Dynamics of fluctuations in a fluid below the onset of Rayleigh-Bénard convection

Evaluation of the shadowgraph method for the determination of mutual and thermal diffusivities

The present work provides a systematic study on the influence of sample properties and experimental conditions on the reliable accessibility of Fick or mutual diffusion coefficients D11 and thermal diffusivities a in binary liquid mixtures using the shadowgraph method. For this, mixtures with varying magnitudes of the Soret coefficient ST and their optical contrast factors were studied at a temperature of 298.15 K and pressures between (0.1 and 0.65) MPa with varying magnitudes and orientations of the applied temperature and concentration gradients ∇T and ∇c. Experimental signals obtained in these investigations were analyzed with respect to the intensities of the signal contributions from non-equilibrium fluctuations (NEFs) in concentration and temperature, and the reliability of the determined D11 and a data was assessed by comparison to literature data. Larger signal intensities from NEFs and, therefore, a more reliable determination of diffusivities were given for sufficiently large magnitudes of ST, the optical contrast factors, and the applied ∇T and ∇c. At very small fluid layer thicknesses L ≤ 0.30 mm, the associated reduction of signal statistics outweighing the expected increase of signal intensities at larger magnitudes of ∇T and ∇c as well as the influence of confinement imposed limitations for the determination of diffusivities in some cases. Furthermore, an influence of the mixture composition on signal intensities from concentration-NEFs was identified, where too small mole fractions of one component can hinder the determination of D11 in mixtures with small magnitudes of the optical contrast factor (∂n/∂c)T,p.

Criterion to determine the wave vector range of heterodyne near-field exposure time-dependent spectrum

Recently, image methods for measuring dynamics of nanoparticles have garnered attention; however, the low-speed frame rate of normal image sensors limits their application. Applying a low-speed detector can extract fast dynamic information by the method of an exposure time-dependent spectrum, whereas its accuracy is too sensitive to the wave vector range selection. In this paper, we present a criterion to determine the wave vector range for the image method of heterodyne near-field light scattering, where the hologram of the particles is analyzed to extract the particle dynamics. A normalized instrument factor ratio 𝓇(q) is defined, and the accuracy of results can be guaranteed when the upper limit q_up is selected at the maximum of 𝓇(q_up)=1, and the lower limit q_low is selected according to the optimal goodness of fit R². The experimental results verify the effectiveness of the proposed criterion. Since most image methods for nanoparticle characterizing are related to the wave vector range selection, it is believed that the idea of this criterion can be extended generally.

European Space Agency experiments on thermodiffusion of fluid mixtures in space

This paper describes the European Space Agency (ESA) experiments devoted to study thermodiffusion of fluid mixtures in microgravity environment, where sedimentation and convection do not affect the mass flow induced by the Soret effect. First, the experiments performed on binary mixtures in the IVIDIL and GRADFLEX experiments are described. Then, further experiments on ternary mixtures and complex fluids performed in DCMIX and planned to be performed in the context of the NEUF-DIX project are presented. Finally, multi-component mixtures studied in the SCCO project are detailed.

Propagating modes in a binary liquid mixture under thermal stress

Nonequilibrium temperature and concentration fluctuations inside a binary liquid mixture under the action of a temperature gradient relax back to equilibrium either due to conduction and diffusion at large wave numbers, or due to the quenching determined by gravity at small wave numbers. We investigate the dynamics of nonequilibrium fluctuations in a binary liquid mixture of polystyrene and toluene heated from above under stationary conditions in a thermodiffusion experiment. We show that the strong gravitational stabilization at small wave numbers determines the appearance of propagating modes of nonequilibrium fluctuations as detected through the structure function of shadowgraph images. The propagating modes are the combined effect of temperature and velocity nonequilibrium fluctuations induced by the buoyancy force. The experimental results are in good agreement with a fluctuating hydrodynamics theroretical model including the coupling of fluctuations of velocity, temperature and concentration.

