We consider materials with large pores interconnected by thin long channels saturated with an incompressible fluid. In the absence of fluid flow, solute transport in the porous network is diffusion controlled, however, solute transport can be enhanced
when the porous network is subjected to a cyclic flow with zero time average velocity. We develop a mathematical model to analyze this physical phenomenon and obtain an effective macroscale diffusion coefficient for solute transport which dependends
on cyclic flow conditions and the geometry of the porous network.