We have uncovered a drop rebound regime, characteristic of highly viscous liquids impacting tilted sublimating surfaces. Here the drops, rather than showing a slide, spread, recoil, and rebound behavior, exhibit a prompt tumbling rebound. As a result, glycerol surprisingly rebounds faster than three orders of magnitude less viscous water. When a viscous drop impacts a sublimating surface, part of its initial linear momentum is converted into angular momentum: Lattice Boltzmann simulations confirmed that tumbling owes its appearance to the rapid transition of the internal angular velocity prior to rebound to a constant value, as in a tumbling solid body.

By introducing the notion of an ideal large-scale filter, a formal statement is given of the hypothesis of the quasisteady quasihomogeneous nature of the interaction between the large and small scales in the near-wall part of turbulent flows. This makes the derivations easier and more rigorous. A method is proposed to find the optimal large-scale filter by multiobjective optimization, with the first objective being a large correlation between large-scale fluctuations near the wall and in the layer at a certain finite distance from the wall and the second objective being a small correlation between the small scales in the same layers. The filter is demonstrated to give good results. Within the quasisteady quasihomogeneous theory, expansions for various quantities are found with respect to the amplitude of the large-scale fluctuations. Including the higher-order terms improves the agreement with numerical data. Interestingly, it turns out that the quasisteady quasihomogeneous theory implies a dependence of the mean profile logarithmic-law constants on the Reynolds number. The main overall result of the present work is the demonstration of the relevance of the quasisteady quasihomogeneous theory for near-wall turbulent flows.

We study the motion of a hot particle in a viscous liquid at low Reynolds numbers, which is inspired by recent experiments with Brownian particles heated by a laser. The difference in temperature between a particle and the ambient fluid causes a spatial variation of the viscosity in the vicinity of the solid body. We derive a general analytical expression determining the force and the torque on a particle for low Péclet numbers by exploiting the Lorentz reciprocal theorem. For small temperature and viscosity variations, a perturbation analysis is implemented to evaluate the leading-order correction to the hydrodynamic force and torque on the particle. The results are applied to describe dynamics of a uniformly hot spherical particle and to spherical particles with a nonuniform surface temperature described by dipole and quadrupole moments. Among other results, we find for dipolar thermal fields that there is coupling of the translational and rotational motions when there are local viscosity variations; such coupling is absent in an isothermal fluid.

We explore the processes by which a dense set of small liquid droplets (a spray) evaporates in a dry, stirred gas phase. A dense spray of micron-sized liquid (water or ethanol) droplets is formed in air by a pneumatic atomizer in a closed chamber. The spray is conveyed in ambient air as a plume whose extension depends on the relative humidity of the diluting medium. Standard shear instabilities develop at the plume edge, forming the stretched lamellar structures familiar with passive scalars. Unlike passive scalars however, these lamellae vanish in a finite time, because individual droplets evaporate at their border in contact with the dry environment. Experiments demonstrate that the lifetime of an individual droplet embedded in a lamellae is much larger than expected from the usual $d^2$ law describing the fate of a single drop evaporating in a quiescent environment. By analogy with the way mixing times are understood from the convection-diffusion equation for passive scalars, we show that the lifetime of a spray lamellae stretched at a constant rate $\gamma$ is $t_v=\frac{1}{\gamma }ln\left(\frac{1+\varphi }{\varphi }\right)$, where $\varphi$ is a parameter that incorporates the thermodynamic and diffusional properties of the vapor in the diluting phase. The case of time-dependent stretching rates is examined too. A dense spray behaves almost as a (nonconserved) passive scalar.

Evaporation of a liquid on a hot solid can be exploited to induce both levitation and self-propulsion if the vapor flow under the liquid is made directional. Here we propose to force an anisotropic flow of vapor with a herringbone pattern at a solid surface. Liquids are found to self-propel on such hot materials, drawn by the underlying flow of vapor. The simplicity of the geometry allows us to predict the direction of vapor flow rectification, to quantitatively model the propulsion, and to discuss how the pattern must be designed to optimize both driving force and drop velocity.

The adhesion and detachment of a capsule on a solid boundary surface is studied via a combination of scaling theory and numerical simulation and the behavior is compared and contrasted with a vesicle. It is shown that the dominant physical property for both capsules and vesicles is the area dilation modulus $K_s$ of the membrane. The nonzero shear modulus $G_s$ for capsules increases the resistance to deformation and thus decreases slightly the equilibrium contact radius for an adhered capsule compared to an adhered vesicle. The detachment process in this study is due to an external axisymmetric flow. Unlike a rigid body that must be pulled away without change of shape, capsules (and vesicles) almost always detach dominantly by peeling in which the contact radius decreases but the minimum separation distance does not change until the final moments of detachment. Compared to a vesicle with the same $K_s$, a capsule maintains a more compact shape and is harder to elongate under a given external flow. Hence, the detachment process is slower for capsules compared to vesicles with the same $K_s$.

