Micro-evaporators for kinetic exploration of phase diagrams

We use pervaporation-based microfluidic devices to concentrate species in aqueous solutions with spatial and temporal control of the process. Using experiments and modelling, we quantitatively describe the advection-diffusion behavior of the concentration field of various solutions (electrolytes, colloids, etc) and demonstrate the potential of these devices as universal tools for the kinetic exploration of the phases and textures that form upon concentration

Intermittency and the Slow Approach to Kolmogorov Scaling

From a simple path integral involving a variable volatility in the velocity differences, we obtain velocity probability density functions with exponential tails, resembling those observed in fully developed turbulence. The model yields realistic scaling exponents and structure functions satisfying extended self-similarity. But there is an additional small scale dependence for quantities in the inertial range, which is linked to a slow approach to Kolmogorov (1941) scaling occurring in the large distance limit.Comment: 10 pages, 5 figures, minor changes to mirror version to appear in PR

Mesoscopic two-phase model for describing apparent slip in micro-channel flows

The phenomenon of apparent slip in micro-channel flows is analyzed by means of a two-phase mesoscopic lattice Boltzmann model including non-ideal fluid-fluid and fluid-wall interactins. The weakly-inhomogeneous limit of this model is solved analytically. The present mesoscopic approach permits to access much larger scales than molecular dynamics, and comparable with those attained by continuum methods. However, at variance with the continuum approach, the existence of a gas layer near the wall does not need to be postulated a priori, but emerges naturally from the underlying non-ideal mesoscopic dynamics. It is therefore argued that a mesoscopic Lattice Boltzmann approach with non-ideal fluid-fluid and fluid-wall interactions might achieve an optimal compromise between physical realism and computational efficiency for the study of channel micro-flows.Comment: 5 pages, 3 figure

Giant slip lengths of a simple fluid at vibrating solid interfaces

It has been shown recently [PRL 102, 254503 (2009)] that in the plane-plane configuration a mechanical resonator vibrating close to a rigid wall in a simple fluid can be overdamped to a frozen regime. Here, by solving analytically the Navier Stokes equations with partial slip boundary conditions at the solid fluid interface, we develop a theoretical approach justifying and extending these earlier findings. We show in particular that in the perfect slip regime the above mentioned results are, in the plane-plane configuration, very general and robust with respect to lever geometry considerations. We compare the results with those obtained previously for the sphere moving perpendicularly and close to a plane in a simple fluid and discuss in more details the differences concerning the dependence of the friction forces with the gap distance separating the moving object (i.e., plane or sphere) from the fixed plane. Finally, we show that the submicron fluidic effect reported in the reference above, and discussed further in the present work, can have dramatic implications in the design of nano-electromechanical systems (NEMS).Comment: submitted to PRE (see also PRL 102, 254503 (2009)

Geometrical statistics of the vorticity vector and the strain rate tensor in rotating turbulence

We report results on the geometrical statistics of the vorticity vector obtained from experiments in electromagnetically forced rotating turbulence. A range of rotation rates $\Omega$ is considered, from non-rotating to rapidly rotating turbulence with a maximum background rotation rate of $\Omega=5$ rad/s (with Rossby number much smaller than unity). Typically, in our experiments ${\rm{Re}}_{\lambda}\approx 100$. The measurement volume is located in the centre of the fluid container above the bottom boundary layer, where the turbulent flow can be considered locally statistically isotropic and horizontally homogeneous for the non-rotating case, see van Bokhoven et al., Phys. Fluids 21, 096601 (2009). Based on the full set of velocity derivatives, measured in a Lagrangian way by 3D Particle Tracking Velocimetry, we have been able to quantify statistically the effect of system rotation on several flow properties. The experimental results show how the turbulence evolves from almost isotropic 3D turbulence ($\Omega\lesssim 0.2$ rad/s) to quasi-2D turbulence ($\Omega\approx 5.0$ rad/s) and how this is reflected by several statistical quantities. In particular, we have studied the orientation of the vorticity vector with respect to the three eigenvectors of the local strain rate tensor and with respect to the vortex stretching vector. Additionally, we have quantified the role of system rotation on the self-amplification terms of the enstrophy and strain rate equations and the direct contribution of the background rotation on these evolution equations. The main effect is the strong reduction of extreme events and related (strong) reduction of the skewness of PDFs of several quantities such as, for example, the intermediate eigenvalue of the strain rate tensor and the enstrophy self-amplification term.Comment: 17 pages, 6 figures, 3 table

Unified Multifractal Description of Velocity Increments Statistics in Turbulence: Intermittency and Skewness

