In advective transport through weakly heterogeneous aquifers of random stationary and isotropic three-dimensional permeability distribution, transverse macrodispersivity α _T is found to be zero. This was determined in the past by solving the transport equation at first order in the log conductivity variance σ _Y ². However, field findings indicate the presence of small but finite α _T . The aim of the paper is to determine α _T for highly heterogeneous formations using a model that contains inclusions of conductivity K, submerged in a matrix of conductivity K ₀, for large = K/K ₀. In the dilute medium approximation, valid for small volume fraction n, but arbitrary , and for spherical inclusions, it is found that α _T = 0 because of the axisymmetry of flow past a sphere. A medium made up of rotational ellipsoids of arbitrary random orientation, macroscopically isotropic, and of the same and n is devised as a counterexample. It is found that because of the intertwining of streamlines α _T > 0, being of order ( − 1)⁴ for → 1. These findings are confirmed by accurate numerical simulations of flow through a large number of interacting inclusions; for = 10 and n = 0.2 (jamming limit), the large value α _T /α _L 0.15 is attained. The numerical simulations display the strong permanent deformation of stream tubes responsible for this phenomenon, coined as “advective mixing.” The two-point covariance, used in practice in order to characterize the aquifer structure, is not able to detect the structures that produce advective mixing. Nevertheless, the presence of high-conductivity lenses inclined with respect to the mean flow may explain the occurrence of finite α _T in field applications.