Quantitative Fourier analysis of schlieren masks: the transition from shadowgraph to schlieren

Modeling and correction of image drift in dynamic shadowgraphy experiments

The study of phoretic transport phenomena under non-stationary conditions presents several challenges, mostly related to the stability of the experimental apparatus. This is particularly true when investigating with optical means the subtle temperature and concentration fluctuations that arise during diffusion processes, superimposed to the macroscopic state of the system. Under these conditions, the tenuous signal from fluctuations is easily altered by the presence of artifacts. Here, we address an experimental issue frequently reported in the investigation by means of dynamic shadowgraphy of the non-equilibrium fluctuations arising in liquid mixtures under non-stationary conditions, such as those arising after the imposition or removal of a thermal stress, where experiments show systematically the presence of a spurious contribution in the reconstructed structure function of the fluctuations, which depends quadratically from the time delay. We clarify the mechanisms responsible for this artifact, showing that it is caused by the imperfect alignment of the sample cell with respect to gravity, which couples the temporal evolution of the concentration profile within the sample with the optical signal collected by the shadowgraph diagnostics. We propose a data analysis protocol that enables disentangling the spurious contributions and the genuine dynamics of the fluctuations, which can be thus reliably reconstructed.

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.

Stabilized convection in a ternary mixture with two Soret coefficients of opposite sign

We performed ground-based experiments on the sample polystyrene-toluene-cyclohexane in order to complement the experimental activities in microgravity conditions related to the ESA projects DCMIX4 and Giant Fluctuations. After applying a stabilizing thermal gradient by heating from above a layer of the fluid mixture, we studied over many hours the density variations in the bidimensional horizontal field by means of a Shadowgraph optical setup. The resulting images evidence the appearance of convective instability after a diffusive time associated with the binary molecular solvent consisting of toluene and cyclohexane, confirming the negative sign of the Soret coefficient of this mixture. After a larger diffusive time related to mass diffusion of the polystyrene in the binary solvent, convection was suppressed by the increasing stabilizing density gradient originated by the Soret-induced concentration gradient of the polymer. This is compatible with a positive sign of the Soret coefficient of the polymer in the binary solvent.

Mass diffusion and Soret coefficient measurements of triethylene glycol/water binary mixtures by dynamic shadowgraphy

The investigation of the transport properties of binary fluid mixtures remains a topic of interest in relation to the more challenging studies of ternary mixtures. In fact, the study of the phase boundary limits of the Gibbs composition triangle can be the initial step for a more complete analysis of ternary mixtures. In this paper, we apply the dynamic shadowgraphy optical technique to study non-equilibrium fluctuations induced by the presence of a gradient of temperature and/or concentration in the triethylene glycol (TEG)/water system. These thermodiffusion and free-diffusion experiments aim at measuring the transport properties of samples of the studied system at different experimental conditions. We scan both the average temperature and the TEG concentration, which allows us investigating both positive and negative thermodiffusive behaviours. The obtained values of mass diffusion coefficient are consistent with data available in the literature in the range of temperature investigated in this study. The mass diffusion coefficient of the sample prepared at 0.7 w/w TEG concentration are characterised by shadowgraphy following the two proposed methods, exhibiting consistent results. An increase of the mass diffusion coefficient as a function of the average temperature is highlighted. On the other hand, the thermodiffusion coefficient appears to be independent of the average temperature of the sample at 0.3 w/w TEG concentration.

The modern structurator: increased performance for calculating the structure function

The autocorrelation function is a statistical tool that is often combined with dynamic light scattering (DLS) techniques to investigate the dynamical behavior of the scattered light fluctuations in order to measure, for example, the diffusive behavior of transparent particles dispersed in a fluid. An alternative approach to the autocorrelation function for the analysis of DLS data has been proposed decades ago and consists of calculating the autocorrelation function starting from difference of the signal at different times by using the so-called structure function. The structure function approach has been proven to be more robust than the autocorrelation function method in terms of noise and drift rejection. Therefore, the structure function analysis has gained visibility, in particular in combination with imaging techniques such as dynamic shadowgraphy and differential dynamic microscopy. Here, we show how the calculation of the structure function over thousands of images, typical of such techniques, can be accelerated, with the aim of achieving real-time analysis. The acceleration is realized by taking advantage of the Wiener-Khinchin theorem, i.e., by calculating the difference of images through Fourier transform in time. The new algorithm was tested both on CPU and GPU hardware, showing that the acceleration is particularly large in the case of CPU.

