Ballitic and diffusive random walks in confinement

Diffusion transport in porous media and concentrated colloidal suspensions plays a crucial role in various transport phenomena in nature and industry. An individual trajectory near the interface can be described as an alternate succession of adsorption steps and random flights in the bulk. Statistical properties of these random flights in various interfacial confining systems are determinant to understand the full transport process. Related to first passage processes, these properties play a central role in numerous problems such as the mean first exit time in a bounded domain, heterogeneous catalytic reactivity and nuclear magnetic relaxation in complex and biological fluids. In the present work, we first consider the various possibilities to connect two points of a smooth interface by a random flight in the bulk. Second, we analyze at the theoretical and experimental points of view a way to probe Brownian flights statistics. Implications concerning diffusive transport in disordered porous materials are discussed.