An analytical expression describing the unsteady pressure evolution of the dispersed phase driven by variations in the carrier phase is presented. In this article, the term “dispersed phase” represents rigid particles, droplets, or bubbles. Letting both the dispersed and continuous phases be inhomogeneous, unsteady, and compressible, the developed pressure equation describes the particle response and its eventual equilibration with that of the carrier fluid. The study involves impingement of a plane traveling wave of a given frequency and subsequent volume-averaged particle pressure calculation due to a single wave. The ambient or continuous fluid's pressure and density-weighted normal velocity are identified as the source terms governing the particle pressure. Analogous to the generalized Faxén theorem, which is applicable to the particle equation of motion, the pressure expression is also written in terms of the surface average of time-varying incoming flow properties. The surface average allows the current formulation to be generalized for any complex incident flow, including situations where the particle size is comparable to that of the incoming flow. Further, the particle pressure is also found to depend on the dispersed-to-continuous fluid density ratio and speed of sound ratio in addition to dynamic viscosities of both fluids. The model is applied to predict the unsteady pressure variation inside an aluminum particle subjected to normal shock waves. The results are compared against numerical simulations and found to be in good agreement. Furthermore, it is shown that, although the analysis is conducted in the limit of negligible flow Reynolds and Mach numbers, it can be used to compute the density and volume of the dispersed phase to reasonable accuracy. Finally, analogous to the pressure evolution expression, an equation describing the time-dependent particle radius is deduced and is shown to reduce to the Rayleigh-Plesset equation in the linear limit.

Heat transfer to fluids at supercritical pressure is different from heat transfer at lower pressures due to strong variations of the thermophysical properties with the temperature. We present and analyze results of direct numerical simulations of heat transfer to turbulent ${\mathrm{CO}}_2$ at 8 MPa in an annulus. Periodic streamwise conditions are imposed so that mean streamwise acceleration due to variations in the density does not occur. The inner wall of the annulus is kept at a temperature of 323 K, while the outer wall is kept at a temperature of 303 K. The pseudocritical temperature $T_{pc}=307.7$ K, which is the temperature where the thermophysical properties vary the most, can be found close to the inner wall. This work is a continuation of an earlier study, in which turbulence attenuation due to the variable thermophysical properties of a fluid at supercritical pressure was studied. In the current work, the direct effects of variations in the specific heat capacity, thermal diffusivity, density, and the molecular Prandtl number on heat transfer are investigated using different techniques. Variations in the specific heat capacity cause significant differences between the mean nondimensionalized temperature and enthalpy profiles. Compared to the enthalpy fluctuations, temperature fluctuations are enhanced in regions with low specific heat capacity and diminished in regions with a large specific heat capacity. The thermal diffusivity causes local changes to the mean enthalpy gradient, which in turn affects molecular conduction of thermal energy. The turbulent heat flux is directly affected by the density, but it is also affected by the mean molecular Prandtl number and attenuated or enhanced turbulent motions. In general, enthalpy fluctuations are enhanced in regions with a large mean molecular Prandtl number, which enhances the turbulent heat flux. While analyzing the Nusselt numbers under different conditions it is found that heat transfer deterioration or enhancement can occur without streamwise acceleration or mixed convection conditions. Finally, through a combination of a relation between the Nusselt number and the radial heat fluxes, a quadrant analysis of the turbulent heat flux, and conditional averaging of the heat flux quadrants, it is shown that heat transfer from a heated surface depends on the density and the molecular Prandtl number of both hot fluid moving away from a heated surface as well as the thermophysical properties of relatively cold fluid moving towards it.

We study the statistical properties of helicity in direct numerical simulations of fully developed homogeneous and isotropic turbulence and in a class of turbulence shell models. We consider correlation functions based on combinations of vorticity and velocity increments that are not invariant under mirror symmetry. We also study the scaling properties of high-order structure functions based on the moments of the velocity increments projected on a subset of modes with either positive or negative helicity (chirality). We show that mirror symmetry is recovered at small scales, i.e., chiral terms are subleading and they are well captured by a dimensional argument plus anomalous corrections. These findings are also supported by a high Reynolds numbers study of helical shell models with the same chiral symmetry of Navier-Stokes equations.

