Enhancement of boiling heat transfer on biphilic (mixed-wettability) surfaces faces a sudden reversal at low pressures, which is brought about by excessive contact-line spreading across the wetting heterogeneities. We employ the diffuse-interface approach to numerically study bubble expansion on a heating surface that consists of opposing wettabilities. The results show a dramatic shift in the dynamics of a traversing contact line across the wettability divide under different gravities, which correspond to variable bubble growth rates. Specifically, it is found that the contact-line propagation tends to follow closely the rapidly expanding bubble at low gravity, with only a brief interruption at the border between the hydrophobic and hydrophilic sections of the surface. Only when the bubble growth becomes sufficiently weakened at high gravity does the contact line get slowed down drastically to the point of being nearly immobilized at the edge of the hydrophilic surface. The following bubble expansion, which faces strong limitations in the direction parallel to the surface, features a consistent apparent contact angle at around $66.4^{\circ }$, regardless of the wettability combination. A simple theoretical model based on the force-balance analysis is proposed to describe the physical mechanism behind such a dramatic transition in the contact-line behavior.

Porous media with hierarchical structures are commonly encountered in both natural and synthetic materials, e.g., fractured rock formations, porous electrodes, and fibrous materials, which generally consist of two or more distinguishable levels of pore structure with different characteristic lengths. The multiphase flow behaviors in hierarchical porous media have remained elusive. In this study, we investigate the influences of hierarchical structures in porous media on the dynamics of immiscible fingering during fluid-fluid displacement. Divided by the breakthrough, such a displacement process includes pre- and postbreakthrough stages during which the fingering evolution is dominated by viscous and capillary effects, respectively. Through conducting a series of numerical simulations, we found that the immiscible fingering can be suppressed due to the existence of secondary porous structures. To characterize the fingering dynamics in hierarchical porous media, a phase diagram, which describes the switch among the three fingering modes (the suppressing, crossover, and dendrite mode), is constructed by introducing a scaling parameter, i.e., the ratio of timescales considering the combined effect of characteristic pore sizes and wettability. The findings presented in this work provide a basis for further research on the application of hierarchical porous media for controlling immiscible fingerings.

We investigate experimentally the defect-mediated turbulence (DMT) which is induced by bubbles injection in a Taylor-Couette flow when the inner cylinder is rotating while the outer cylinder is fixed. Bubbles of 1.2 mm in diameter are injected at the bottom of a Taylor-Couette device of radii ratio equal to 0.91. The tangential Reynolds number range is $[2200,19300]$ and the air injection rate varies up to 800 ml/min. For these conditions of the experiments, bubbles are trapped in the gap by the Taylor vortices and arranged as patterns (toroidal, wavy toroidal, spirals, and wavy spirals). Visualizations of the bubble patterns were carried out. When decreasing the Reynolds number or increasing the air injection rate, spiral and toroidal patterns can coexist in a composite flow. Defects occur in the bubble's patterns (merging or splitting of the Taylor vortex pairs). By analyzing the space-time diagram of bubbles patterns and their complex demodulation, we highlight different regimes and transitions in the DMT of the bubbly Taylor-Couette flow. The control parameter of the transitions is the air volumetric fraction, which evolves as the ratio between the axial injection Reynolds number and the tangential Reynolds number. By increasing the air volumetric fraction, the defects in the DMT flows are classified as three flow regimes: (i) structured composite flow where the defects are periodic in space and time, (ii) intermittency defects chaos where the defects zones alternate randomly with the patterns in time and space, and (iii) developed defects chaos with a large defects density. The statistical properties of these three regimes of the DMT are analyzed in the framework of the complex Ginzburg-Landau equation.

