Mixing dynamics in flows are governed by the coupled action of diffusion and stretching by velocity gradients. This leads to the development of elongated lamellar structures in scalar fields where concentration fluctuations exist at scales set by the Batchelor scale. Because the latter is generally too small to be resolved experimentally, observation of these mechanisms remains an outstanding challenge. Here we present high-resolution experiments allowing for the precise quantification of the evolution of concentration distributions at the scale of a single lamella experiencing diffusion, stretching and aggregation with other lamellae. Quantitative agreement is found with analytical predictions for the lamella’s concentration profile, Batchelor time, Batchelor length scale, and concentration distribution for a large range of Péclet numbers and without adjustable parameter. This benchmark configuration is used to set the experimental spatial resolution required to quantify the concentration probability density functions (PDFs) of scalar mixtures in fluids. The diffusive coalescence of two nearby lamellae, the mechanism by which scalar mixtures ultimately reach uniformity, is shown to induce a complex transient evolution of the concentration PDFs.

The transient method of the mass flow rate measurements through a microporous media is developed and analyzed. This method is based on the constant volume technique and the exponential fit of the pressure evolution in each tank which allows calculating the permeability directly. The pressure relaxation time, a single fitting parameter, is introduced and its behaviors are analyzed in a large pressure range. By measuring the pressure relaxation time for one gas, the permeability of a microporous sample can be derived for the other gases. With the actual experimental setup, we measured the mass flow rate through the microporous media in the range 5 • 10 −7 − 5 • 10 −12 [kg s −1 ] and the permeability in the range 10 −14 − 10 −11 [m 2 ].