Magnetic Resonance Relaxation in Heterogeneous Materials is Analogous to First-Order Chemical Reaction

Abstract

Biological tissue, pharmaceutical tablets, wood, porous rocks, catalytic reactors, concrete, and foams are examples of heterogeneous systems that may contain one or several fluid phases. Fluids in such systems carry chemical species that may participate in chemical reactions in the bulk of a fluid, as homogeneous reactions, or at the fluid/fluid or fluid/solid interfaces, as heterogeneous reactions. Magnetic resonance relaxation measures the return of ¹H nuclear magnetization in chemical species of these fluids to an equilibrium state in a static magnetic field. Despite the perceived difference between reaction–diffusion and relaxation–diffusion in heterogeneous systems, similarities between the two are remarkable. This work draws a close parallel between magnetic resonance relaxation–diffusion and chemical reaction–diffusion for elementary unitary reaction \({\text{A}}\to {\text{B}}\) in a dilute solution—both in heterogeneous systems. A striking similarity between the dimensionless numbers that characterize their relevant behavior is observed: the Damköhler number of the second kind \({{\text{Da}}}^{{\text{II}}}\) for reaction and the Brownstein–Tarr number \({{\text{BT}}}_{i}\) for relaxation. The new vision of analogy between reaction- and magnetic resonance relaxation–diffusion in heterogeneous systems encourages the exploitation of similarities between reaction and relaxation processes to noninvasively investigate the dynamics of chemical species and reactions. One such example of importance in chemical engineering is provided for solid–fluid reaction in packed beds.