Rheology modulated non-equilibrium fluctuations in time-dependent diffusion processes

TL;DR

This paper theoretically investigates how non-Newtonian rheology, modeled by a Maxwell viscoelastic fluid, influences non-equilibrium concentration fluctuations during diffusion processes, revealing significant effects at long times and complex frequency-dependent behaviors.

Contribution

It introduces a theoretical analysis of non-equilibrium fluctuations in viscoelastic fluids, highlighting rheology's impact on fluctuation peaks and dynamic structure factors in diffusion.

Findings

Rheology affects the location and magnitude of fluctuation peaks at long times.

Presence of time-dependent peaks in free diffusion at small times, weakly influenced by rheology.

Different regimes of the dynamic structure factor depend on fluid relaxation time and diffusivity.

Abstract

The effect of non-Newtonian rheology, manifested through a viscoelastic linearized Maxwell model, on the time-dependent non-equilibrium concentration fluctuations due to free diffusion as well as thermal diffusion of a species is analyzed theoretically. The non-equilibrium process is quantified through the concentration fluctuation auto-correlation function, also known as the dynamic structure factor. The analysis reveals that the effect of rheology is prominent for both the cases of free diffusion and thermal diffusion at long times where the rheology dictates not only the location of the peaks in concentration auto-correlations, but also the magnitudes; such peaks in the auto-correlation function are absent in the case of a Newtonian fluid. At smaller times, for the case of free diffusion presence of time-dependent peak(s) are observed, which are weakly dependent on the influence of rheology, a phenomenon which is absent in the case of thermal diffusion. Lastly, different regimes of the frequency dependent overall dynamic structure factor depending on the interplay of the fluid relaxation time and momentum diffusivity are evaluated.