Surrounded by a spherically symmetric solute cloud, chemically active homogeneous spheres do not undergo conventional autophoresis when suspended in an unbounded liquid domain. When exposed to external flows, solute advection deforms that cloud, resulting in a generally asymmetric distribution of diffusio-osmotic slip which, in turn, modifies particle motion. Inspired by classical forced-convection analyses [Acrivos and Taylor, Phys. Fluids 5, 387 (1962); Frankel and Acrivos, Phys. Fluids 11, 1913 (1968)] we illustrate this phoretic phenomenon using two prototypic configurations, one where the particle sediments under a uniform force field and one where it is subject to a simple shear flow. In addition to the Péclet number $\mathrm{Pe}$ associated with the imposed flow, the governing nonlinear problem also depends upon $\alpha$, the intrinsic Péclet number associated with the chemical activity of the particle. As in the forced-convection problems, the small-Péclet-number limit is nonuniform, breaking down at large distances away from the particle. Calculation of the leading-order autophoretic effects thus requires use of matched asymptotic expansions, the outer region being at distances that scale inversely with $\mathrm{Pe}$ and ${\mathrm{Pe}}^{1/2}$ in the respective sedimentation and shear problems. In the sedimentation problem we find an effective drag reduction of fractional amount $\alpha /8$; in the shear problem we find that the magnitude of the stresslet is decreased by a fractional amount $\alpha /4$. For a dilute particle suspension the latter result is manifested by a reduction of the effective viscosity.

A one-dimensional numerical simulation is carried out to study the oscillation characteristics of satellite droplets in the beads-on-a-string structure of an Oldroyd-B viscoelastic liquid jet. The oscillation of satellite droplets is compared with the linear oscillation of a single viscoelastic droplet. It is found that, contrary to the predictions of linear theory, the period of oscillation of satellite droplets decreases with time, despite the increase in droplet volume. The mechanism may lie in the existence of the filament, which exerts an extra resistance on droplets. On the other hand, the oscillation of droplets does not influence very much the thinning of the filament. The influence of the axial wave number, viscosity, and elasticity on the oscillation of satellite droplets is examined. Increasing the wave number may result in the decrease in the period and the increase in the decay rate of oscillation, while increasing viscosity may lead to the increase in both the period and the decay rate of oscillation. Elasticity is shown to suppress the oscillation at large wave numbers, but its influence is limited at small wave numbers.

Inspired by the flow processes in the technology of carbon dioxide $\left({\mathrm{CO}}_2\right)$ storage in saline formations, we modeled a homogeneous porous media flow in a Hele-Shaw cell to investigate density-driven convection due to dissolution. We used an analogy of the fluid system to mimic the diffusion and subsequent convection when ${\mathrm{CO}}_2$ dissolves in brine, which generates a heavier solution. By varying the permeability, we examined the onset of convection, the falling dynamics, the wavelengths of fingers, and the rate of dissolution, for the Rayleigh number $\text{Ra}$ (a dimensionless forcing term which is the ratio of buoyancy to diffusivity) in the range of $2.0\times {10}^4\le \text{Ra}\le 8.26\times {10}^5$. Our results reveal that the effect of permeability influences significantly the initial convective speed, as well as the later coarsening dynamics of the heavier fingering plumes. However, the total dissolved mass, characterized by a nondimensional Nusselt number $\text{Nu}$, has an insignificant dependence on $\text{Ra}$. This implies that the total dissolution rate of ${\mathrm{CO}}_2$ is nearly constant in high $\text{Ra}$ geological porous structures.

We demonstrate how to suspend various magnetic and nonmagnetic particles in liquid metals and characterize their properties relevant to magnetohydrodynamics (MHD). The suspending method uses an acid as a flux to eliminate oxidation from both metal particles and liquid, which allows the particles to be wetted and suspended into the liquid if the particles have higher conductivity than the liquid. With this process we were able to suspend a wide range of particle materials and sizes from 40 nm to 500 $\mu \mathrm{m}$ into three different liquid metal bases and volume fractions $\varphi$ up to the liquid-solid transition ${\varphi }_c$. By controlling the volume fraction of iron particles in liquid eGaIn, we increased the magnetic permeability by a factor of 5.0 and the electrical conductivity by 13% over that of the pure liquid metal, which gives these materials the potential to exhibit strong MHD effects on the laboratory scale that are usually only observable in the cores of planets and stars. By adding nonmagnetic zinc particles, we increased the viscosity by a factor of 160 while keeping the magnetic and electrical properties nearly constant, which would allow independent control of MHD effects from turbulence. We show that the suspensions flow like Newtonian fluids up to the volume fraction of the liquid-solid transition ${\varphi }_c$.

The angular dynamics of a very small ellipsoidal particle in a viscous flow decouples from its translational dynamics and the particle angular velocity is given by Jeffery's theory. It is known that cuboid particles share these properties. In the literature a special case is most frequently discussed, namely that of axisymmetric particles with a continuous rotation symmetry. Here we compute the angular dynamics of crystals that possess a discrete rotation symmetry and certain mirror symmetries but do not have a continuous rotation symmetry. We give examples of such particles that nevertheless obey Jeffery's theory. However, there are other examples where the angular dynamics is determined by a more general equation of motion.

