Torsion estimation of particle paths through porous media observed by in-situ time-resolved microtomography

The torsion distribution of cell paths in two-phase flow of a cell suspension through a porous medium is an important quantity for chromatographic processes. It can be estimated from cell tracking in sequences of three-dimensional images of a suspension pumped through the medium, where the images are acquired by in-situ time-resolved microtomography using synchrotron radiation and inline phase contrast modus. This contribution presents a new method for estimating path torsion from discrete positions, where the estimation is based on an appropriate discretization of the differential-geometric formula of the torsion of a space curve. Investigations performed for an alcoholic suspension of silica gel particles pumped through a partially open polyurethane foam show that the shape of the inner surface of the foam has a considerable impact on the particle paths. It turns out that the variance of the torsion for slow particle moving close to the surface is a half order of magnitude smaller than that of fast particles, which underlines the importance of torsion for filter efficiency.