Effect of Gravity on the Dynamics of Nonequilibrium Fluctuations in a Free‐Diffusion Experiment

Abstract

Diffusion is commonly believed to be a homogeneous process at the mesoscopic scale, being driven only by the random walk of fluid molecules. On the contrary, very large amplitude, long wavelength fluctuations always accompany diffusive processes. In the presence of gravity, fluctuations in a fluid containing a stabilizing gradient are affected by two different processes: diffusion, which relaxes them, and the buoyancy force, which quenches them. These phenomena affect both the overall amplitude of fluctuations and their time dependence. For the case of free diffusion, the time-correlation function of the concentration fluctuations is predicted to exhibit an exponential decay with correlation time depending on the wave vector q. For large wave vector fluctuations, diffusion dominates, and the correlation time is predicted to be 1 / (Dq2). For small wave vector fluctuations, gravitational forces have time to play a significant role, and the correlation time is predicted to be proportional to q2. The effects of gravity and diffusion are comparable for a critical wave vector q(c) determined by fluid properties and gravity. We have utilized a quantitative dynamic shadowgraph technique to obtain the temporal correlation function of a mixture of LUDOX(R) TMA and water undergoing free diffusion. This technique allows one to simultaneously measure correlation functions achieving good statistics for a number of different wave vectors in a single measurement. Wave vectors as small as 70 cm(-1) have been investigated, which is very difficult to achieve with ordinary dynamic light-scattering techniques. We present results on the transition from the diffusive decay of fluctuations to the regime in which gravity is dominant.

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

“…The optical technique we employed is known as Near-Field Scattering [36][37][38][39][40][41][42][43][44][45] by means of a shadowgraph setup [46][47][48]. The shadowgraph optical setup involves a low coherence light source (Super Lumen Diodes, Broad Lighter S680) connected with a single-mode fiber whose output is collimated by an achromatic doublet lens ( f = 15 cm, φ = 5 cm).…”

“…The dynamic near-field imaging technique has been shown to provide direct access to the structure function of the sample for all the wave vectors in the optical system by means of a statistical analysis of differences of images. Details of the dynamic analysis can be found elsewhere [46,47,49,50]. Here we just recall the working equation that is used to fit experimental data: …”

“…In this case, we apply double-frame differential analysis [49,47,46,[50][51][52] in order to extract both the static structure factor and the temporal correlation function. Since this processing requires a heavy computational effort, we make use of custom-made software in the CUDA/C++ language, taking advantage of the parallelization capabilities of a graphic board (Nvidia, TESLA C2050).…”

Differential dynamic microscopy microrheology of soft materials: A tracking-free determination of the frequency-dependent loss and storage moduli

“…Similar to PT, it is based on real-space movies collected in microscopy experiments. These data are treated via an image processing algorithm [22] or equivalent versions of it [23] that combines image differences and spatial Fourier transformations to obtain as a result the intermediate scattering function f (q,t) that is typically probed in DLS experiments as a function of the scattering wave vector q and time t [24]. Since its introduction, DDM has been profitably used and also extended by several groups [25][26][27][28][29][30][31][32][33][34] for a variety of applications [35].…”

Concentration dependent refractive index of a binary mixture at high pressure

“…Just to give some examples close to our experience: fluid properties like the mass diffusion coefficient of binary mixtures, 1 the Soret coefficient, [1][2][3][4][5] phenomena like non-equilibrium fluctuations [6][7][8][9][10][11][12][13] have been extensively studied through techniques such as Mach-Zehnder interferometry, 1 static and dynamic light scattering, 10,11,[14][15][16][17] beam deflection, [2][3][4][5] shadowgraph 6, 8-10, 12, 13 and other scattering in the near field (SINF) techniques. 11,12,[18][19][20][21] In most of the aforementioned cases one needs to know a priori the dependence of the refractive index of the liquid under analysis on the relevant parameter (concentration, temperature, etc.)…”