We study the dynamics of fragmentation for Newtonian and viscoelastic liquids in rotary atomization. In this common industrial process centripetal acceleration destabilizes the liquid torus that forms at the rim of a spinning cup or disk due to the Rayleigh-Taylor instability. The resulting ligaments leave the liquid torus with a remarkably repeatable spacing that scales inversely with the rotation rate. The fluid filaments then follow a well-defined geometrical path-line that is described by the involute of a circle. Knowing the geometry of this phenomenon we derive the detailed kinematics of this process and compare it with the experimental observations. We show that the ligaments elongate tangentially along the involute of the circle and thin radially as they separate from the cup. We use these kinematic conditions to develop an expression for the spatial variation of the filament deformation rate and show that it decays away from the spinning cup. Once the ligaments are sufficiently far from the cup, they are not stretched sufficiently fast to overcome the critical rate of capillary thinning and consequently undergo capillary-driven breakup forming droplets. We couple these kinematic considerations with the known properties of several Newtonian and viscoelastic test liquids to develop a quantitative understanding of this commercially important fragmentation process that can be compared in detail with experimental observations. We also investigate the resulting droplet size distributions and observe that the appearance of satellite droplets during the pinch-off process lead to the emergence of bidisperse droplet size distributions. These binary distributions are well described by the superposition of two separate $\mathrm{\Gamma }$ distributions that capture the physics of the disintegration process for the main and satellite droplets, respectively. Furthermore, as we consider more viscous Newtonian liquids or weakly viscoelastic test fluids, we show that changes in the liquid viscosity or viscoelasticity have a negligible effect on the average droplet size. However, incorporation of viscous/viscoelastic effects delays the thinning dynamics in the ligaments and thus results in broader droplet size distributions. The ratio of the primary to satellite droplet size increases monotonically with both viscosity and viscoelasticity. We develop a simple physical model that rationalizes the observed experimental trends and provides us a better understanding of the principal dynamical features of rotary fragmentation for both Newtonian and weakly viscoelastic liquids.

In this paper, the numerical investigation of the bubble formation and rise in gas-liquid-solid flow systems has been done through a coupled numerical method, the so-called volume of fluid (VOF) method, and a discrete element model (DEM). VOF is used to capture the interface of the bubble and DEM is employed to track the movement of particles. This coupled numerical method is validated through the good consistency of our calculated results to those experimental data (from other literature) of a bubble rising in a gas-liquid-solid system. The calculation results in this paper disclose that the detachment time of the first formed bubble is longer for case I (when particles are lying at the bottom of the container) than for case II (when the particles are settling freely). The main reason is that a stronger circulation (induced by the sedimentation of particles) near the bottom of the container plays a stronger cutting role and speeds up the detachment of the bubble. Then, the effects of some factors including particle volume fractions, gas velocities, orifice sizes, surface tensions, and liquid densities on the bubble formation and rise have also been investigated systematically. This work is useful for further research on the gas-liquid-solid fluidized bed system.

Existing works on sound propagation in rarefied gases have focused on wave transmission at adiabatic conditions, where a reference uniform equilibrium state prevails. To extend these studies, we analyze the propagation of acoustic waves in a slightly rarefied gas at nonadiabatic conditions, where arbitrarily large reference temperature and density gradients are imposed. Considering a planar slab configuration, constant wall heating is applied at the confining walls to maintain the nonuniform reference thermodynamic distributions. Acoustic excitation is then enforced via small-amplitude harmonic wall oscillations and normal heat-flux perturbations. Focusing on continuum-limit conditions of small Knudsen numbers and high actuation frequencies (yet small compared with the mean collision frequency), the gas domain affected by wall excitation is confined to a thin layer (termed “acoustic layer”) in the vicinity of the excited boundary, and an approximate solution is derived based on asymptotic expansion of the acoustic fields. The application of thermoacoustic wall excitation necessitates the formation of an ever thinner “thermal layer” that governs the transmission of the wall's unsteady heat flux into sound waves. The results of the approximate analysis, supported by continuum-model finite differences and direct simulation Monte Carlo calculations, clarify the impacts of system nonadiabaticity and the gas kinetic model of interaction on sound propagation. Primarily, reference wall heating results in an extension of the acoustic layer and consequent sound-wave radiation over larger distances from the wall source. Considering the entire range of inverse power law (repulsion point center) interactions, it is also found that wave attenuation is affected by the kinetic model of gas collisions, yielding stronger decay rates in gases with softer molecular interactions. The results are used to generalize the counterpart adiabatic-system findings for the amount of boundary heat flux required for the silencing of vibroacoustic sound at nonadiabatic reference conditions.