The phenomenology of velocity statistics in turbulent flows, up to now, relates to different models dealing with either signed or unsigned longitudinal velocity increments, with either inertial or dissipative fluctuations. In this paper, we are concerned with the complete probability density function (PDF) of signed longitudinal increments at all scales. First, we focus on the symmetric part of the PDFs, taking into account the observed departure from scale invariance induced by dissipation effects. The analysis is then extended to the asymmetric part of the PDFs, with the specific goal to predict the skewness of the velocity derivatives. It opens the route to the complete description of all measurable quantities, for any Reynolds number, and various experimental conditions. This description is based on a single universal parameter function D(h) and a universal constant R*.Comment: 13 pages, 3 figures, Extended version, Publishe

Transitions and Probes in Turbulent Helium

Previous analysis of a Paris turbulence experiment \cite{zoc94,tab95} shows a transition at the Taylor Reynolds number \rel \approx 700. Here correlation function data is analyzed which gives further evidence for this transition. It is seen in both the power spectrum and in structure function measurements. Two possible explanations may be offered for this observed transition: that it is intrinsic to the turbulence flow in this closed box experiment or that it is an effect of a change in the flow around the anemometer. We particularly examine a pair of ``probe effects''. The first is a thermal boundary layer which does exist about the probe and does limit the probe response, particularly at high frequencies. Arguments based on simulations of the response and upon observations of dissipation suggests that this effect is only crucial beyond \rel\approx 2000. The second effect is produced by vortex shedding behind the probe. This has been seen to produce a large modification in some of the power spectra for large \rel. It might also complicate the interpretation of the experimental results. However, there seems to be a remaining range of data for \rel < 1300 uncomplicated by these effects, and which are thus suggestive of an intrinsic transition.Comment: uuencoded .ps files. submitted to PRE. 12 figures are sent upon request to jane wang ([email protected]

Studying Flow Close to an Interface by Total Internal Reflection Fluorescence Cross Correlation Spectroscopy: Quantitative Data Analysis

Total Internal Reflection Fluorescence Cross Correlation Spectroscopy (TIR-FCCS) has recently (S. Yordanov et al., Optics Express 17, 21149 (2009)) been established as an experimental method to probe hydrodynamic flows near surfaces, on length scales of tens of nanometers. Its main advantage is that fluorescence only occurs for tracer particles close to the surface, thus resulting in high sensitivity. However, the measured correlation functions only provide rather indirect information about the flow parameters of interest, such as the shear rate and the slip length. In the present paper, we show how to combine detailed and fairly realistic theoretical modeling of the phenomena by Brownian Dynamics simulations with accurate measurements of the correlation functions, in order to establish a quantitative method to retrieve the flow properties from the experiments. Firstly, Brownian Dynamics is used to sample highly accurate correlation functions for a fixed set of model parameters. Secondly, these parameters are varied systematically by means of an importance-sampling Monte Carlo procedure in order to fit the experiments. This provides the optimum parameter values together with their statistical error bars. The approach is well suited for massively parallel computers, which allows us to do the data analysis within moderate computing times. The method is applied to flow near a hydrophilic surface, where the slip length is observed to be smaller than 10nm, and, within the limitations of the experiments and the model, indistinguishable from zero.Comment: 18 pages, 12 figure

Mean- Field Approximation and a Small Parameter in Turbulence Theory

Numerical and physical experiments on two-dimensional (2d) turbulence show that the differences of transverse components of velocity field are well described by a gaussian statistics and Kolmogorov scaling exponents. In this case the dissipation fluctuations are irrelevant in the limit of small viscosity. In general, one can assume existence of critical space-dimensionality $d=d_{c}$, at which the energy flux and all odd-order moments of velocity difference change sign and the dissipation fluctuations become dynamically unimportant. At $d<d_{c}$ the flow can be described by the ``mean-field theory'', leading to the observed gaussian statistics and Kolmogorov scaling of transverse velocity differences. It is shown that in the vicinity of $d=d_{c}$ the ratio of the relaxation and translation characteristic times decreases to zero, thus giving rise to a small parameter of the theory. The expressions for pressure and dissipation contributions to the exact equation for the generating function of transverse velocity differences are derived in the vicinity of $d=d_{c}$. The resulting equation describes experimental data on two-dimensional turbulence and demonstrate onset of intermittency as $d-d_{c}>0$ and $r/L\to 0$ in three-dimensional flows in close agreement with experimental data. In addition, some new exact relations between correlation functions of velocity differences are derived. It is also predicted that the single-point pdf of transverse velocity difference in developing as well as in the large-scale stabilized two-dimensional turbulence is a gaussian.Comment: 25 pages, 1 figur

Vorticity statistics in the two-dimensional enstrophy cascade

We report the first extensive experimental observation of the two-dimensional enstrophy cascade, along with the determination of the high order vorticity statistics. The energy spectra we obtain are remarkably close to the Kraichnan Batchelor expectation. The distributions of the vorticity increments, in the inertial range, deviate only little from gaussianity and the corresponding structure functions exponents are indistinguishable from zero. It is thus shown that there is no sizeable small scale intermittency in the enstrophy cascade, in agreement with recent theoretical analyses.Comment: 5 pages, 7 Figure