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

A model of thermophoresis of colloidal proteins in water using non-Fickian diffusion currents | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article A model of thermophoresis of colloidal proteins in water using non-Fickian diffusion currents Arijit bhattacharyay, MAYANK sharma, Angad Singh This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8877403/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version 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 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 ST 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. Physical sciences/Physics/Statistical physics, thermodynamics and nonlinear dynamics/Thermodynamics Physical sciences/Physics/Chemical physics Biological sciences/Biophysics/Molecular biophysics/Kinetics Full Text Additional Declarations There is NO Competing Interest. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8877403","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":592179865,"identity":"1bb74db1-d6fc-4ca1-9b57-1a013b084aeb","order_by":0,"name":"Arijit bhattacharyay","email":"data:image/png;base64,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","orcid":"","institution":"Indian Institute of Science Education and Research Pune","correspondingAuthor":true,"prefix":"","firstName":"Arijit","middleName":"","lastName":"bhattacharyay","suffix":""},{"id":592179866,"identity":"934451c3-4d85-4412-87d5-ca21c5efb5d4","order_by":1,"name":"MAYANK sharma","email":"","orcid":"https://orcid.org/0000-0001-8207-1379","institution":"Indian Institute of Science Education and Research Pune","correspondingAuthor":false,"prefix":"","firstName":"MAYANK","middleName":"","lastName":"sharma","suffix":""},{"id":592179867,"identity":"741be66b-f0b2-4006-b393-1645f5f77db7","order_by":2,"name":"Angad Singh","email":"","orcid":"","institution":"Indian Institute of Science Education and Research Pune","correspondingAuthor":false,"prefix":"","firstName":"Angad","middleName":"","lastName":"Singh","suffix":""}],"badges":[],"createdAt":"2026-02-14 06:20:48","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8877403/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8877403/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":104399856,"identity":"fc2b88f8-5314-48a0-be27-4c2a6b9e40a5","added_by":"auto","created_at":"2026-03-11 12:07:52","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":463442,"visible":true,"origin":"","legend":"Article File","description":"","filename":"fileone.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8877403/v1_covered_8417b4e2-be49-4114-8526-6287c2b5a26d.pdf"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"A model of thermophoresis of colloidal proteins in water using non-Fickian diffusion\r\ncurrents","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-8877403/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8877403/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"In 1928, Chapman generalised Einstein’s theory of diffusion for non-uniform fluids to show the\r\npresence of a non-Fickian diffusion current, which he considered important in thermodiffusion\r\n(Ludwig-Soret effect). In 1941, Kiyosi Itô proposed the formal methods of stochastic calculus in the\r\npresence of spatially dependent diffusion, yielding the same non-Fickian diffusion current as shown\r\nby Chapman. The phenomenon of thermodiffusion and thermophoresis happens in the presence\r\nof a temperature gradient, which makes diffusion space-dependent. The role of solvation forces in\r\nthermophoresis will only be clearer once that of diffusion is understood properly. In this paper,\r\nwe investigate the importance of Chapman’s non-Fickian diffusion current on the thermophoretic\r\nmotion of colloidal particles in water (with weak salt concentration). We show that all the general\r\nfeatures of variations of the Soret coefficient ST with temperature can be captured using Chapman’s\r\nnon-Fickian diffusion current. We compare our theoretical results with experimental plots of the\r\nSoret coefficients for three polypeptides in aqueous solution: Lysozyme, BLGA, and Poly-L-Lysine,\r\nand find a strong match. We emphasise that, in addition to the yet-to-be-understood details of\r\nsolvation forces, Chapman’s non-Fickian diffusion current is an indispensable element that needs to\r\nbe taken into account for a complete understanding of thermophoresis and thermodiffusion.","manuscriptTitle":"A model of thermophoresis of colloidal proteins in water using non-Fickian diffusion\ncurrents","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-02-17 11:48:23","doi":"10.21203/rs.3.rs-8877403/v1","editorialEvents":[],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"7dfa96cc-f523-46cd-839b-7db5cc2cd388","owner":[],"postedDate":"February 17th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":63012125,"name":"Physical sciences/Physics/Statistical physics, thermodynamics and nonlinear dynamics/Thermodynamics"},{"id":63012126,"name":"Physical sciences/Physics/Chemical physics"},{"id":63012127,"name":"Biological sciences/Biophysics/Molecular biophysics/Kinetics"}],"tags":[],"updatedAt":"2026-03-28T05:05:46+00:00","versionOfRecord":[],"versionCreatedAt":"2026-02-17 11:48:23","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8877403","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8877403","identity":"rs-8877403","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}