The coating and drying of nonflat discrete objects is a key manufacturing step for a wide variety of products. Flow of a thin nonvolatile liquid film on the outside of a rotating cylinder is commonly used as a model problem to study the coating of discrete objects. However, the behavior of a volatile particle-laden coating remains an important open problem. In this work we use lubrication theory to study the evolution of a liquid film laden with colloidal particles in the presence of solvent evaporation. Two coupled evolution equations describing variations in coating thickness and composition as a function of time and the angular coordinate are solved numerically. In the limit of a rapidly rotating cylinder, gravitational effects are negligible and linear stability analysis and nonlinear simulations demonstrate that nonuniform drying at higher drying rates may cause thickness and composition disturbances to regrow after initially decaying. When gravitational effects are significant, poor liquid redistribution at lower rotation rates and higher drying rates leads to less uniform coatings. Colloidal particles hinder liquid redistribution at high concentrations by increasing the viscosity, but help prevent rupture of the coating at more moderate concentrations. A parametric study reveals that both thickness and composition variations are minimized at high rotation rate, low drying rate, and moderate initial particle concentration.

Solitary traveling waves are prominent features covering the surface of a falling liquid film and are known to promote heat and mass transfer. We focus on the little studied case where they are subject to an extremely confined countercurrent gas flow, and we identify two secondary instabilities. At high gas velocities, a catastrophic instability develops, leading to flooding through wave reversal and liquid arrest. At lower gas velocities, an oscillatory instability occurs, producing a high-frequency periodic modulation of the wave height. Conjunction of this self-sustained oscillatory state and vortices forming in the liquid is shown to enhance mixing. We also show that the gas flow can cause extreme local film thinning, leading to almost dry patches where the liquid thickness is very small.

This work investigates the orbital dynamics of a fluid-filled deformable prolate capsule in unbounded simple shear flow at zero Reynolds number using direct simulations. The motion of the capsule is simulated using a model that incorporates shear elasticity, area dilatation, and bending resistance. Here the deformability of the capsule is characterized by the nondimensional capillary number $\mathrm{Ca}$, which represents the ratio of viscous stresses to elastic restoring stresses on the capsule. For a capsule with small bending stiffness, at a given $\mathrm{Ca}$, the orientation converges over time toward a unique stable orbit independent of the initial orientation. With increasing $\mathrm{Ca}$, four dynamical modes are found for the stable orbit, namely rolling, wobbling, oscillating-swinging, and swinging. On the other hand, for a capsule with large bending stiffness, multiplicity in the orbit dynamics is observed. When the viscosity ratio $\lambda \lesssim 1$, the long axis of the capsule always tends toward a stable orbit in the flow-gradient plane, either tumbling or swinging, depending on $\mathrm{Ca}$. When $\lambda \gtrsim 1$, the stable orbit of the capsule is a tumbling motion at low $\mathrm{Ca}$, irrespective of the initial orientation. Upon increasing $\mathrm{Ca}$, there is a symmetry-breaking bifurcation away from the tumbling orbit, and the capsule is observed to adopt multiple stable orbital modes including nonsymmetric precessing and rolling, depending on the initial orientation. As $\mathrm{Ca}$ increases further, the nonsymmetric stable orbit loses existence at a saddle-node bifurcation, and rolling becomes the only attractor at high $\mathrm{Ca}$, whereas the rolling state coexists with the nonsymmetric state at intermediate values of $\mathrm{Ca}$. A symmetry-breaking bifurcation away from the rolling orbit is also found upon decreasing $\mathrm{Ca}$. The regime with multiple attractors becomes broader as the aspect ratio of the capsule increases, while it narrows as the viscosity ratio increases. We also report the particle contribution to the stress, which also displays multiplicity.