Coupled non-equilibrium fluctuations in a polymeric ternary mixture

We investigate by dynamic shadowgraphy the non-equilibrium fluctuations at the steady state of a thermodiffusion experiment in a polymeric ternary mixture of polystyrene-toluene-n-hexane. The structure function of the refractive index reveals the existence of quite different decay times, thus requiring the analysis of a wide range of correlation times. This is related to the simultaneous presence of three distinct decay modes corresponding to (from fastest to slowest) the relaxation of temperature fluctuations, of the concentration fluctuations of the mixed solvent, and of the concentration fluctuations of the polymer in the binary solvent. An investigation of the decay times at the corresponding diffusive regimes provides a measurement of the thermal diffusivity and the two eigenvalues of the mass diffusion matrix of the ternary mixture. Similar experiments were performed in the past but here, to suppress the confinement effect and obtain a more direct comparison with the theory, a thicker sample is studied. Moreover, also a faster camera is used allowing the experimental observation of faster modes, like the propagative ones. The experimental values of the decay times are eventually compared with those predicted by different available theories. Finally, we present a more complete theoretical model to describe the non-equilibrium fluctuations in the bulk of a ternary mixture at the steady state of a thermodiffusion experiment.

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.

Asymmetric time-cross-correlation of nonequilibrium concentration fluctuations in a ternary liquid mixture

Equilibrium phenomena are characterized by time symmetry. Thermodynamic fluctuations are also time-symmetric at equilibrium. Conversely, diffusion of a solute in a liquid in the presence of a gradient is a nonequilibrium phenomenon, which gives rise to long-range fluctuations with amplitude much larger than the equilibrium one for small enough wave number. In the case of diffusion in binary mixtures such fluctuations are time-symmetric, notwithstanding the fact that they are generated by a nonequilibrium condition. In this paper, we investigate diffusion of two solutes in a ternary liquid mixture by means of fluctuating hydrodynamics theory. We show that the time-cross-correlation function of the concentrations is not time-symmetric, hence showing that time symmetry is violated for such nonequilibrium fluctuations. We discuss the feasibility of experiments aimed at the detection of the asymmetry of the cross-correlation function of nonequilibrium concentration fluctuations in ternary mixtures, as envisaged in the Giant Fluctuations (NEUF-DIX) microgravity project of the European Space Agency.

Kinetics of growth of non-equilibrium fluctuations during thermodiffusion in a polymer solution

A thermal diffusion process occurring in a binary liquid mixture is accompanied by long ranged non-equilibrium concentration fluctuations. The amplitude of these fluctuations at large length scales can be orders of magnitude larger than that of equilibrium ones. So far non-equilibrium fluctuations have been mainly investigated under stationary or quasi-stationary conditions, a situation that allows to achieve a detailed statistical characterization of their static and dynamic properties. In this work we investigate the kinetics of growth of non-equilibrium concentration fluctuations during a transient thermodiffusion process, starting from a configuration where the concentration of the sample is uniform. The use of a large molecular weight polymer solution allows to attain a slow dynamics of growth of the macroscopic concentration profile. We focus on the development of fluctuations at small wave vectors, where their amplitude is strongly limited by the presence of gravity. We show that the growth rate of non-equilibrium fluctuations follows a power law [Formula: see text] as a function of time, without any typical time scale and independently of the wave vector. We formulate a phenomenological model that allows to relate the rate of growth of non-equilibrium fluctuations to the growth of the macroscopic concentration profile in the absence of arbitrary parameters.

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 analysis of the light scattered by the non-equilibrium fluctuations of a ternary mixture of polystyrene-toluene-n-hexane

Dynamic analysis of the light scattered by non-equilibrium fluctuations in a thermodiffusion experiment has been performed on a sample of polystyrene-toluene-n -hexane, at 0.9-49.55-49.55% mass fraction. Time decays of the non-equilibrium fluctuations have been obtained revealing the accurate detectability of three modes. The slowest mode has been attributed to the mass diffusion of the polymer into the binary solvent; the intermediate one to mass diffusion of the two molecular components of the solvent; finally, the fastest one has been attributed to the thermal diffusivity of the overall mixture. The two eigenvalues of the mass diffusion matrix have been evaluated with accuracy in the order of 1%. Neglecting cross-diffusion effects we obtain a simplified expression for the relative amplitude of the two mass diffusion modes, allowing a parameterized determination of polystyrene and toluene Soret coefficients in the ternary mixture. We suggest that a two wavelength shadowgraph experiment is needed for a complete determination of all the coefficients.

