Chemical hydrodynamics of nuclear spin states

Quantum mechanical equations of motion are strictly linear in density operators, but equations describing chemical kinetics and hydrodynamics may be nonlinear in concentrations. This incompatibility is fundamental, but special cases can be handled-for example, in magnetic resonance where nuclear spin interactions may be too weak influence concentration dynamics. For isolated spins and first-order reactions, this is a well-researched topic, but time evolution of complex nuclear spin systems in the presence of second-order kinetics, diffusion, and flow has so far remained intractable. In this communication, we report a numerically stable formalism for time-domain description of nuclear spin dynamics and relaxation in the simultaneous presence of diffusion, flow, and second-order chemical reactions. As an illustration, we use Diels-Alder cycloaddition of acrylonitrile to cyclopentadiene in the presence of diffusion and flow in a microfluidic NMR probe (a finite element model with thousands of Voronoi cells) with a spatially localized stripline radio frequency coil.