Ballistic and diffusive random walks in confinement
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0899-N08-03.1
Ballitic and diffusive random walks in confinement P. Levitz, D. Grebenkov, D. Petit and C.Vigouroux Laboratoire de Physique de la Matière Condensée, UMR 7643 du CNRS Ecole Polytechnique, 91128 Palaiseau, France. [email protected]
ABSTRACT 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. INTRODUCTION Porous materials, concentrated colloidal suspensions are example of confining systems developing large specific surface, presenting a rich variety of shapes and exhibiting complex and irregular morphologies on a large length scale. Such a confinement strongly influences the molecular dynamics of embedded fluids and the diffusive motion of Brownian particles entrapped inside these materials. In this general frame, a close inspection of particle and or molecular trajectories is instructive. The particle reaches the interface after a random walk in the bulk. It can be either adsorbed or transferred with some probability or it can be reflected, performing a new diffusion step in the bulk. Until definitive loss by adsorption or finale escaping, the particle trajectory can be described as an alternate succession of surface encounters and flights in the bulk (also called bridges this paper). The statistics of times and the displacements between two interface hits are determinant to understand the full transport process. This question is related to a first passage problem and plays a central role in the evaluation of the mean first exit time from a bounded domain [1-3] or in better understanding of nuclear magnetic relaxation processes in complex fluids and porous media[4]. Interesting enough, these bridge statistics have to be used whatever are the surface boundary conditions ranging from strong adsorption (Dirichlet) to complete reflection (Neumann) with the intermediate situation of partially reflected motion. In the present work, we review some statistical properties of these random flights in various interfacial confining systems. First, we consider the various possibilities to connect two points of a smooth interface by a random flig
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