. In order to investigate the behavior of these structures theoretically, we use resolvent and structured singular value analysis, with the aforementioned DNS serving as a data basis for comparison, hence simultaneously exploring the capabilities of resolvent and structured singular value analysis in capturing the characteristics of these structures. Through detailed parameter studies, we examine how the pressure gradient influences the length and width of streamwise elongated rolls, noting a shortening and narrowing effect as the flow becomes increasingly pressure driven, and compare these effects to the ones observed in the DNS work. Additional insights into the development of coherent structures are gained, as their wall-normal positions are successfully linked to the occurrence of critical layers within the flow, particularly through structured singular value analysis. The results show that the modified response modes from structured singular value analysis show the best agreement with the DNS observations, suggesting that these analytical approaches can effectively replicate the phenomena otherwise obtained only through costly DNS, and provide deeper insights into the underlying fluid dynamics.

The time-averaged and spectral characteristics of the scalar dissipation rate and a related turbulent burning velocity of premixed flames are investigated experimentally. The Karlovitz and turbulent Reynolds numbers are varied from about 0.1 to 34.5 and 62 to 1115, respectively. The hot-wire anemometry is performed to characterize the background turbulence. The Rayleigh scattering measurement is carried out to obtain the instantaneous two-dimensional temperature field, which is used to estimate the scalar dissipation rate and a related turbulent burning velocity. It is observed that, for lengthscales smaller than a few times the laminar flame thickness (yet larger than the resolving limit of the measurements), the power spectral densities of the scalar dissipation rate and the corresponding burning velocity collapse and decay following power-law relations. The slope of the decay is nearly independent of the background turbulence but depends on the examined fuel mixture. For lengthscales larger than a few times the laminar flame thickness, increasing the background turbulent Reynolds number generally increases the power spectral density of the scalar dissipation rate and the related turbulent burning velocity. This experimental study quantifies the role of intermediate- and large-scale turbulence in how fast premixed flames burn. The results suggest that quantifying the impact of large eddies on the turbulent burning velocity using merely the integral lengthscale may not be sufficient, and a range of lengthscales larger than two to four times the laminar flame thickness should be considered for studying such impact.

We investigate the intricate dynamics arising from the vibrations of a thin sheet in a compressible fluid medium. The system comprises a closed chamber that is filled with an ideal gas and is divided into two parts by a thin sheet. We develop an analytical model that combines the elasticity of thin sheets with the hydrodynamics of compressible fluids to analyze how the sheet's material properties and compression affect the system's lowest mode of vibration. We employ a linear stability analysis around three distinct solutions of the static equations and show that the lowest mode consists of either a vortexlike patterned flow that is localized around the area of the sheet or an extended, oscillating net flow. While these eigenmodes are influenced mainly by the ratio between the thermal energy of the fluid and the bending rigidity of the sheet, the frequency of the vibrations also depends on the mass ratio between the sheet and the fluid. Notably, our findings can provide guidelines for the design of technological applications that require precise control over elastohydrodynamic interactions.

Motivated by the aim of understanding the effect of media heterogeneity on the swimming dynamics of flagellated bacteria, we study the rotation and swimming of rigid helices in dilute suspensions experimentally and theoretically. We first measure the torque experienced by, and thrust force generated by, helices rotating without translating in suspensions of neutrally buoyant particles with varying concentrations and sizes. Using the ratio of thrust to drag forces ${\xi }_{F\mathrm{\Gamma }}$ as an empirical proxy for propulsion efficiency, our experiments indicate that ${\xi }_{F\mathrm{\Gamma }}$ increases with the concentration of particles in the fluid, with the enhancement depending strongly on the geometric parameters of the helix. To rationalize these experimental results, we then develop a dilute theoretical approach that accounts for the additional hydrodynamic stress generated by freely suspended spheres around the helical tail. We predict similar enhancements in the drag coefficient ratio and propulsion at a given angular speed in a suspension and study its dependence on the helix geometry and the spatial distribution of the suspended spheres. These results are further reinforced by experiments on freely swimming artificial swimmers, which propel faster in dilute suspensions, with speed increases over $60\%$ for optimal geometries. Our findings quantify how biological swimmers might benefit from the presence of suspended particles, and could inform the design of artificial self-propelled devices for biomedical applications.