Spectra and one-point statistics of velocity and thermodynamic variables in isotropic turbulence of compressible fluid are examined by using numerical simulations with solenoidal forcing at the turbulent Mach number $M_t$ from 0.05 to 1.0 and at the Taylor Reynolds number ${\text{Re}}_{\lambda }$ from 40 to 350. The velocity field is decomposed into a solenoidal component and a compressible component in terms of the Helmholtz decomposition, and the compressible velocity component is further decomposed into a pseudosound component, namely, the hydrodynamic component associated with the incompressible field and an acoustic component associated with sound waves. It is found that the acoustic mode dominates over the pseudosound mode at turbulent Mach numbers $M_t\ge 0.4$ in our numerical simulations. At turbulent Mach numbers $M_t\le 0.4$, there exists a critical wave number $k_c$ beyond which the pseudosound mode dominates while the acoustic mode dominates at small wave numbers $k<k_c$. In the pseudosound-mode-dominated region, the compressible velocity is fully enslaved to the solenoidal velocity, and its spectrum scales as $M_t^4{k}^{-3}$ in the inertial range. It is also found that in the inertial range, the spectra of pressure, density, and temperature exhibit a $k^{-7/3}$ scaling for $M_t\le 0.3$ and a $k^{-5/3}$ scaling for $M_t\ge 0.5$.

We report about an intriguing boiling regime occurring for small heaters embedded on the boundary in subcooled water. The microheater is realized by focusing a continuous wave laser beam to about $10\mu \mathrm{m}$ in diameter onto a 165-nm-thick layer of gold, which is submerged in water. After an initial vaporous explosion a single bubble oscillates continuously and repeatedly at several $100\mathrm{kHz}$ albeit with constant laser power input. The microbubble's oscillations are accompanied with bubble pinch-off, leading to a stream of gaseous bubbles in the subcooled water. The self-driven bubble oscillation is explained with a thermally kicked oscillator caused by surface attachment and by the nonspherical collapses. Additionally, Marangoni stresses induce a recirculating streaming flow which transports cold liquid towards the microheater, reducing diffusion of heat along the substrate and therefore stabilizing the phenomenon to many million cycles. We speculate that this oscillate boiling regime may overcome the heat transfer thresholds observed during the nucleate boiling crisis and offers a new pathway for heat transfer under microgravity conditions.

We present numerical simulations of ideal magnetohydrodynamics showing suppression of the Richtmyer-Meshkov instability in spherical implosions in the presence of an octahedrally symmetric magnetic field. This field configuration is of interest owing to its high degree of spherical symmetry in comparison with previously considered dihedrally symmetric fields. The simulations indicate that the octahedral field suppresses the instability comparably to the other previously considered candidate fields for light-heavy interface accelerations while retaining a highly symmetric underlying flow even at high field strengths. With this field, there is a reduction in the root-mean-square perturbation amplitude of up to approximately $50\%$ at representative time under the strongest field tested while maintaining a homogeneous suppression pattern compared to the other candidate fields.

The collapse dynamics of an axisymmetric fluid cavity that wets the bottom of a rotating bucket bound by vertical sidewalls are studied. Lubrication theory is applied to the governing field equations for the thin film to yield an evolution equation that captures the effect of capillary, gravitational, and centrifugal forces on this converging flow. The focus is on the quasistatic spreading regime, whereby contact-line motion is governed by a constitutive law relating the contact-angle to the contact-line speed. Surface tension forces dominate the collapse dynamics for small holes with the collapse time appearing as a power law whose exponent compares favorably to experiments in the literature. Gravity accelerates the collapse process. Volume dependence is predicted and compared with experiment. Centrifugal forces slow the collapse process and lead to complex dynamics characterized by stalled spreading behavior that separates the large and small hole asymptotic regimes.

We study the fluid drift due to a time-dependent dumbbell model of a microswimmer. The model captures important aspects of real microswimmers such as a time-dependent flagellar motion and a no-slip body. The model consists of a rigid sphere for the body and a time-dependent moving Stokeslet representing the flagella. We analyze the paths of idealized fluid particles displaced by the swimmer. The simplicity of the model allows some asymptotic calculations very near and far away from the swimmer. The displacements of particles near the swimmer diverge in a manner similar to an isolated no-slip sphere, but with a smaller coefficient due to the action of the flagellum. Far from the swimmer, the time dependence becomes negligible due to both being very fast and decaying with distance. Finally, we compute the probability distribution of particle displacements and find that our model has fatter tails than previous steady models, due to the presence of a no-slip surface that drags particles along.

