Accurate measurements of particle number density along with particle diameters and velocities are strongly required both in academic and industrial fields. A new imaging technique, through the evaluation of the effective depth of field of a camera, is developed using standard solid particles with constant diameters. To measure the effective depth of field for a wide range of particle diameters, three optical setups, named microscale, mesoscale, and macroscale setups, are used for the diameters of 50 μm - 201 μm, 201 μm - 3.97 mm, and 3.97 mm - 15 mm, respectively. The measured effective depth of field is further applied to measure the size dependence of the number density of entrained bubbles by breaking waves in a wind-wave tank. The results show that the slopes of the number density of the entrained bubbles in the experiments corresponded to those measured by a phase Doppler particle analyzer under 500 μm, and was -5 over 500 μm in both fresh and salt waters. This emphasizes that the present imaging technique can measure the diameters and particle number density with high precision and is important for measurements of droplets, bubbles, and solid particles with a wide range of diameters.
In this study, density-driven natural convection in porous media associated with Rayleigh–Taylor instability was visualized by X-ray computed tomography to investigate the effect of the thickness of the diffusing interface on convection. The thickness of the interface was changed by molecular diffusion with time, and the effective diffusivity in a porous medium was estimated. Compared with the thick interface, for the thin interface, many fine fingers formed and extended rapidly in a vertical direction. The onset time of natural convection increased proportionally with the thickness of the interface, being correlated with Rayleigh number and Péclet number. For the thinner initial interface, the finger number density increased more rapidly after onset and reached a higher value. Next, we discussed the mass transport in Rayleigh–Taylor convection to show how dispersion affects mass transport based on finger extension velocity and concentration in fingers. Increasing the interface thickness delayed the onset of convection, while the finger extension velocity remained the same. The reduced finger extension velocity changed nonlinearly with the Péclet number, reflecting the effect of dispersion. High transverse dispersion and longitudinal dispersion quickly reduced finger density. Transverse dispersion between ascending and descending fingers decreased the density; the density decreased linearly along the finger on both sides of the symmetric plane. As a result, the Sherwood number was proportional to the Rayleigh number, whereas the coefficient changed nonlinearly with Péclet number because of dispersion, reflecting the nonlinear dependences of the reduced velocity and the reduced density difference on Péclet number.