Dynamic scaling for the growth of non-equilibrium fluctuations during thermophoretic diffusion in microgravity

Diffusion processes are widespread in biological and chemical systems, where they play a fundamental role in the exchange of substances at the cellular level and in determining the rate of chemical reactions. Recently, the classical picture that portrays diffusion as random uncorrelated motion of molecules has been revised, when it was shown that giant non-equilibrium fluctuations develop during diffusion processes. Under microgravity conditions and at steady-state, non-equilibrium fluctuations exhibit scale invariance and their size is only limited by the boundaries of the system. In this work, we investigate the onset of non-equilibrium concentration fluctuations induced by thermophoretic diffusion in microgravity, a regime not accessible to analytical calculations but of great relevance for the understanding of several natural and technological processes. A combination of state of the art simulations and experiments allows us to attain a fully quantitative description of the development of fluctuations during transient diffusion in microgravity. Both experiments and simulations show that during the onset the fluctuations exhibit scale invariance at large wave vectors. In a broader range of wave vectors simulations predict a spinodal-like growth of fluctuations, where the amplitude and length-scale of the dominant mode are determined by the thickness of the diffuse layer.

Non-equilibrium concentration fluctuations in binary liquids with realistic boundary conditions

Because of the spatially long-ranged nature of spontaneous fluctuations in thermal non-equilibrium systems, they are affected by boundary conditions for the fluctuating hydrodynamic variables. In this paper we consider a liquid mixture between two rigid and impervious plates with a stationary concentration gradient resulting from a temperature gradient through the Soret effect. For liquid mixtures with large Lewis and Schmidt numbers, we are able to obtain explicit analytical expressions for the intensity of the non-equilibrium concentration fluctuations as a function of the frequency ω and the wave number q of the fluctuations. In addition we elucidate the spatial dependence of the intensity of the non-equilibrium fluctuations responsible for a non-equilibrium Casimir effect.

Static versus dynamic analysis of the influence of gravity on concentration non-equilibrium fluctuations

In a binary fluid mixture subject to gravity and a stabilizing concentration gradient, concentration non-equilibrium fluctuations are long-ranged. While the gradient leads to an enhancement of the respective equilibrium fluctuations, the effect of gravity is a damping of fluctuations larger than a "characteristic" size. This damping is visible both in the fluctuation power spectrum probed by static and the temporal correlation function probed by dynamic light scattering. One aspect of the "characteristic" size can be appreciated by the dynamic analysis; in fact at the corresponding "characteristic" wave vector q* one can observe a maximum of the fluctuation time constant indicating the more persistent fluctuation of the system. Also in the static analysis a "characteristic" size can be extracted from the crossover wave vector. According to common theoretical concepts, the result should be the same in both cases. In the present work we provide evidence for a systematic difference in the experimentally observed "characteristic" size as obtained by static and dynamic measurements. Our observation thus points out the need for a more refined theory of non-equilibrium concentration fluctuations.

Gradient-driven fluctuations in microgravity

Equilibrium fluctuations of thermodynamic variables, such as density or concentration, are known to be small and typically occur at a molecular length scale. In contrast, theory predicts that non-equilibrium fluctuations grow very large both in amplitude and spatial size. On earth, the presence of gravity and buoyancy forces severely limits the development of the fluctuations. We will present the results of a 14-year long international collaboration on an experiment on non-equilibrium fluctuations in a single liquid and in a polymer solution under microgravity conditions. Non-equilibrium conditions are generated by applying a temperature gradient across millimetre-size liquid slabs. Phase modulations introduced by fluctuations are measured using a quantitative shadowgraph method, with the optical axis parallel to the temperature gradient. Thousands of images are analysed and their two-dimensional power spectra yield the fluctuation structure function S(q), once data are reduced accounting for the instrumental transfer function T(q). The mean-squared amplitude of the fluctuations exhibits an impressive power-law dependence at larger q and a crossover at low q showing that the fluctuation size is limited by the sample thickness. The shape of the structure function, its increase due to removing gravity, and its dependence on applied gradient are in reasonable agreement with available theoretical predictions.

