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

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.