With the aim to predict energy transport by internal waves incident upon observed density staircases in the ocean, the theory for internal wave tunneling through a single finite-size mixed region is extended to predict the transmission of internal waves through a piecewise-constant density profile with an arbitrary number of steps. An analytic solution is found if all steps have equal vertical extent. From this solution, bounds are established for the relative incident horizontal wave number and frequency of waves that have negligible transmission, a result that is independent of the number of steps. If the step sizes vary randomly about a mean vertical extent, the transmission can be computed numerically for several random realizations. Provided the horizontal wavelength is much longer than the total vertical extent of the staircase, the standard deviation of the computed transmission coefficients is small and the mean agrees well with the analytic prediction for equally spaced steps. The results are applied to thermohaline staircases observed in the ocean in order to put lower bounds on the wavelengths of long inertia gravity waves that significantly transmit to great depth.

The stability of an interface separating less dense, clear salt water above from more dense, sediment-laden fresh water below is explored via direct numerical simulations. We find that the destabilizing effects of double diffusion and particle settling amplify each other above the diffusive interface, whereas they tend to cancel each other below. For moderate settling velocities, plumes form both above and below the interface, whereas for large settling velocities plume formation below the interface is suppressed. We identify the dimensionless parameter that determines in which regime a given flow takes place, along with the critical value at which the transition between the regimes takes place.

This study investigated the relationship between the pinch-off of axisymmetric vortex rings and the evolution of pressure in the shear layer being entrained into the vortex rings. A piston-cylinder apparatus was used to generate the vortex rings, and five cases of constant piston acceleration over distances ranging from zero (impulsive start) to eight piston diameters were investigated. It was determined that increasing the distance over which the piston accelerated increased the dimensionless formation time at which the vortex ring pinches off, consistent with previous observations. A limiting value of vortex ring formation number of approximately seven is approached when the piston is accelerated over more than six piston diameters. For each case, the evolution of pressure in the shear layer was calculated based on PIV measurements of the velocity field and spatial integration of the corresponding pressure gradients using a recently developed algorithm. Plots of the shear layer pressure in X-T diagrams aided in identifying key features of the pressure associated with the evolution of vortex rings, including a high-pressure region that forms behind the leading ring. By extrapolating the motion of this high-pressure region back to the nozzle exit plane in the X-T diagram, its time of first appearance can be estimated. It is found that the appearance of the extrapolated local pressure maximum in the shear layer at the nozzle exit plane coincides with vortex ring pinch-off, as conventionally quantified by the vortex ring formation number.

The influence of particle-polymer interactions on the ensemble average stress is derived as a function of the Deborah number for a dilute suspension of spheres in an Oldroyd-B fluid in the limit of small polymer concentrations. The slow rate of decay of the particle-induced polymer stress with separation from a particle presents a challenge to the derivation of the average stress, which can be overcome by removing the linearized polymer stress disturbance before computing the bulk average stress from the particle-induced disturbance. The linearized stress can be shown to have zero ensemble average. The polymer influence on the particle's stresslet is computed with the aid of a generalized reciprocal theorem based on a regular perturbation from Newtonian flow for small polymer concentration. The analysis shows that the particle-polymer contributions to the shear stress and first normal stress difference shear thicken as has been observed in the experiments of Scirocco et al. [Shear thickening in filled Boger fluids, J. Rheol. 49, 551 (2005)]. The particle-polymer contribution to the second normal stress difference is positive at small Deborah numbers but changes sign at a Deborah number of about 2.3.

The impact of drops of concentrated non-Brownian suspensions (cornstarch and polystyrene spheres) onto a solid surface is investigated experimentally. The spreading dynamics and maximal deformation of the droplet of such shear thickening liquids are found to be markedly different from the impact of Newtonian drops. A particularly striking observation is that the maximal deformation is independent of the drop velocity and that the deformation suddenly stops during the impact phase. Both observations are due to the shear thickening rheology of the suspensions, as is explained theoretically from a balance between the kinetic energy and the viscously dissipated energy, from which we establish a scaling relation between the maximal deformation of the drop and rheological parameters of concentrated suspensions.

Determination of energy transport is crucial for understanding the energy budget and fluid circulation in density varying fluids such as the ocean and the atmosphere. However, it is rarely possible to determine the energy flux field $\mathit{J}=p\mathit{u}$, which requires simultaneous measurements of the pressure and velocity perturbation fields $p$ and $\mathit{u}$, respectively. We present a method for obtaining the instantaneous $\mathit{J}(x,z,t)$ from density perturbations alone: A Green's function-based calculation yields $p$; $\mathit{u}$ is obtained by integrating the continuity equation and the incompressibility condition. We validate our method with results from Navier-Stokes simulations: The Green's function method is applied to the density perturbation field from the simulations and the result for $\mathit{J}$ is found to agree typically to within 1% with $\mathit{J}$ computed directly using $p$ and $\mathit{u}$ from the Navier-Stokes simulation. We also apply the Green's function method to density perturbation data from laboratory schlieren measurements of internal waves in a stratified fluid and the result for $\mathit{J}$ agrees to within $6\%$ with results from Navier-Stokes simulations. Our method for determining the instantaneous velocity, pressure, and energy flux fields applies to any system described by a linear approximation of the density perturbation field, e.g., to small-amplitude lee waves and propagating vertical modes. The method can be applied using our matlab graphical user interface EnergyFlux.