Two-phase flows involving the dynamic interaction of gas and liquid phases are fundamental to both natural and industrial systems. A critical phenomenon in these flows is bubble fragmentation, which affects interfacial area and mass/momentum transfer. Direct numerical simulations (DNS) of turbulent two-phase bubbly flows allow for improved control of physical parameters and access to local flow variables that are challenging to obtain from traditional experiments. In this work, we perform numerical experiments of bubble breakup in decaying isotropic turbulence, at moderate Weber number regimes. By analyzing the interfacial strain rate and turbulent kinetic energy exchange, we provide new insights into the interplay between turbulence and bubble breakup dynamics. Different bubble sizes around the integral scale are simulated for a fixed bubble Weber number, which defines the ratio of turbulent and surface tension forces, maintaining the level of deformability. Results reveal that bubbles closest to the turbulence integral scale have the highest deformation levels and are most efficient in extracting energy from the flow. Smaller bubbles show the least amount of deformation and are unable to capture energy from the larger eddies, in agreement with the Kolmogorov-Hinze hypothesis.

In this study, we investigated the dynamics of a droplet impacting and oscillating a polycarbonate cantilever beam of nine varying lengths. We analyzed the cantilever's damping and vibration frequency in relation to a resonance length, where the frequencies of the droplet and the cantilever are equal. In shorter beam lengths, the beam vibrates at a frequency higher than that of the droplet. Upon reaching the resonance length, the frequencies of both the droplet and the cantilever align, and the cantilever is out of phase with the oscillation of the droplet's apex. This leads to increased damping rates. At this resonance length, the droplet's force and the direction of the cantilever oppose each other. When the cantilever length exceeds the resonance length, it synchronizes more with the droplet apex. This alignment allows the droplet force and the cantilever to work in phase. Our findings provide fundamental insights into the damping effect of droplet impacts on elastic surfaces around resonance.

This study provides an investigation of parametrization of the probability density function (PDF) of streamwise wall-shear stress in turbulent channel flows, specifically focusing on the friction Reynolds numbers ranging from 180 to 5200. The PDF of wall-shear stress (WSS) is calculated using accurate direct numerical simulation (DNS) data. The analysis of the data demonstrates that as the Reynolds number increases, the probability of extreme WSS events also increases, confirming the findings of previous studies. A lognormal parametrization is determined to be more accurate than a Gaussian one for both the original and the rescaled PDF of WSS. Additionally, the PDF of the inner-outer-decomposed WSS fluctuations is also examined. The PDF of the demodulated inner WSS fluctuations can be excellently collapsed and parametrized by a lognormal distribution at high Reynolds numbers. However, visible Reynolds number dependence exists in the PDFs of the modulated inner WSS fluctuations, which implies that its intermittency is probably due to the amplitude modulation effect. The PDF of the outer WSS fluctuations highly depends on the Reynolds number. When the PDF is rescaled, it can be precisely parametrized by a Gaussian distribution.

This study investigates the dynamics of cavities formed by the water entry of an impacting air jet. Utilizing a fine tube that continuously injects air and falls freely, we observe the creation and subsequent collapse of air jet cavities. Our experimental observations reveal that these cavities do not undergo a surface seal event, and the Worthington jet exhibits rippling and droplet breakup after deep seal. The behavior of the air jet cavity is influenced by dual Froude numbers, resulting in distinct cavity types. Additionally, we report four cavity seal regimes and identify the mechanisms underlying their pinch-off. To give the mathematical description of the cavity's evolution, we extend the theory in Duclaux et al. [J. Fluid Mech. 591, 1 (2007)] and compare it with our experiments. The theoretical model successfully captures the air jet cavity development and subsequent pinch-off events.

In this work, a nonequilibrium wall model is proposed for the prediction of turbulent flows experiencing adverse pressure gradients, including separated flow regimes. The mean-flow nonequilibrium is identified by comparing two characteristic velocities: the friction velocity ($u_{\tau }$) and the viscous-pressure-gradient velocity ($u_p$). In regions where the pressure-gradient velocity is comparable to the friction velocity ($u_p\sim u_{\tau }$), the near-wall turbulent closure is modified to include the effect of the pressure-gradient and convective terms. The performance of this wall model is evaluated in two canonical flows experiencing smooth body separation: the NASA/Boeing speed bump and the Bachalo-Johnson bump. Improvements in the predictive capabilities of the proposed model for the conventional equilibrium wall model are theorized and then demonstrated through numerical experiments. In particular, the proposed wall model is able to capture the onset of boundary layer separation observed in experiments or direct numerical simulations at resolutions where the equilibrium wall model fails to separate.