This paper presents an analytical exploration of the two-dimensional concentration distribution of a solute under the influence of first-order bulk and wall chemical reactions in a viscous, couple stress fluid flowing between two parallel plates. The analytical expressions for mean and transverse concentration distributions up to third order are derived using Mei and Vernescu's multiscale homogenization technique. This paper meticulously investigates the impact of a couple stress parameter $\left(\alpha \right)$ and the chemical reaction parameters on Taylor dispersion through a reactive solute's dispersion coefficient, mean, and transverse concentration distributions. Results reveal that the effect of couple stress is most significant for smaller values of $\alpha$ (i.e., $20>\alpha \ge 1$), in which the dispersion increases and the tracer particle's mean concentration decreases. As $\alpha$ increases, there is a decreasing trend in dispersion, and for a large value of $\alpha$ a subtle decrease in dispersion is observed, which implies that the increment in viscosity impacts the dispersion coefficient. However, the negligible effect of couple stress $(\alpha \gg 20)$ results in a subtle increase in the mean concentration distribution. Increasing the value of the bulk chemical reaction parameter uniformly decreases the transverse concentration more effectively for smaller values of $\alpha$. Both couple stress and wall reactions significantly impact the concentration variation by inducing nonuniformity. Interestingly, at the center of the channel cross section, the bulk chemical reaction is more efficient in decreasing the transverse concentration profile when compared to wall chemical reactions, especially for smaller values of $\alpha$ where the couple stress is notably high. The results are effective as they are pivotal in advancing the design and performance of microfluidic devices, enhancing the separation of fluids and components, and improving fluid mixing efficiency.

We present a mesoscopic hydrodynamic model for a spreading drop of volatile partially wetting liquid on a solid porous layer of small thickness. Thereby, evaporation takes place under strong confinement, i.e., we consider a drop that spreads on one of two parallel plates that form a narrow gap. Our gradient dynamics model describes the coupled dynamics of the vertically averaged vapor density profile, the drop height profile, and the vertically averaged saturation profile in the porous layer. The underlying free energy incorporates saturation-dependent wettability, capillarity of the drop and within the porous layer, air and vapor entropy, and an entropic contribution relevant close to the complete filling of the porous layer. After developing the model, we discuss the resulting sorption isotherm and illustrate typical drop spreading and imbibition behavior, including the formation of a saturation halo within the porous substrate.

We investigate the behavior of a flexible stem completely submerged under a surface gravity wave of finite amplitude using fully resolved direct numerical simulations. By varying the rigidity of the stem over ten orders of magnitude, we explore its motion in the drag-dominated regime with realistic air and water properties. Our findings reveal two distinct structural responses of the stem depending on the ratio between its natural frequency ($f_{\mathrm{nat}}$) and the wave frequency ($f_{\mathrm{wave}}$). For $f_{\mathrm{nat}}/f_{\mathrm{wave}}\gg 1$, the stem maintains on average a straight configuration and exhibits streamwise oscillations in phase opposition with the wave, moving symmetrically with respect to the vertical direction. Conversely, for $f_{\mathrm{nat}}/f_{\mathrm{wave}}\ll 1$, the stem reconfigures under the influence of the Stokes drift, bending forward and breaking the symmetry, and exhibits oscillations that are more coherent with the surrounding flow field. Resonance is observed when $f_{\mathrm{nat}}\approx f_{\mathrm{wave}}$. These results provide insights into the dynamics of slender vegetation and manmade structures in wave fields, offering valuable implications for marine biology and engineering.

The drying of droplets of colloidal suspensions in cavities is of importance for applications such as inkjet printing, pattern analysis of dried blood, and fabrication of printed electronics. Nonuniformity of particle deposition can lead to a pinch point, a sharp local minimum of particle number density that is detrimental for some applications. In contrast to prior work that assumes the droplet contact line is pinned, here we focus on how cavity shape, solvent evaporation rate, and thermal Marangoni flow affect particle deposition when the contact line is free to move. A lubrication-theory-based model is developed to derive nonlinear evolution equations for the droplet height and vertically averaged particle concentration. Contact-line motion is accounted for by using a precursor film and disjoining pressure and solvent evaporation is described using the one-sided model. Finite-difference solutions for trapezoidal-like cavities show that a pressure maximum appears at the droplet edge as the evaporation rate or thermal Marangoni flows increase, or as the cavity depth decreases. The resulting inward flow causes the contact line to depin, which leads to an increase in the uniformity of particle deposition but also to the occurrence of a pinch point near the droplet edge.