X-ray correlations assemble a complete velocity field

To see what happens inside a pile of sand or another volume of granular material, researchers rely either on deformation observations at the surface, which don’t always reflect any internal flows, or on simulations. Several existing techniques can image interior flows, but they each have one or more disadvantages, such as limited spatial and temporal resolutions, high costs, and invasiveness. A new technique, developed by James Baker , Itai Einav , and their colleagues at the University of Sydney, overcame those hurdles by using sets of two-dimensional x-ray radiographs to uncover the three-dimensional velocity field inside a volume of opaque grains.

X rays were fired from three orthogonal locations through a container of opaque grains that were being sheared from below by a conveyor belt, as shown in the diagram above. By spatially correlating successive radiographs, the researchers extracted the probability density functions (PDFs) of the two displacement components orthogonal to the x-ray direction for each grid cell. Each PDF was then sampled evenly to generate an unsorted array of the different displacements through the beam direction.

By combining the PDF results orthogonal to each other and solving a Sudoku-style puzzle, the researchers were able to reconstruct the 3D velocity field shown from 2D projections. As in Sudoku, the displacement values that should be placed in each row and column are known from the two sets of PDFs, but how to arrange those displacements in space defines the puzzle. Unlike in Sudoku, though, there is no unique solution. To find the optimal solution, Baker and his colleagues applied an algorithm that minimized discrepancies between the two sets of observations. Since the imaging method isn’t just for granular flows, researchers who study foams, suspensions, and other soft materials may now have a new way to look inside opaque media. (J. Baker et al., Nat. Commun. 9, 5119, 2018. )