Fractal fronts of diffusion in microgravity

Spatial scale invariance represents a remarkable feature of natural phenomena. A ubiquitous example is represented by miscible liquid phases undergoing diffusion. Theory and simulations predict that in the absence of gravity diffusion is characterized by long-ranged algebraic correlations. Experimental evidence of scale invariance generated by diffusion has been limited, because on Earth the development of long-range correlations is suppressed by gravity. Here we report experimental results obtained in microgravity during the flight of the FOTON M3 satellite. We find that during a diffusion process a dilute polymer solution exhibits scale-invariant concentration fluctuations with sizes ranging up to millimetres, and relaxation times as large as 1,000 s. The scale invariance is limited only by the finite size of the sample, in agreement with recent theoretical predictions. The presence of such fluctuations could possibly impact the growth of materials in microgravity.

Theory and simulations predict scale-invariant concentration fluctuations during diffusion in liquids, but on Earth, large-scale fluctuations are damped by gravity. Microgravity experiments by Vailati et al. reveal the scale-invariant nature of diffusion, associated with fractal fronts and long-ranged correlations.

Characterization of voltage-gated K+ currents contributing to subthreshold membrane potential oscillations in hippocampal CA1 interneurons

CA1 inhibitory interneurons at the stratum lacunosum-moleculare and radiatum junction (LM/RAD-INs) display subthreshold membrane potential oscillations (MPOs) involving voltage-dependent Na(+) and A-type K(+) currents. LM/RAD-INs also express other voltage-gated K(+) currents, although their properties and role in MPOs remain unclear. Here, we characterized these voltage-gated K(+) currents and investigated their role in MPOs. Using outside-out patch recordings from LM/RAD-IN somata, we distinguished four voltage-gated K(+) currents based on their pharmacology and activation/inactivation properties: a fast delayed rectifier current (I(Kfast)), a slow delayed rectifier current (I(Kslow)), a rapidly inactivating A-type current (I(A)), and a slowly inactivating current (I(D)). Their relative contribution to the total K(+) current was I(A) > I(Kfast) > I(Kslow) = I(D). The presence of I(D) and the relative contributions of K(+) currents in LM/RAD-INs are different from those of other CA1 interneurons, suggesting the presence of differential complement of K(+) currents in subgroups of interneurons. We next determined whether these K(+) currents were sufficient for MPO generation using a single-compartment model of LM/RAD-INs. The model captured the subthreshold voltage dependence of MPOs. Moreover, all K(+) currents were active at subthreshold potentials but I(D), I(A), and the persistent sodium current (I(NaP)) were most active near threshold. Using impedance analysis, we found that I(A) and I(NaP) contribute to MPO generation by modulating peak spectral frequency during MPOs and governing the voltage range over which MPOs occur. Our findings uncover a differential expression of a complement of K(+) channels that underlies intrinsic rhythmic activity in inhibitory interneurons.

Scattering information obtained by optical microscopy: differential dynamic microscopy and beyond

We describe the use of a bright-field microscope for dynamic light scattering experiments on weakly scattering samples. The method is based on collecting a time sequence of microscope images and analyzing them in the Fourier space to extract the characteristic time constants as a function of the scattering wave vector. We derive a theoretical model for microscope imaging that accounts for (a) the three-dimensional nature of the sample, (b) the arbitrary coherence properties of the light source, and (c) the effect of the finite numerical aperture of the microscope objective. The model is tested successfully against experiments performed on a colloidal dispersion of small spheres in water, by means of the recently introduced differential dynamic microscopy technique [R. Cerbino and V. Trappe, Phys. Rev. Lett. 100, 188102 (2008)]. Finally, we extend our model to the class of microscopy techniques that can be described by a linear space-invariant imaging of the density of the scattering centers, which includes, for example, dynamic fluorescence microscopy.

