A model of thermophoresis of colloidal proteins in water using non-Fickian diffusion currents

TL;DR

This paper demonstrates that Chapman's non-Fickian diffusion current effectively models the thermophoretic behavior of colloidal proteins in water, aligning well with experimental data and highlighting its importance in understanding thermophoresis.

Contribution

It introduces the application of Chapman's non-Fickian diffusion current to model thermophoresis of colloidal proteins, providing a better theoretical match with experimental observations.

Findings

Chapman's non-Fickian diffusion current captures the variation of Soret coefficient with temperature.

Theoretical results strongly match experimental data for Lysozyme, BLGA, and Poly-L-Lysine.

Non-Fickian diffusion current is essential for understanding thermophoresis in aqueous solutions.

Abstract

In 1928, Chapman generalised Einstein's theory of diffusion for non-uniform fluids to show the presence of a non-Fickian diffusion current, which he considered important in thermodiffusion (Ludwig-Soret effect). In 1941, Kiyosi It\^o proposed the formal methods of stochastic calculus in the presence of spatially dependent diffusion, yielding the same non-Fickian diffusion current as shown by Chapman. The phenomenon of thermodiffusion and thermophoresis happens in the presence of a temperature gradient, which makes diffusion space-dependent. The role of solvation forces in thermophoresis will only be clearer once that of diffusion is understood properly. In this paper, we investigate the importance of Chapman's non-Fickian diffusion current on the thermophoretic motion of colloidal particles in water (with weak salt concentration). We show that all the general features of variations of the Soret coefficient $S_T$ with temperature can be captured using Chapman's non-Fickian diffusion current. We compare our theoretical results with experimental plots of the Soret coefficients for three polypeptides in aqueous solution: Lysozyme, BLGA, and Poly-L-Lysine, and find a strong match. We emphasise that, in addition to the yet-to-be-understood details of solvation forces, Chapman's non-Fickian diffusion current is an indispensable element that needs to be taken into account for a complete understanding of thermophoresis and thermodiffusion.