Ligament-mediated spray formation

The spray formed when a fast gas stream blows over a liquid volume presents a wide distribution of fragment sizes. The process involves a succession of changes of the liquid topology, the last being the elongation and capillary breakup of ligaments torn off from the liquid surface. The coalescence of the liquid volumes constitutive of a ligament at the very moment it detaches from the liquid bulk produces larger drops. This aggregation process has its counterpart on the shape of the size distribution associated with the ligament breakup, found to be very well represented by gamma distributions. The exponential shape of the overall distribution in the spray coincides with the large excursion wing of these elementary distributions, underlying the crucial role played by the ligament dynamics in building up the broad statistics of sprays

Dissipation Scale Fluctuations and Chemical Reaction Rates in Turbulent Flows

Small separation between reactants, not exceeding $10^{-8}-10^{-7}cm$, is the necessary condition for various chemical reactions. It is shown that random advection and stretching by turbulence leads to formation of scalar-enriched sheets of {\it strongly fluctuating thickness} $\eta_{c}$. The molecular-level mixing is achieved by diffusion across these sheets (interfaces) separating the reactants. Since diffusion time scale is $\tau_{d}\propto \eta_{c}^{2}$, the knowledge of probability density $Q(\eta_{c},Re)$ is crucial for evaluation of chemical reaction rates. In this paper we derive the probability density $Q(\eta_{c},Re,Sc)$ and predict a transition in the reaction rate behavior from ${\cal R}\propto \sqrt{Re}$ ($Re\leq 10^{4}$) to the high-Re asymptotics ${\cal R}\propto Re^{0}$. The theory leads to an approximate universality of transitional Reynolds number $Re_{tr}\approx 10^{4}$. It is also shown that if chemical reaction involves short-lived reactants, very strong anomalous fluctuations of the length-scale $\eta_{c}$ may lead to non-negligibly small reaction rates

Shear effects on passive scalar spectra

The effects of a large-scale shear on the energy spectrum of a passively advected scalar field are investigated. The shear is superimposed on a turbulent isotropic flow, yielding an Obukhov-Corrsin $k^{-5/3}$ scalar spectrum at small scales. Shear effects appear at large scales, where a different, anisotropic behavior is observed. The scalar spectrum is shown to behave as $k^{-4/3}$ for a shear fixed in intensity and direction. For other types of shear characteristics, the slope is generally intermediate between the -5/3 Obukhov-Corrsin's and the -1 Batchelor's values. The physical mechanisms at the origin of this behaviour are illustrated in terms of the motion of Lagrangian particles. They provide an explanation to the scalar spectra shallow and dependent on the experimental conditions observed in shear flows at moderate Reynolds numbers.Comment: 10 LaTeX pages,3 eps Figure

How vortices mix

International audienceThe advection of a passive scalar blob in the deformation field of an axisymmetric vortex is a simple mixing protocol for which the advection-diffusion problem is amenable to a near-exact description. The blob rolls-up in a spiral which ultimately fades away in the diluting medium. The complete transient concentration field in the spiral is accessible from the Fourier equations in a properly chosen frame. The concentration histogram of the scalar wrapped in the spiral presents unexpected singular transient features and its long time properties are discussed in connection with mixtures from the real world

Hybrid binomial Langevin-multiple mapping conditioning modeling of a reacting mixing layer

A novel, stochastic, hybrid binomial Langevin-multiple mapping conditioning (MMC) model—that utilizes the strengths of each component—has been developed for inhomogeneous flows. The implementation has the advantage of naturally incorporating velocity-scalar interactions through the binomial Langevin model and using this joint probability density function (PDF) to define a reference variable for the MMC part of the model. The approach has the advantage that the difficulties encountered with the binomial Langevin model in modeling scalars with nonelementary bounds are removed. The formulation of the closure leads to locality in scalar space and permits the use of simple approaches (e.g., the modified Curl’s model) for transport in the reference space. The overall closure was evaluated through application to a chemically reacting mixing layer. The results show encouraging comparisons with experimental data for the first two moments of the PDF and plausible results for higher moments at a relatively modest computational cost

Van Hove singularities in Probability Density Functions of scalars

A general theory for the Probability Density Function (PDF) of a scalar stirred in an axisymmetric time-dependent flow is derived. This theory reveals singularities, discontinuities and cusps occurring as soon as the spatial gradient of the scalar concentration vanishes somewhere in the field. These singularities are similar to the Van Hove singularities obtained in the density of vibration modes of a crystal. This feature, ubiquitous in convection–diffusion problems, is documented experimentally for the mixing of a dye in a Lamb–Oseen vortex

The destabilization of an initially thick liquid sheet edge

International audienceBy forcing the sudden dewetting of a free soap film attached on one edge to a straight solid wire, we study the recession and subsequent destabilization of its free edge. The newly formed rim bordering the sheet is initially thicker than the film to which it is attached, because of the Plateau border preexisting on the wire. The initial condition is thus that of an immobile massive toroidal rim connected to a thin liquid film of thickness h. The terminal Taylor-Culick receding velocity V = sqrt(2 sigma/rho h), where sigma and rho are the liquid surface tension and density, respectively, is only reached after a transient acceleration period which promotes the rim destabilization. The selected wavelength and associated growth time coincide with those of an inertial instability driven by surface tension

Impacts on thin elastic sheets

International audienceWe study transverse impacts of rigid objects on a free elastic membrane, using thin circular sheets of natural rubber as experimental models. After impact, two distinct axisymmetric waves propagate in and on the sheet. First a tensile wave travels at sound speed leaving behind the wave front a stretched domain. Then, a transverse wave propagates on the stretched area at a lower speed. In the stretched area, geometrical confinement induces compressive circumferential stresses leading to a buckling instability, giving rise to radial wrinkles. We report on a set of experiments and theoretical remarks on the conditions of occurrence of these wrinkles, their dynamics and wavelength

Drop deformation by laser-pulse impact

A free-falling absorbing liquid drop hit by a nanosecond laser-pulse experiences a strong recoil-pressure kick. As a consequence, the drop propels forward and deforms into a thin sheet which eventually fragments. We study how the drop deformation depends on the pulse shape and drop properties. We first derive the velocity field inside the drop on the timescale of the pressure pulse, when the drop is still spherical. This yields the kinetic-energy partition inside the drop, which precisely measures the deformation rate with respect to the propulsion rate, before surface tension comes into play. On the timescale where surface tension is important the drop has evolved into a thin sheet. Its expansion dynamics is described with a slender-slope model, which uses the impulsive energy-partition as an initial condition. Completed with boundary integral simulations, this two-stage model explains the entire drop dynamics and its dependance on the pulse shape: for a given propulsion, a tightly focused pulse results in a thin curved sheet which maximizes the lateral expansion, while a uniform illumination yields a smaller expansion but a flat symmetric sheet, in good agreement with experimental observations.Comment: submitted to J. Fluid Mec

Self-similar impulsive capillary waves on a ligament

We study the short-time dynamics of a liquid ligament, held between two solid cylinders, when one is impulsively accelerated along its axis. A set of one-dimensional equations in the slender-slope approximation is used to describe the dynamics, including surface tension and viscous effects. An exact self-similar solution to the linearized equations is successfully compared to experiments made with millimetric ligaments. Another non-linear self-similar solution of the full set of equations is found numerically. Both the linear and non-linear solutions show that the axial depth at which the liquid is affected by the motion of the cylinder scales like $\sqrt{t}$. The non-linear solution presents the peculiar feature that there exists a maximum driving velocity $U^\star$ above which the solution disappears, a phenomenon probably related to the de-pinning of the contact line observed in experiments for large pulling velocities