Nanoparticle characterization by using tilted laser microscopy: back scattering measurement in near field

By using scattering in near field techniques, a microscope can be easily turned into a device measuring static and dynamic light scattering, very useful for the characterization of nanoparticle dispersions. Up to now, microscopy based techniques have been limited to forward scattering, up to a maximum of 30 degrees . In this paper we present a novel optical scheme that overcomes this limitation, extending the detection range to angles larger than 90 degrees (back-scattering). Our optical scheme is based on a microscope, a wide numerical aperture objective, and a laser illumination, with the collimated beam positioned at a large angle with respect to the optical axis of the objective (Tilted Laser Microscopy, TLM). We present here an extension of the theory of near field scattering, which usually applies only to paraxial scattering, to our strongly out-of-axis situation. We tested our instrument and our calculations with calibrated spherical nanoparticles of several different diameters, performing static and dynamic scattering measurements up to 110 degrees . The measured static spectra and decay times are compatible with the Mie theory and the diffusion coefficients provided by the Stokes-Einstein equation. The ability of performing backscattering measurements with this modified microscope opens the way to new applications of scattering in near field techniques to the measurement of systems with strongly angle dependent scattering.

Scaling of the spatial power spectrum of excitations at the onset of solutal convection in a nanofluid far from equilibrium

We investigate pattern formation in the very early stages of solutal convective instabilities in a suspension of highly thermophilic nanoparticles heated from above. The processing of shadowgraph images allows us to recover the spatial power spectrum of the excitations at the onset. Remarkably, the power spectra obtained at large solutal Rayleigh numbers 2.56 x 10;{6}< or =Ra_{s}< or =4.53 x 10;{8} scale onto a single curve without adjustable parameters. The critical wave number exhibits power-law scaling with exponent 1/4 as a function of Ra_{s} , in excellent agreement with recent theoretical predictions.

Nonequilibrium velocity fluctuations and energy amplification in planar Couette flow

In this paper we investigate intrinsic thermally excited nonequilibrium velocity fluctuations in laminar planar Couette flow. For this purpose we have complemented the solution of the stochastic Orr-Sommerfeld equation for the intensity of the fluctuations of the wall-normal velocity, presented in a previous publication, with a solution of the stochastic Squire equation for the intensity of the fluctuations of the wall-normal vorticity. We have obtained exact solutions of these equations without boundary conditions and solutions in a Galerkin approximation when appropriate boundary conditions are included. These results enable us to make a quantitative assessment of the intensity of these nonequilibrium fluctuations, as well as of the related energy amplification, which are always present, even in the absence of any externally imposed noise.

Characterization of anisotropic nano-particles by using depolarized dynamic light scattering in the near field

Light scattering techniques are widely used in many fields of condensed and soft matter physics. Usually these methods are based on the study of the scattered light in the far field. Recently, a new family of near field detection schemes has been developed, mainly for the study of small angle light scattering. These techniques are based on the detection of the light intensity near to the sample, where light scattered at different directions overlaps but can be distinguished by Fourier transform analysis. Here we report for the first time data obtained with a dynamic near field scattering instrument, measuring both polarized and depolarized scattered light. Advantages of this procedure over the traditional far field detection include the immunity to stray light problems and the possibility to obtain a large number of statistical samples for many different wave vectors in a single instantaneous measurement. By using the proposed technique we have measured the translational and rotational diffusion coefficients of rod-like colloidal particles. The obtained data are in very good agreement with the data acquired with a traditional light scattering apparatus.

Nano-particle characterization by using Exposure Time Dependent Spectrum and scattering in the near field methods: how to get fast dynamics with low-speed CCD camera

Light scattering detection in the near field, a rapidly expanding family of scattering techniques, has recently proved to be an appropriate procedure for performing dynamic measurements. Here we report an algorithm, first suggested by Oh et al. (Phys. Rev. E 69, 21106 (2004)), based on the evaluation of the exposure time dependent spectrum (ETDS), which makes it possible to measure the fast dynamics of a colloidal suspension with the aid of a simple near field scattering apparatus and a CCD camera. The algorithm consists in acquiring static spectra in the near field at different exposure times, so that the measured decay times are limited only by the exposure time of the camera and not by its frame rate. The experimental set-up is based on a modified microscope, where the light scattered in the near field is collected by a commercial objective, but (unlike in standard microscopes) the light source is a He-Ne laser which increases the instrument sensitivity. The apparatus and the algorithm have been validated by considering model systems of standard spherical nano-particle.

