A physically-based fractional diffusion model for semi-dilute suspensions of rods in a Newtonian fluid

The rheological behavior of suspensions involving interacting (functionalized) rods remains nowadays incompletely understood, in particular with regard to the evolution of the elastic modulus with the applied frequency in small-amplitude oscillatory flows. In a previous work, we addressed this issue by assuming a fractional diffusion mechanism, however the approach followed was purely phenomenological. The present work revisits the topic from a physical viewpoint, with the aim of justifying the fractional nature of diffusion. After accomplishing this first objective, we explore by means of numerical experiments the consequences of the proposed fractional modeling approach in linear and non-linear rheology.