  Natural porous systems, such as soil, membranes, and biological tissues
comprise disordered structures characterized by dead-end pores connected to a
network of percolating channels. The release and dispersion of particles,
solutes, and microorganisms from such features is key for a broad range of
environmental and medical applications including soil remediation, drug
delivery and filtration. Yet, the role of microscopic structure and flow for
the dispersion of particles and solutes in such disordered systems has been
only poorly understood, in part due to the stagnant and opaque nature of these
microscopic systems. Here, we use a microfluidic model system that features a
pore structure characterized by dead-ends to determine how particles are
transported, retained and dispersed. We observe strong tailing of arrival time
distributions at the outlet of the medium characterized by power-law decay with
an exponent of 2/3. Using numerical simulations and an analytical model, we
link this behavior to particles initially located within dead-end pores, and
explain the tailing exponent with a hopping and rolling mechanism along the
streamlines inside vortices within dead-end pores. These dynamics are
quantified by a stochastic model that predicts the full evolution of arrival
times. Our results demonstrate how microscopic flow structures can impact
macroscopic particle transport.