Dynamics of long-wavelength fluctuations in a fluid layer heated from above

We report an experimental study of the dynamics of thermal fluctuations in a 4.86 mm thick layer of CS2 heated from above. Stabilizing gradients ranged from 10.3 to 61.7 K/cm. Power spectral measurements were made over the wave vector range 9 cm(-1)<q<100 cm(-1), using a shadowgraph apparatus. Over this range, the spectra change from having a well-resolved oscillatory mode at low q to monotonic decay at higher q. For the smallest gradient, the results for the power spectra compare very well with theory, but slight deviations are seen for larger gradients.

Universality in early-stage growth of phase-separating domains near the critical point

We present both the experimental and computational methods and results of phase-separating experiments performed with sulfur hexafluoride (SF6) close to its critical density. These experiments were performed in microgravity to suppress buoyancy and convection-driven effects. Phase separation under reduced gravity is analyzed for both 0.3 mK and 3.6 mK temperature quenches in order to derive the early-stage growth law. We found a 1/3 growth law for early stages of phase separation for a volume fraction of minority domains of 50%. Our findings support the hypothesis of a crossover between Brownian motion and hydrodynamic effects in the early stages of phase separation. The temperature inside the bulk of the pure fluid was estimated using a proposed histogram method. Our histogram method allowed temperature estimation below thermistors' sensitivity and detected small temperature variations inside the bulk of the pure fluid.

Nondiffusive decay of gradient-driven fluctuations in a free-diffusion process

We report the results of an experimental study of the static and dynamic properties of long wavelength concentration fluctuations in a mixture of glycerol and water undergoing free diffusion. The shadowgraph method was used to measure both the mean-squared amplitude and the temporal correlation function of the fluctuations for wave vectors so small as to be inaccessible to dynamic light scattering. For a fluid with a stabilizing vertical concentration gradient, the fluctuations are predicted to have a decay rate that increases with decreasing wave vector q , for wave vectors below a cutoff wave vector qC, determined by gravity and the fluid properties. This behavior is caused by buoyant forces acting on the fluctuations. We find that for wave vectors above approximately qC, the decay rate does vary in the normal diffusive manner as Dq2, where D is the mass diffusion coefficient. Furthermore, for q approximately less than qC we find that longer wavelength fluctuations decay more rapidly than do shorter wavelength fluctuations, i.e., the behavior is nondiffusive, as predicted.

Dynamics of fluctuations below a stationary bifurcation to electroconvection in the planar nematic liquid crystal N4

We fitted C(k,tau,epsilon) proportional to exp([-sigma(k,epsilon)tau] to time-correlation functions C(k,tau,epsilon) of structure factors S(k,t,epsilon) of shadowgraph images of fluctuations below a supercritical bifurcation at V(0)=V(c) to electroconvection of a planar nematic liquid crystal in the presence of a voltage V=sqrt[2]V(0)cos((2pift) [k=(p,q) is the wave vector and epsilon identical with V(2)(0)/V(2)(c)-1]. There were stationary oblique (normal) rolls at small (large) f. Fits of a modified Swift-Hohenberg form to sigma(k,epsilon) gave f-dependent critical behavior for the minimum decay rates sigma(0)(epsilon) and the correlation lengths xi(p,q)(epsilon).

Nonequilibrium fluctuations in the Rayleigh-Benard problem for binary fluid mixtures

We have employed a simple Galerkin-approximation scheme to calculate nonequilibrium temperature and concentration fluctuations in a binary fluid subjected to a temperature gradient with realistic boundary conditions. When a fluid mixture is driven outside thermal equilibrium, there are two instability mechanisms, namely a Rayleigh (stationary) and a Hopf (oscillatory) instability, causing long-ranged fluctuations. The competition of these two mechanisms causes the structure factor associated with the temperature fluctuations to exhibit two maxima as a function of the wave number q of the fluctuations, in particular, close to the convective instability. In the presence of thermally conducting but impermeable walls the intensity of the temperature fluctuations vanishes as q goes to zero, while the intensity of the concentration fluctuations remains finite in the limit of vanishing q. Finally, we propose a simpler small-Lewis-number approximation scheme, which is useful to represent nonequilibrium concentration fluctuations for mixtures with positive separation ratio, even close to (but below) the convective instability.