Statistical mechanics with three-dimensional particle tracking velocimetry experiments in the study of anomalous dispersion. II. Experiments

Abstract

In paper I [Phys. Fluids 13, 75 (2001)] we provided a theory for simulating anomalous dispersion which relied on the self-part of the intermediate scattering function. Here we obtain Lagrangian trajectories for a conservative tracer in a porous medium and then use these trajectories to obtain the self-part of the intermediate scattering function. We then use the scattering function as data for the inverse problem and obtain the generalized wave-vector and frequency dependent dispersion tensor developed in paper I. The transverse components of this tensor are then examined as a function of wave vector to see if or when the dispersive process goes asymptotic (Fickian). The matched index (of refraction) technique has been used to obtain a transparent porous medium and three dimensional particle tracking has been used to obtain the trajectories. Over the life of the experiment the transverse dispersive process remained anomalous, though it was gradually approaching the Fickian limit.

Measurements of Transitional and Turbulent Flow in a Randomly Packed Bed of Spheres with Particle Image Velocimetry

“…Figure 7 also indicates self-similarity for the lowest range of Re p with a relatively flat plateau of the most probable u * x for u * x < 0.4 and then the probability of the velocity spectrum drops rather abruptly which was also observed by Maier et al (1998) and Moroni et al (2001). Johns et al (2000) who studied porous media with MRI obtained a peak for the most probable u * x at Re of about 1.…”

“…10. Also Moroni et al (2001), Johns et al (2000); Lebon et al (1996) reported a symmetric distribution for u y for low Re p . As Re p increases the maximum changes slightly toward the negative side and the curves becomes basically the same, self-similar, for 1170 ≤ Re p ≤ 3230.…”

“…7 also shows that there are negative u * x for all Re p . A number of studies have reported the presence of recirculation zones as well, i.e., Moroni et al (2001), Maier et al (1998), Saeger et al (1991Saeger et al ( , 1995, Lebon et al (1996), Hill et al (2001). The percentage negative u * x , which is an indication of recirculation zones, vary with Re p according to There is less recirculation within the plane 6 mm from the midplane than within the other planes probably because the overall porosity is about 20 % higher than for the other planes.…”

“…However, optical techniques in porous media require all phases be transparent refractive index-matched (RIM) materials. This limits the range of materials that can be used but it still makes these techniques powerful for generic studies of the flow in porous beds with PTV (Johnston et al 1975;Stephenson and Stewart 1986;Saleh et al 1992;Northrup et al 1993;Peurrung et al 1995;Moroni et al 2001;Huang et al 2008;Lachhab et al 2008), PIV (Patil and Liburdy 2013) and Laser Doppler Anemometry (Yarlagadda and Yoganathan 1989). PIV require the flow to be seeded with a relatively large number of particles (Raffel 2007;Westerweel 1997).…”

Transitional and Turbulent Flow in a Bed of Spheres as Measured with Stereoscopic Particle Image Velocimetry

“…Peurrung et al (1995) applied particle tracking velocimetry (PTV) to low Re laminar flow in a bed of spheres and found that the flow rate measured with PTV is in good agreement with the flow rate given by the syringe pump used. In Moroni and Cushman (2001), the same technique was used to find 3D trajectories inside a porous medium to determine the dispersion tensor. Huang et al (2008) used PTV to study the flow in a cylinder filled with monosized spheres at Re = 28.…”