Tracer Dispersion Between Two Lines in Two-Dimensional Percolation Porous Media

we study the statistical behaviour of the tracer motion between two lines in two-dimensional percolation porous media, based upon the direct numerical solutions of the Stokes equations on 20000 different percolation structures. At the critical threshold p = p_c, the travelling length has the exponential distribution rather than the power-law distribution. Numerical simulations show that the ensemble average travelling length ～ L^1.21 and ～ L for p = p_c and p > p_c, respectively. The region of the tracer dispersion is wide when p = p_c and rather narrow when p > p_c. Numerical simulations indicate that the transverse fluctuation has the same scale as the correlation length of the percolation structure, which is the system size L when p = p_c and is constant for the large system size L when p > p_c. It is also shown that the travelling time has the power-law behaviour when p = p_c.