The deformation, stationarity, and stability of a drop rotating axisymmetrically in an immiscible viscous fluid, under the influence of an externally imposed flow, are studied. The ambient fluid, slightly heavier or lighter than the drop, is under simultaneous rotating and compressional or extensional forcing flow at infinity. The problem is formulated and solved via an integral equation having unknown surface velocity, considering low Reynolds number with equal viscosity inside the drop and of the ambient fluid. Numerical simulations are carried out by using the boundary integral method. The drop stationarity is discussed for a variety of Bond numbers, Bo, and capillary numbers, Ca, for the simultaneous action of both flow fields. The critical bounds of Ca for the stability of stationary flat and extended shapes of the drop were established for the considered range of Bo.

We compute the rheological properties of inelastic hard spheres in steady shear flow for general shear rates and densities. Starting from the microscopic dynamics we generalize the Integration Through Transients formalism to a fluid of dissipative, randomly driven granular particles. The stress relaxation function is computed approximately within a mode-coupling theory—based on the physical picture that relaxation of shear is dominated by slow structural relaxation, as the glass transition is approached. The transient build-up of stress in steady shear is thus traced back to transient density correlations which are computed self-consistently within mode-coupling theory. The glass transition is signaled by the appearance of a yield stress and a divergence of the Newtonian viscosity, characterizing linear response. For shear rates comparable to the structural relaxation time, the stress becomes independent of shear rate and we observe shear thinning, while for the largest shear rates Bagnold scaling, i.e., a quadratic increase of shear stress with shear rate, is recovered. The rheological properties are qualitatively similar for all values of $\varepsilon$, the coefficient of restitution; however, the magnitude of the stress as well as the range of shear thinning and thickening show significant dependence on the inelasticity.

We study the flow topology dynamics in terms of the paramount nonlinearities of enstrophy and strain production at hard turbulent regimes of Rayleigh-Bénard convection (RBC). To do so, a data set of direct numerical simulations for air turbulent RBC at Rayleigh numbers $\text{Ra}=\{{10}^8,{10}^{10},{10}^{11}\}$ is analyzed. Considering the bulk dynamics therein, the classical two-dimensional mean Lagrangian evolution of $Q_{\mathsf{G}}$ and $R_{\mathsf{G}}$ invariants of $\mathsf{G}\equiv \mathbf{\nabla }\mathit{u}$ is extended to three dimensions by decomposing $R_{\mathsf{G}}$ into two parts: the strain production $R_{\mathsf{S}}$ and the enstrophy production $\text{tr}\left({\mathrm{\Omega }}^2\mathsf{S}\right)$. In this way, the three-dimensional phase space $(Q_{\mathsf{G}},R_{\mathsf{S}},\text{tr}\left({\mathrm{\Omega }}^2\mathsf{S}\right))$ allows us to identify separately the nonlinear straining and rotational mechanisms in turbulence. The main resultant observations attest that, when the turbulent regime is notably hard, a rising local self-amplification of the velocity gradient takes place in strain-dominated areas. This process is strongly aided by vortex contraction. Concomitantly, a pronounced increase in the linear contributions of vortex stretching is also identified, particularly relevant to strain-dominated slots.

This paper provides insights into the process driving the fast transition of an impulsively accelerated, then decelerated interface between gases of different densities, such as the one produced by the Richtmyer-Meshkov instability, when the timescale of this transitional process is of the same order as the characteristic timescales representative of the resulting turbulence. In this context, a new experimental approach is exposed. For the first time, it allows to design well-defined initial gaseous interfaces in a multiparametric and controlled way, giving access to a precise statistical analysis of the flow. An overview of the main results obtained by means of strioscopic, particle image velocimetry and tomoscopic measurements is provided. They unravel the fast transition of the mixing zone to a turbulent state, as the imprint of the initial condition is lost and the dynamical spectral content covers a wide range of scales, compatible with the achievement of a self-similar trend on very short timescales.

