The Gaussian Diffusion Approximation for Complex Fluids is Generally Invalid

TL;DR

This paper demonstrates that the commonly used Gaussian diffusion approximation fails in complex fluids, showing that particle displacement distributions have exponential tails and that experimental interpretations based on Gaussian assumptions may be unreliable.

Contribution

It provides a theoretical analysis showing the invalidity of the Gaussian diffusion approximation in complex fluids, challenging standard experimental analysis methods.

Findings

Displacement probability distribution has exponential wings.

The incoherent scattering function can significantly deviate from Gaussian predictions.

Experimental methods assuming Gaussian diffusion may produce inaccurate results.

Abstract

Simulations are made of a probe particle diffusing through a complex fluid. Probe particle motions are described by the Mori-Zwanzig equation and Mori's orthogonal hierarchy of random forces scheme, subject to the approximation that the fluid creates a rapidly-fluctuating random force corresponding to solvent motions and a slowly fluctuating random force corresponding to solute (e.~g., matrix polymer) motions. The Gaussian diffusion approximation is seriously incorrect in this physically-plausible model system. $P(x,t)$ has exponential wings. $g^{(1s)}(q,t)$ can differ from $\exp(-q^{2} \langle x^{2}\rangle/2)$ by up to orders of magnitude. Experimental interpretations that rely on the Gaussian approximation, such as the Stejskal-Tanner equation for pulsed-field-gradient NMR or particle tracking, can not be assumed to be reliable in complex fluids.