A universal theory of linear instabilities in swirling flows, occurring in both natural settings and industrial applications, is formulated. The theory encompasses a wide range of open and confined flows, including spiral isothermal flows and baroclinic flows driven by radial temperature gradients and natural gravity in rotating fluids. By employing short-wavelength local analysis, the theory generalizes previous findings from numerical simulations and linear stability analyses of specific swirling flows, such as spiral Couette flow, spiral Poiseuille flow, and baroclinic Couette flow. A general criterion, extending and unifying existing criteria for instability to both centrifugal and shear-driven perturbations in swirling flows is derived, taking into account viscosity and thermal diffusion, and guiding experimental and numerical investigations in the otherwise inaccessible parameter regimes.

Orbital sloshing is a technique to gently mix a container's liquid content and it is commonly used in fermentation and cell cultivation processes. Besides the rich wave dynamics observed at the interface, Bouvard et al. [Phys. Rev. Fluids 2, 084801 (2017)] unveiled the structure of the Lagrangian mean flow hiding in the fluid bulk. The latter flow shows a global toroidal (azimuthal) rotation codirected with the wave and nontrivial poloidal vortices near the contact line. Rotating sloshing waves are known to induce a net motion of fluid particles and hence a wave-averaged difference between the Eulerian flow—viscous streaming—and the Lagrangian flow, that is commonly referred to as Stokes drift. Nevertheless, discerning these two components in an experiment is challenging as they scale similarly with the forcing amplitude and frequency. Their relative contributions remain therefore unquantified, particularly for highly viscous fluids, for which prior analysis, based on inviscid arguments, fails. In this work, we construct a truncated asymptotic approximation of the problem, where the solution at each order is computed numerically to describe as accurately as possible the contact line region, otherwise analytically untractable. The results of this weakly nonlinear analysis in terms of first-order wave and second-order mean flow are then thoroughly compared with the experiments by Bouvard et al. [Phys. Rev. Fluids 2, 084801 (2017)], showing a remarkable agreement for off-resonance frequencies. When viscosity matters, our findings suggest that it is incorrect to attribute the poloidal patterns solely to the Eulerian streaming flow and that viscous corrections to the Stokes drift are equally important in the resulting mean Lagrangian flow.

Erosion and deposition are prevalent and integral phenomena in natural and industrial settings such as agriculture, dam construction, and fluid filtration, among others. As such, we develop a mathematical continuum model that exhibits the behavior of these processes in an idealized two-dimensional porous medium and that allows for predictions of values and limitations of parameters such as porosity, shear stress, particle concentration, and porous medium deformation. By exploiting established governing equations such as Darcy's law, advection-diffusion-reaction, and Navier-Cauchy equations, and then simplifying calculations via nondimensionalization and asymptotic analysis based on the small aspect ratio of the medium, we successfully model from a macroscale perspective how the erosion and deposition processes alter the internal morphology of an elastic porous medium. The essence of our results, beyond displaying how the medium evolves subject to the complex interplay among multiple parameters, covers how the total volume of the medium changes as we vary quantities of coefficients that measure the tendency of particles to erode or become deposited based on the physical properties of those particles and of the fluid and medium in which they travel.

We numerically investigate the effects of mixed convection on the nonlinear dynamics and heat transfer of the flow through a two-dimensional wavy channel with varying degrees of symmetry at Reynolds numbers ranging from 100 to 2200. Our findings reveal that the introduction of mixed convection significantly alters the routes to chaos of the system compared to its isothermal counterpart. We demonstrate that (i) a symmetric channel can host both the Ruelle-Takens-Newhouse and degenerate period-doubling routes to chaos, (ii) an asymmetric channel can host only the latter route, and (iii) a semiwavy channel can host no routes to chaos under the present conditions. Crucially, the Pomeau-Manneville intermittency route to chaos, previously observed in the isothermal system, is absent under mixed convection. Furthermore, our analysis of the heat transfer characteristics reveals quadratic and cubic relationships for the Nusselt number and the thermal performance factor, respectively, as functions of the Reynolds number. This study provides valuable insights for understanding and manipulating chaotic flow in wavy channels under mixed convection, with potential applications for enhancing the performance of thermal management devices.

