Effective diffusion in random composites measured by NMR

Highlights: • We have introduced a hierarchical model of heterogeneous magnetic material. • On the base of renormalisation group method we calculated diffusion attenuation signal and diffusion tensor invariants. • Calculation was done in slow and fast diffusion limits. • We found links between internal physical parameters and geometry and effective properties of magnetic composite. The measuring of diffusion attenuation by nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI) is used to reveal information about the internal structure of various random magnetic composites including heterogeneous soft matter and biological tissues. The response of these materials on the applied external static and space-time varying magnetic fields encodes intrinsic dynamic correlations and depends on links between macroscopic effective diffusivity and structure on the microscopic scale. In the current work we carry out a computational analysis of the time dependent diffusion attenuation and tensor invariants and demonstrate their relation to the microscopic architectural elements while also considering Euclidean dimensionality. The proposed numerical method of hierarchical recursive iterations is efficient in the simulation of NMR (MRI) experiments in two- and three-dimensional heterogeneous magnetic media, by choosing and modelling the influence of the concentration of components of composites and internal hierarchical characteristics of physical parametres.