Merging of different streams in channel junctions represents a common mixing process that occurs in systems ranging from soda fountains and bathtub faucets to chemical plants and microfluidic devices. Here, we report a spontaneous trapping of colloidal particles in a merging flow junction when the merging streams have a salinity contrast. We show that the particle trapping is a consequence of nonequilibrium interactions between the particles, solutes, channel, and the freestream flow. A delicate balance of transport processes results in a stable near-wall vortex that traps the particles. We use three-dimensional particle visualization and numerical simulations to provide a rigorous understanding of the observed phenomenon. Such a trapping mechanism is unique from the well-known inertial trapping enabled by vortex breakdown [Proc. Natl. Acad. Sci. USA 111, 4770 (2014)], or the solute-mediated trapping enabled by diffusiophoresis [Phys. Rev. X 7, 041038 (2017)], as the current trapping is facilitated by both the solute and the inertial effects, suggesting a new mechanism for particle trapping in flow networks.

Active matter systems such as eukaryotic cells and bacteria continuously transform chemical energy to motion. Hence living systems exert active stresses on the complex environments in which they reside. One recurring aspect of this complexity is the viscoelasticity of the medium surrounding living systems: Bacteria secrete their own viscoelastic extracellular matrix, and cells constantly deform, proliferate, and self-propel within viscoelastic networks of collagen. It is therefore imperative to understand how active matter modifies, and gets modified by, viscoelastic fluids. Here we present a two-phase model of active nematic matter that dynamically interacts with a passive viscoelastic polymeric phase and perform numerical simulations in two dimensions to illustrate its applicability. Motivated by recent experiments we first study the suppression of cell division by a viscoelastic medium surrounding the cell. We further show that the self-propulsion of a model keratocyte cell is modified by the polymer relaxation of the surrounding viscoelastic fluid in a nonuniform manner and find that increasing polymer viscosity effectively suppresses the cell motility. Last, we explore the hampering impact of the viscoelastic medium on the generic hydrodynamic instabilities of active nematics by simulating the dynamics of an active stripe within a polymeric fluid. The model presented here can provide a framework for investigating more complex dynamics such as the interaction of multicellular growing systems with viscoelastic environments.

Depending on the reflectional and rotational symmetries of annular combustors for aeroengines and gas turbines, self-sustained azimuthal thermoacoustic eigenmodes can be standing, spinning, or a mix of these two types of waves. These thermoacoustic limit cycles are unwanted because the resulting intense acoustic fields induce high-cycle fatigue of the combustor components. This paper presents a new theoretical framework for describing, in an idealized annular combustor, the dynamics of the slow-flow variables, which define the state of an eigenmode, i.e., if the latter is standing, spinning or mixed. The acoustic pressure is expressed as a hypercomplex field and this ansatz is inserted into a one-dimensional wave equation that describes the thermoacoustics of a thin annulus. Slow-flow averaging of this wave equation is performed by adapting the classic Krylov-Bogoliubov method to the quaternion field to derive a system of coupled first-order differential equations for the four slow-flow variables, i.e., the amplitude, the nature angle, the preferential direction, and the temporal phase of the azimuthal thermoacoustic mode. The state of the mode can be conveniently depicted by using the first three slow-flow variables as spherical coordinates for a Bloch sphere representation. Stochastic forcing from the turbulence in annular combustors is also accounted for. This new analytical model describes both rotational and reflectional explicit symmetry-breaking bifurcations induced by the nonuniform distribution of thermoacoustic sources along the annulus circumference and by the presence of a mean swirl.

