Mass transport properties of the tetrahydronaphthalene/n-dodecane mixture measured by investigating non-equilibrium fluctuations

Abstract

We present preliminary near-field light scattering (NFS) data concerning the analysis of the static power spectrum and of the relaxation time constant as a function of the wave vector for non-equilibrium fluctuations (NEFs). The goal of these measurements is to obtain information about the Soret and the mass diffusion coefficients of a binary mixture undergoing thermodiffusion. In particular, we show how the interaction between NEFs and the gravity force gives rise to a critical wavelength that provides additional information about the Soret coefficient. We suggest that a quantitative analysis can be performed by means of this non-invasive optical technique. In our setup, the sample is monitored parallel to the imposed temperature gradient, thus being insensitive to the refractive index profile along the vertical axis, while at the same time we are able to detect the light scattered by the refractive index fluctuations in horizontal planes. We select a shadowgraph layout for the NFS setup due to the extremely small wave vectors we aim to analyze. From a double-frame differential analysis of the acquired images, we obtain both the static power spectrum and the dynamics of NEFs. As a proof-of-principle experiment, we present Soret and diffusion coefficient data on a liquid mixture of tetrahydronaphthalene/n-dodecane.

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

“…While theoretical predictions have generally been confirmed and the impact of gravity has been studied experimentally both on the statics [11,12] and on the dynamics [7,8,13,14] of NEFs, in this paper we point out a small but systematic difference between the "characteristic" wave vector q * as obtained from the two different experimental approaches. The latter points out the need for a more refined theory of concentration NEFs.…”

“…In this work we expand on two experiments published recently [7,8,13,14]: Soret-driven experiments, where a temperature gradient is applied to an initially homogeneous binary mixture to get a concentration gradient by means of the Soret effect, and free-diffusion experiments where an isothermal liquid is put on top to a denser one at the same temperature and the system is let evolve by mass diffusion only towards the equilibrium homogeneous state.…”

“…The two sapphires are then in contact with two Peltier elements and two thermistors that are connected to a controller able to maintain two distinct temperatures of the external sides of the sapphires with a rms stability of about 2 mk over a day. More details about the experimental setup can be found in [7,8].…”

“…The acquired images are then analyzed by means of the Differential Dynamic Algorithm [7,8,13,14,27,28] allowing the extraction of the structure function of the fluctuations. This procedure has been described in detail in previous papers, we just mention here that due to the massive use of Fourier transforms in this analysis it is worth performing it by using parallel computing on a graphics processing unit (GPU) [28].…”

“…These quantities are directly accessible by means of static and dynamic light scattering and much experimental effort has been devoted over the last decades to the verification and testing of the available theoretical models [1]. More recently this analysis has also been employed to measure the transport properties of binary liquid mixtures like Soret and mass diffusion coefficients [7,8]. Moreover two remarkable experiments on non-equilibrium fluctuations Contribution to the Topical Issue "Thermal nonequilibrium phenomena in multi-component fluids" edited by Fabrizio Croccolo and Henri Bataller.…”