Soret coefficient of the n-dodecane-n-hexane binary mixture under high pressure

In the present work, the Soret coefficient has been determined at high pressure for a binary hydrocarbon mixture by combining the thermogravitational column and the dynamic near-field imaging techniques. The analyzed mixture is an iso-massic n -dodecane-n -hexane mixture at 298.15K. The molecular diffusion coefficient has been measured up to 20MPa by means of the dynamic analysis of the light scattered by non-equilibrium concentration fluctuations. With a cylindrical thermogravitational column the thermodiffusion coefficient was determined from 0.1MPa to 10MPa. Density, as well as, mass expansion and thermal expansion have been measured with a high pressure densimeter. Dynamic viscosity at up to 20MPa has been determined with a high pressure viscometer. This work shows the decreasing tendency of both the molecular diffusion and the thermodiffusion coefficient with increasing pressure.

Non-equilibrium concentration fluctuations in superparamagnetic nanocolloids

We investigate non-equilibrium concentration fluctuations during the free diffusion of a colloidal suspension against pure water. We investigate Fe₂O₃ superparamagnetic nanocolloids with sizes between 1 and 10 nm by means of a shadowgraph apparatus to determine the mixture mass diffusion coefficient and kinematic viscosity. The experiments were performed in three distinct conditions: Experiment 1 is without any magnetic field; Experiment 2 with a vertical magnetic field; Experiment 3 after turning off the magnetic field. We found no correlation between the kinematic viscosity coefficient and the external magnetic field. Conversely, we found that the mass diffusion coefficient decreases in the presence of the external magnetic field and slowly rebounds after the magnetic field was turned off.

Confinement effect on the dynamics of non-equilibrium concentration fluctuations far from the onset of convection

In a recent letter (C. Giraudet et al., EPL 111, 60013 (2015)) we reported preliminary data showing evidence of a slowing-down of non-equilibrium fluctuations of the concentration in thermodiffusion experiments on a binary mixture of miscible fluids. The reason for this slowing-down was attributed to the effect of confinement. Such tentative explanation is here experimentally corroborated by new measurements and theoretically substantiated by studying analytically and numerically the relevant fluctuating hydrodynamics equations. In the new experiments presented here, the magnitude of the temperature gradient is changed, confirming that the system is controlled solely by the solutal Rayleigh number, and that the slowing-down is dominated by a combined effect of the driving force of buoyancy, the dissipating force of diffusion and the confinement provided by the vertical extension of the sample cell. Moreover, a compact phenomenological interpolating formula is proposed for easy analysis of experimental results.

Microgravity in a thin film: How confinement kills gravity

Fluctuations in the presence of concentration gradients are long-ranged and decay diffusively for small spatial scales. At larger scales fluctuations are influenced by gravity and confinement. The confinement in the direction of the concentration gradient couples to gravity generating a slowing down that ends up in a diffusion-like behavior of fluctuations of size comparable to the vertical extension of the sample. The resulting enhanced diffusion coefficient depends on the solutal Rayleigh number of the system. For small (in modulus) values of the solutal Rayleigh number the apparent diffusion coefficient tends towards the normal one and a simple diffusive behavior is obtained. This is quite similar to what happens in microgravity conditions when the solutal Rayleigh number is drastically reduced because of the reduction of g by about 6 orders of magnitude. Experiments are shown for positive and negative solutal Rayleigh numbers smaller (in modulus) than 1000. The effect of the confinement on the statics is also investigated. Comparison with microgravity data obtained through the GRADFLEX project is performed.

The NEUF-DIX space project - Non-EquilibriUm Fluctuations during DIffusion in compleX liquids

Diffusion and thermal diffusion processes in a liquid mixture are accompanied by long-range non-equilibrium fluctuations, whose amplitude is orders of magnitude larger than that of equilibrium fluctuations. The mean-square amplitude of the non-equilibrium fluctuations presents a scale-free power law behavior q^-4 as a function of the wave vector q, but the divergence of the amplitude of the fluctuations at small wave vectors is prevented by the presence of gravity. In microgravity conditions the non-equilibrium fluctuations are fully developed and span all the available length scales up to the macroscopic size of the systems in the direction parallel to the applied gradient. Available theoretical models are based on linearized hydrodynamics and provide an adequate description of the statics and dynamics of the fluctuations in the presence of small temperature/concentration gradients and under stationary or quasi-stationary conditions. We describe a project aimed at the investigation of Non-EquilibriUm Fluctuations during DIffusion in compleX liquids (NEUF-DIX). The focus of the project is on the investigation in micro-gravity conditions of the non-equilibrium fluctuations in complex liquids, trying to tackle several challenging problems that emerged during the latest years, such as the theoretical predictions of Casimir-like forces induced by non-equilibrium fluctuations; the understanding of the non-equilibrium fluctuations in multi-component mixtures including a polymer, both in relation to the transport coefficients and to their behavior close to a glass transition; the understanding of the non-equilibrium fluctuations in concentrated colloidal suspensions, a problem closely related with the detection of Casimir forces; and the investigation of the development of fluctuations during transient diffusion. We envision to parallel these experiments with state-of-the-art multi-scale simulations.