The Faraday instability has been extensively studied in bounded containers but only recently has research on this phenomenon in flexible domains been conducted. Here, we study floating liquid droplets with Faraday waves excited on their surface, which undergo a slow time evolution toward a stable noncircular shape. We develop a theoretical model for the evolution of the boundary of the droplet, thus allowing us to simulate its full transient motion toward steady state. By changing the forcing frequency and amplitude of our system, we observe a variety of stable droplet shapes. We experimentally measure the geometrical properties of these droplets and conditions under which different shapes are stable, which match our theoretical predictions well. Interesting transient behavior such as hysteresis is also discussed, where the final droplet shape depends on its previous shape. Finally, we touch upon droplets that do not reach a steady state shape, instead oscillating periodically in time or rotating at a constant angular velocity.

Viscoelastic shear flows support additional chaotic states beyond simple Newtonian turbulence. In vanishing Reynolds number flows, the nonlinearity in the polymer evolution equation alone can sustain inertialess “elastic” turbulence (ET) while “elasto-inertial” turbulence (EIT) appears to rely on an interplay between elasticity and finite-$Re$ effects. Despite their distinct phenomenology and industrial significance, transition routes and possible connections between these states are unknown. We identify here a common Ruelle-Takens transition scenario for both of these chaotic regimes in two-dimensional direct numerical simulations of FENE-P fluids in a straight channel. The primary bifurcation is caused by a recently discovered “polymer diffusive instability” associated with small but nonvanishing polymer stress diffusion which generates a finite-amplitude, small-scale traveling wave localized at the wall. This is found to be unstable to a large-scale secondary instability which grows to modify the whole flow before itself breaking down in a third bifurcation to either ET or EIT. The secondary large-scale instability waves resemble “center” and “wall” modes, respectively—instabilities which have been conjectured to play a role in viscoelastic chaotic dynamics but were previously only thought to exist far from relevant areas of the parameter space.

We theoretically and experimentally study the propagation of a bubble in a Hele-Shaw cell under a uniform background flow at low Reynolds number. We consider situations where both the capillary number $\mathrm{Ca}$ and the ratio $\epsilon$ of the cell height to the bubble diameter are small. The bubble is then flattened into a pancake-like shape, with an approximately circular profile when viewed from above, and thin liquid films lie between the bubble and the cell walls. Bubble motion and deformation are determined by an interplay between the Hele-Shaw viscous pressure, the pressure drop due to the thin films, and the capillary pressure due to the in-plane curvature of the apparent bubble boundary. Numerical and asymptotic results indicate that, with all other parameters held constant, the in-plane aspect ratio of the bubble varies nonmonotonically with its size, with smaller bubbles being flattened in the flow direction and larger bubbles being elongated. These theoretical predictions are validated experimentally, as well as the expected loss of fore-aft symmetry of the bubble shape due to differences between the advancing and retreating menisci. Measurements of the bubble velocity are also shown to agree well with theoretical predictions. We extend our results to describe a bubble moving in an inclined cell due to buoyancy. Experimental results for the bubble velocity, as well as results found in the literature, are shown to collapse under a scaling motivated by the theory. As in the case of a horizontal Hele-Shaw cell, we find that, with increasing bubble size, the bubble shape can switch from being flattened to elongated in the direction of motion.

Experimental investigations of the exit dynamics of a horizontal cylindrical object were performed in water and silicone oil (50 cS). The fully immersed cylinder was initially at rest in a still fluid tank before being pushed (or pulled according to the measurement procedure) upwards at a constant velocity. The cylinder geometry was chosen to approach two-dimensional conditions in the transverse direction. First, we demonstrate that these conditions are better satisfied for a large aspect ratio cylinder equipped with vertical end plates. Second, the influence of the initial depth on the liquid entrained and the wake generated by the cylinder is discussed. It is shown that the wake destabilizes in the form of symmetry breaking in the case of water, while it remains symmetrical in the case of oil even for long travel in the bath. The deformation of the interface is found to be independent of the starting depth when the starting depth is larger than six times the cylinder diameter. In the present case, this criterion reflects also the finite acceleration of the cylinder to reach the determined constant exit velocity. Measurements in a range of exit speeds between 0.1 and 1 m/s indicate that the thickness of the liquid above the cylinder when the cylinder starts crossing the interface increases with the speed according to a logarithmic law of the Froude number. During the subsequent drainage, the evolution of the coated liquid thickness is found to first decrease exponentially with time just after the crossing of the interface. At later times, a change of regime occurs and the drainage follows the inverse of the square root of time irrespective of the crossing speed. Finally, the force necessary to maintain a constant exit speed during the motion of the cylinder inside and outside the bath is analyzed. This global measurement of the entrained liquid confirms the square root scaling of the thinning with time during the drainage process.

