Use of dynamic schlieren interferometry to study fluctuations during free diffusion

Abstract

We used a form of schlieren interferometry to measure the mean-squared amplitude and temporal autocorrelation function of concentration fluctuations driven by the presence of a gradient during the free diffusion of a urea solution into water. By taking and processing sequences of images separated in time by less than the shortest correlation time of interest, we were able to simultaneously measure dynamics at a number of different wave vectors. The technique is conceptually similar to the shadowgraph method, which has been used to make similar measurements, but the schlieren method has the advantage that the transfer function is wave-vector independent rather than oscillatory.

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

“…It is worth pointing out again that the deviation from the diffusive behavior is related to the effect of gravity on larger size fluctuations (smaller wave vectors). This deviation generates the characteristic bell-shape of τ (q), which has already been observed and studied in a number of experiments addressing concentration non-equilibrium fluctuations in a free-diffusion experiment [46,47,49]. Fig.…”

“…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).…”

“…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: …”

“…Under non-equilibrium conditions, the gradient of one variable couples the spontaneous fluctuations of the velocity of the fluid molecules with the fluctuations of the relevant variable, thus providing a huge enhancement of the intensity of the fluctuations, increasing with their size. This phenomenon has been widely investigated in the latest decades and a sound theoretical description (see for example [59][60][61][62][63]) as well as many experimental studies [46,47,49,[64][65][66][67] can be found in the literature. Here, we would like to recall the essential equations that describe the intensity of the light scattered by concentration fluctuations generated in a fluid out of equilibrium and in the presence of the terrestrial gravitational field.…”

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.) in order to derive accurate measurements.…”