The free rise of isolated, deformable, finite-size bubbles in otherwise homogeneous isotropic turbulence is investigated by direct numerical simulation. The Navier-Stokes equations are solved in both phases subject to the pertinent velocity and stress conditions at the deformable gas-liquid interface. The bubble rise velocity is found to be drastically reduced by turbulence, as is widely known for microbubbles. The probability distribution functions of the horizontal bubble acceleration component are well fitted by a log-normal distribution. The distributions of the vertical components are negatively skewed, a property related to the fact that bubbles experience on average stronger decelerations than accelerations. An assessment of the correlations of bubble acceleration with properties of the surrounding flow is used to define estimates of the liquid velocity and vorticity entering in liquid acceleration and lift forces. Finally, fast rising bubbles are found to preferentially sample downflow regions of the flow, whereas those subjected to a higher turbulence level have an increased residence time in swirling regions, some features similar to those of small bubbles.

Unsteady motion of a rarefied gas between two parallel plates caused when one of the plates starts a harmonic oscillation in its normal direction is investigated under a slightly rarefied condition, i.e., for small Knudsen numbers. The compressible Navier-Stokes equations are employed and their appropriate temperature jump condition is derived systematically. The equations with the correct boundary conditions are solved numerically to give the unsteady flow field. In particular, the time-periodic solution established at later times is investigated in detail and it is shown that the one-period average of the oscillating part of the momentum and that of the energy transferred from the oscillating plate to the resting one take nonzero values in contrast to the linear theory. This confirms the numerical result based on the Bhatnagar-Gross-Krook model of the Boltzmann equation for intermediate Knudsen numbers [T. Tsuji and K. Aoki, Microfluid. Nanofluid. 16, 1033 (2014)]. It is also shown that the gas approaches the time-periodic motion exponentially fast in time.

A mixed suspension of red blood cells (RBCs) and microparticles flows through a cylindrical channel with a constriction mimicking a stenosed blood vessel. Our three-dimensional Lattice-Boltzmann simulations show that the RBCs are depleted right ahead of and after the constriction. Although the RBC mean concentration (hematocrit) is 16.5% or 23.7%, their axial concentration profile is very similar to that of isolated tracer particles flowing along the central axis. Most importantly, however, we find that the stiff microparticles exhibit the opposite behavior. Arriving on a marginated position near the channel wall, they can pass through the constriction only if they find a suitable gap to dip into the dense plug of RBCs occupying the channel center. This leads to a prolonged dwell time and, as a consequence, to a pronounced increase in microparticle concentration right in front of the constriction. For biochemically active particles such as drug delivery agents or activated platelets this clustering may have important physiological consequences, e.g., for the formation of microthrombi.

Understanding the gravity-driven motion of droplets on inclined substrates in the presence of external shear and substrate permeability is important for applications such as spray coating and filtration. In this paper, we use a lubrication-theory-based model to study how external shear and substrate permeability affect droplet wetting transitions. A nonlinear evolution equation for the droplet height as a function of time and two spatial variables is derived and numerically solved. The contact-line region is described using a precursor film and disjoining pressure. Depending on its direction, external shear can either suppress or drive wetting transitions, but does not appear to significantly change the critical droplet speeds associated with these transitions. Substrate permeability generally suppresses wetting transitions due to liquid absorption and does appear to significantly affect these critical droplet speeds. The strong influence of substrate permeability and external shear on droplet wetting transitions indicates that it will be important to account for these effects when developing accurate models for industrial applications.

The three-dimensional development of instabilities and the subsequent spray formation in a gas-liquid mixing layer are important fundamental problems in the area of multiphase flows. It is highly desirable to visualize this detailed atomization process and to analyze the instabilities and mechanisms involved, and massive numerical simulations are required, in addition to experiment. Rapid development of numerical methods and computer technology in the past decade now allows large-scale three-dimensional direct numerical simulations of atomization to be performed. Nevertheless, the fundamental question, whether all the physical scales involved in the primary breakup process are faithfully resolved, has eluded researchers until now. In the present study, we conduct direct numerical simulations of spray formation in a gas-liquid mixing layer with state-of-the-art computational resources (using up to $4\times {10}^9$ cells and $16384$ cores), in order to obtain a high-fidelity numerical closeup of the detailed mechanisms of spray formation. We also aim to examine whether present computational resources are sufficient for a fully resolved direct numerical simulation of atomization.