The current research was conducted to investigate bedload transport in sparsely vegetated channels through theoretical derivation. Most research on bedload transport in vegetated channels has relied on theories developed for bare beds. The classical Engelund formula is highly effective in predicting bedload transport rate on bare beds, but is based on four oversimplified assumptions. Meng et al. [Int. J. Sediment Res. 31, 251 (2016)] modified those oversimplified assumptions and proposed an improved version of the Engelund formula for bare beds. In this work, the improved Engelund formula was successfully extended to sparsely vegetated channels through the redefinition of key parameters. For instance, we adjusted the number of moving sediment particles per unit bed area and the effective Shields number (dimensionless bed shear stress acting on sediment movement in vegetated channels) to account for the impact of emergent rigid vegetation. Parameter calibration was accomplished using published data from a variety of reliable sources, ensuring the accuracy and applicability of the extended model. The prediction results correlated well with measured data across a broad range of bedload transport rates, particularly in scenarios of medium and high bedload transport rates.

The perturbation evolution of both free and forced falling jets has been studied in the presence of insoluble surfactants. The effects of gravity, surface tension, and Marangoni stress on the nonparallel basic flow are investigated. On the basis of the steady basic flow, the maximum growth rate and corresponding leading frequency of the perturbation of the free jet are calculated. For globally stable or critical jets, their responses to the external forcing with different frequencies are further investigated. The mechanisms of the nonparallel effect of the falling jet due to gravitational stretching and the inhomogeneous distribution of the surfactants in the linear stability stage are highlighted. The results show that both surfactant and gravity act to stabilize the jets and that gravity also causes the optimal forcing frequency of the stable basic jets to be greater than their intrinsic frequency. However, the optimal forcing frequency of the critical jets is always equal to their intrinsic frequency, which is similar to the resonance behavior.

The oscillatory boundary layer over an array of wall-mounted flexible filaments is studied using a penalty-immersed boundary method to explore the dynamic interaction between the boundary layer and filaments in two-dimensional (2D) flows. It is found that as the bending rigidity increases, the motion of the filament exhibits two patterns, undulation and sway. The undulating pattern exhibits a shorter wavelength of filament displacement and a reduced average filament height. In the swaying pattern, resonance occurs when the flow frequency is close to the natural frequency of the submerged filament, resulting in a peak value in the mechanical energy of the filament. When shifting the profile of the root mean square of the disturbance velocity downwards by the average height of the filament, the curves collapse for different filament parameters and the smooth wall, indicating that the presence of filaments can be modeled as an offset on the bottom boundary. A complex-valued slip length is introduced at the incoming flow frequency to quantify the velocity-velocity gradient relation near the filament tip, which takes into account both the magnitude and the phase lag of the slip velocity. Although this slip length varies dramatically inside the filament layer, it reaches a plateau at the upper edge of the filaments, with a smaller absolute value than those of the smooth wall. This finding provides insight into modeling the effective boundary condition of the filament-attached wall. Furthermore, the three-dimensional (3D) effects of the finite-span filaments are discussed. The 3D vortex has a U shape for very small aspect ratios, which transits to a ring-shape with the increasing aspect ratio. The spanwise range of the 3D effects is approximately one filament length on each side, and these effects can be neglected for the aspect ratios greater than 2, 4, and 8 in swaying, periodic undulating, and aperiodic undulating patterns, respectively.

