A model of thermophoresis of colloidal proteins in water using non-Fickian diffusion currents
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arXiv
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2026
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| author | Sharma, Mayank Singh, Angad Bhattacharyay, A. |
| author_facet | Sharma, Mayank Singh, Angad Bhattacharyay, A. |
| contents | 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 Itô 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_13328 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A model of thermophoresis of colloidal proteins in water using non-Fickian diffusion currents Sharma, Mayank Singh, Angad Bhattacharyay, A. Soft Condensed Matter Statistical Mechanics Biological Physics 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 Itô 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. |
| title | A model of thermophoresis of colloidal proteins in water using non-Fickian diffusion currents |
| topic | Soft Condensed Matter Statistical Mechanics Biological Physics |
| url | https://arxiv.org/abs/2602.13328 |