The internal dynamics during the coalescence of a sessile droplet and a subsequently deposited impacting droplet, with either identical or distinct surface tension, is studied experimentally in the regime where surface tension is dominant. Two color high-speed cameras are used to capture the rapid internal flows and associated mixing from both side and bottom views simultaneously by adding an inert dye to the impacting droplet. Given sufficient lateral separation between droplets of identical surface tension, a robust surface jet is identified on top of the coalesced droplet. Image processing shows this jet is the result of a surface flow caused by the impact inertia and an immobile contact line. By introducing surface tension differences between the coalescing droplets, the surface jet can be either enhanced or suppressed via a Marangoni flow. The influence of the initial droplet configuration and relative surface tension on the long-term dynamics and mixing efficiency, plus the implications for emerging applications such as reactive inkjet printing, are also considered.

We present a detailed study of the dynamics of soft liquid interfaces undergoing viscous stresses due to bulk flows generated by a momentum transfer from light to a turbid liquid. Using a continuous laser wave, light-induced flow is observed and analyzed through the deformability of very soft interfaces up to instability and jet formation. These dynamics are investigated experimentally and numerically below and above the interface instability threshold. Below instability, we show that the dynamics of the interface deformation at short timescales does not vary with the parameters of the laser excitation. We confirm that the mechanism responsible for the interface deformation is a nonlocal effect associated to the viscous stress induced by the bulk flow. Then, we characterize the jetting instability regarding the numerical velocity field within the jet, the jet radius and the fluid flow rate. A satisfying agreement is obtained when comparing quantitatively experimental results and numerical predictions. Our investigation illustrates how light can induce a bulk flow in a turbid liquid, such as a suspension, and how this flow can be used to deform an interface and produce well-controlled liquid jets.

We present an experimental study of the preferential concentration of sub-Kolmogorov inertial particles in active-grid-generated homogeneous and isotropic turbulence, characterized via Voronoi tessellations. We show that the detection and quantification of clusters and voids are influenced by the intensity of the laser and high values of particles volume fraction ${\varphi }_v$. Different biases on the statistics of Voronoi cells are analyzed to improve the reliability of the detection and the robustness in the characterization of clusters and voids. We do this by adapting big-data techniques that allow us to process the particle images up to 10 times faster than standard algorithms. Finally, as preferential concentration is known to depend on multiple parameters, we perform experiments where one parameter is varied and all others are kept constant (${\varphi }_v$, the Reynolds number based on the Taylor length scale ${\text{Re}}_{\lambda }$, and residence time of the particles interacting with the turbulence). Our results confirm, in agreement with published work, that clustering increases with both ${\varphi }_v$ and ${\text{Re}}_{\lambda }$. On the other hand, we find evidence that the mean size of clusters increases with ${\text{Re}}_{\lambda }$ but decreases with ${\varphi }_v$ and that the cluster settling velocity is strongly affected by ${\text{Re}}_{\lambda }$ up to the maximum value studied here, ${\text{Re}}_{\lambda }=250$.

Rotating fluids are well-known to be susceptible to waves. This has received much attention from the geophysics, oceanographic and atmospheric research communities. Inertial waves, which are driven by restoring forces, for example, the Coriolis force, have been detected in the research fields mentioned above. This paper investigates inertial waves in turbine rim seal flows in turbomachinery. These are associated with the large-scale unsteady flow structures having distinct frequencies, unrelated to the main annulus blading, identified in many experimental and numerical studies. These unsteady flow structures have been shown in some cases to reduce sealing effectiveness and are difficult to predict with conventional steady Reynolds-averaged Navier-Stokes (RANS) approaches. Improved understanding of the underlying flow mechanisms and how these could be controlled is needed to improve the efficiency and stability of gas turbines. This study presents large-eddy simulations for three rim seal configurations—chute, axial, and radial rim seals—representative of those used in gas turbines. Evidence of inertial waves is shown in the axial and chute seals, with characteristic wave frequencies limited within the threshold for inertial waves given by classic linear theory (i.e., $|f^{*}/f_{\mathrm{rel}}|\le 2$) and instantaneous flow fields showing helical characteristics. The radial seal, which limits the radial fluid motion with the seal geometry, restricts the Coriolis force and suppresses the inertial wave.