In many thermal convection studies, enclosure inclination against gravity (measured as $\mathrm{\Phi }$) changes both flow features and heat transport. We numerically investigated thermal convection in a quasi-two-dimensional circular enclosure in the range ${10}^7\le \text{Ra}\le {10}^{10}, 0.1\le \text{Pr}\le 15$, and $0\le \mathrm{\Phi }\le \pi /2$, where $\text{Ra}$ is the Rayleigh number and $\text{Pr}$ is the Prandtl number. The dimensionless heat transport follows a nonmonotonic trend due to the change in plume nature near the walls, elimination of secondary rolls, core bulk instabilities, and flow stratification. Our scaling analysis shows dimensionless heat transport is proportional to ${\left(\text{Ra}\text{cos}\mathrm{\Phi }\right)}^{1/3}$ at small $\mathrm{\Phi }(0\le \mathrm{\Phi }<\frac{\pi }{9})$ and to ${\left(\text{Ra}\text{sin}\mathrm{\Phi }\right)}^{1/4}$ at large $\mathrm{\Phi }(\frac{\pi }{9}\le \mathrm{\Phi }\le \frac{\pi }{2})$. In contrast, the Reynolds number based on the global root-mean-square velocity shows a continuous decrease with $\mathrm{\Phi }$ due to the reduction in buoyancy fluxes, which convert the available potential energy into kinetic energy. Though the buoyancy flux decreases, convection persists through irreversible mixing, which is the dominant mechanism in inclined thermal convection.

The amplitude modulation phenomena, defined originally by Mathis et al. [J. Fluid Mech. 628, 311 (2009)], corresponds to a unique nonlinear interaction between Reynolds number $\left({\text{Re}}_{\tau }\right)$ dependent large-scale motions and ${\text{Re}}_{\tau }$-invariant inner-scale motions observed in canonical wall-bounded flows. While similar nonlinear interactions have been quantified previously in non-canonical wall-bounded flows, linking them solely to amplitude modulation is questionable due to the fact that each non-canonical effect is associated with distinct variations in the energies of both the large and inner scaled motions. This study revisits analysis of nonlinear triadic interactions, with consideration to various non-canonical effects, by analyzing published hot-wire datasets acquired in the large Melbourne wind tunnel. It is found that triadic interactions, across the entire turbulence scale hierarchy, may become statistically significant with increasing intensity of non-canonical effects such as wall roughness, pressure gradients, and spanwise or wall-normal forcing (when compared relative to their respective canonical baseline cases at matched ${\text{Re}}_{\tau }$). This stands in contrast to previous observations made in canonical flows, where only the interaction between inner scales and inertia-dominated large scales was considered dynamically significant for increasing ${\text{Re}}_{\tau }$. The implications of these findings are discussed for near-wall flow prediction models in non-canonical flows, which should take into account all nonlinear interactions coexisting in wall-bounded flows.

In this paper, we provide the semianalytical solution of the temperature and flow fields of a fluid confined in a narrow space between two parallel plates. The temperature increase is triggered by photothermal effects of fluids and/or boundaries due to the absorption of a focused Gaussian beam irradiated perpendicular to the fluid film, and then the temperature variation induces the flow fields through a buoyancy force and/or thermo-osmotic slip. The semianalytical solution to this optothermal fluidic system is validated by comparing with the results of numerical simulation, and is applied to typical optothermal fluidic problems. In particular, the optothermal trap of nanoparticles observed in our previous experiment [Tsuji et al., Electrophoresis 42, 2401 (2021)] is investigated in terms of thermophoretic force and flow drag that are obtained semianalytically. The semianalytical solution can be shared through open-source codes that are available to researchers without the background of fluid mechanics.

A detailed description of coupled heat and momentum transfer in a one-dimensional porous medium saturated by a supercritical fluid subject to a heat flux at one of its boundaries is reported in this study. The derivation is performed with an asymptotic analysis of the linearized macroscopic mass, momentum, and energy equations, assuming a van der Waals supercritical fluid and the mean-field theory, considering Darcy's law for momentum transfer. Three regimes of heat transfer separated by two crossovers are highlighted. The first regime, far enough from the critical point (CP), corresponds to the classical piston effect (PE), as in a plain fluid. While nearing the CP, a first crossover is found, giving rise to a second regime in which the PE in the bulk fluid is supplemented by a temperature gradient that results from a pressure gradient buildup. Below this crossover, the critical speeding up by thermocompression of the bulk stops and a porous saturation of the characteristic heat transfer timescale is reached. Closer to the CP, a second crossover is identified that corresponds to the presence of a viscous pressure drop in the whole domain. Below this second crossover, the PE is faded away and, in this third regime, heat transfer returns to a classical diffusive process. The two crossovers are characterized by a single parameter that is the ratio between the acoustic time (i.e., the sound wave travel time through a pore) and the pore-scale viscous diffusion time, namely, the acoustic pore Reynolds number.