Quantitative measurement of acoustic pressure in the focal zone of acoustic lens-line focusing using the Schlieren method

This paper proposes a theory and method for quantitative measurement of the acoustic lens-line focusing ultrasonic (ALLFU) field in its focal spot size and acoustic pressure using the Schlieren imaging technique. Using Fourier transformation, the relationship between the brightness of the Schlieren image and the acoustic pressure was introduced. The ALLFU field was simulated using finite element method and compared with the Schlieren acoustic field image. The measurement of the focal spot size was performed using the Schlieren method. The acoustic pressure in the focal zone of the ALLFU field and the transducer-transmitting voltage response were quantitatively determined by measuring the diffraction light fringe intensity. The results show that the brightness of the Schlieren image is a linear function of the acoustic intensity when the acousto-optic interaction length remains constant and the acoustic field is weak.

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.

High-pressure mass transport properties measured by dynamic near-field scattering of non-equilibrium fluctuations

High-pressure mass diffusion and Soret coefficients of the equimassic 1,2,3,4-tetrahydronaphthalene and n-dodecane binary mixture are obtained from dynamic light scattering analysis of concentration non-equilibrium fluctuations at the steady state of Soret-driven separation. A high-pressure shadowgraph set-up has been developed to investigate thermodiffusion in free medium from atmospheric pressure up to 20 MPa. Results at atmospheric pressure show excellent agreement with benchmark values. High-pressure results for the mass diffusion coefficient confirm theoretical predictions by Leffler-Cullinan relation. Further calculation of the thermodiffusion coefficient allows also comparison with previous experimental results with, again, very good agreement.

Inclined layer convection in a colloidal suspension with negative Soret coefficient at large solutal Rayleigh numbers

Convection in an inclined layer of fluid is affected by the presence of a component of the acceleration of gravity perpendicular to the density gradient that drives the convective motion. In this work we investigate the solutal convection of a colloidal suspension characterized by a negative Soret coefficient. Convection is induced by heating the suspension from above, and at large solutal Rayleigh numbers (of the order of 10(7)-10(8)) convective spoke patterns form. We show that in the presence of a marginal inclination of the cell as small as 19 mrad the isotropy of the spoke pattern is broken and the convective patterns tend to align in the direction of the inclination. At intermediate inclinations of the order of 33 mrad ordered square patterns are obtained, while at inclination of the order of 67 mrad the strong shear flow determined by the inclination gives rise to ascending and descending sheets of fluid aligned parallel to the direction of inclination.

Effect of a marginal inclination on pattern formation in a binary liquid mixture under thermal stress

Convective motions in a fluid layer are affected by its orientation with respect to the gravitational field. We investigate the long-term stability of a thermally stressed layer of a binary liquid mixture and show that pattern formation is strongly affected by marginal inclinations as small as a few milliradians. At small Rayleigh numbers, the mass transfer is dominated by the induced large scale shear flow, while at larger Rayleigh numbers, it is dominated by solutal convection. At the transition, the balance between the solutal and shear flows gives rise to drifting columnar flows moving in opposite directions along parallel lanes in a superhighway configuration.

A light scattering study of non equilibrium fluctuations in liquid mixtures to measure the Soret and mass diffusion coefficient

We use dynamic near field scattering to measure the dynamics of concentration non equilibrium fluctuations at the steady-state of Soret separation. The analysis reveals that above a threshold wave vector q(c), the dynamics is governed by diffusion while at smaller wave vectors, gravity dominates. From the measurements, we extract both the mass diffusion and the Soret coefficients. Comparing our results with literature data, we find good agreement confirming that the proposed experimental technique can be considered a sound approach for the study of thermodiffusion processes.

Note: Quasi-real-time analysis of dynamic near field scattering data using a graphics processing unit

We present an implementation of the analysis of dynamic near field scattering (NFS) data using a graphics processing unit. We introduce an optimized data management scheme thereby limiting the number of operations required. Overall, we reduce the processing time from hours to minutes, for typical experimental conditions. Previously the limiting step in such experiments, the processing time is now comparable to the data acquisition time. Our approach is applicable to various dynamic NFS methods, including shadowgraph, Schlieren and differential dynamic microscopy.