Disclosed are chromatography methods and matrix geometries which permit high resolution, high productivity separation of mixtures of solutes, particularly biological materials. The method involves passing fluids through specially designed chromatography matrices at high flow rates. The matrices define first and second interconnected sets of pores and a high surface area for solute interaction in fluid communication with the members of the second set of pores. The first and second sets of pores are embodied, for example, as the interstices among particles and throughpores within the particles. The pores are dimensioned such that, at achievable high fluid flow rates, convective flow occurs in both pore sets, and the convective flow rate exceeds the rate of solute diffusion in the second pore set. This approach couples convective and diffusive mass transport to and from the active surface and permits increases in fluid velocity without the normally expected bandspreading.