{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,11,11]],"date-time":"2023-11-11T00:14:56Z","timestamp":1699661696814},"reference-count":32,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2021,10,25]],"date-time":"2021-10-25T00:00:00Z","timestamp":1635120000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021,12,15]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Sodium dodecyl sulphate (SDS), a commonly used laundry surfactant, has been known to cause some damage to epithelial cells in skin. Further, independent experiments have shown that a single laundry wash with rinsing leaves a residue of around 10% of the chemicals used in a wash cycle. A realistic nonlinear system of partial differential equations is developed for coupled water and solute transport through a drying porous medium when the solute has a mobile state (monomers) as well as an immobile state (micelles). An accurate finite difference scheme is developed and tested against known exact solutions of the nonlinear porous medium equation for transport of water and against known conservation laws. It shows that at the end of atmosphere-controlled stage 1 of drying when little water remains, the concentration of SDS near the drying surface, where it may contact skin, is commonly an order of magnitude higher than its initial value. The problem is exacerbated by successive regular wash cycles and by higher evaporation rates in electronic dryers. The numerical solutions show the partitioning between the two phases of SDS.<\/jats:p>","DOI":"10.1093\/imammb\/dqab014","type":"journal-article","created":{"date-parts":[[2021,10,7]],"date-time":"2021-10-07T23:44:42Z","timestamp":1633650282000},"page":"474-489","source":"Crossref","is-referenced-by-count":0,"title":["Diffusion of dermatological irritant in drying laundered cloth"],"prefix":"10.1093","volume":"38","author":[{"given":"P","family":"Broadbridge","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, La Trobe University, Bundoora, Victoria 3086, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"B S","family":"Tilley","sequence":"additional","affiliation":[{"name":"Center for Industrial Mathematics and Statistics, Department of Mathematical Sciences, Worcester Polytechnic Institute, 100 Institute Rd, Worcester, MA 01609, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2021,10,25]]},"reference":[{"key":"2021120106451949800_ref1","doi-asserted-by":"crossref","first-page":"296","DOI":"10.2340\/0001555571296300","article-title":"Susceptibility of atopic dermatitis patients to irritant dermatitis caused by sodium laurel sulfate","volume":"71","author":"Agner","year":"1991","journal-title":"Acta Derm. Venereol."},{"key":"2021120106451949800_ref2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1111\/j.1600-0536.1995.tb00438.x","article-title":"The sodium lauryl sulfate model: an overview","volume":"33","author":"Lee","year":"1995","journal-title":"Contact Dermatitis"},{"key":"2021120106451949800_ref3","doi-asserted-by":"crossref","first-page":"156","DOI":"10.1533\/9780857090348.156","article-title":"Retention of anionic surfactant following garment laundering and its potential effect on dermatitis sufferers","volume-title":"Medical and Healthcare Textiles","author":"Rowe","year":"2010"},{"key":"2021120106451949800_ref4","doi-asserted-by":"crossref","first-page":"708","DOI":"10.1111\/j.1346-8138.2003.tb00463.x","article-title":"Residual washing detergent in cotton clothes: a factor of winter deterioration of dry skin in atopic dermatitis","volume":"30","author":"Kiriyama","year":"2003","journal-title":"J. Dermatology"},{"key":"2021120106451949800_ref5","doi-asserted-by":"crossref","first-page":"1892","DOI":"10.1016\/j.jaci.2018.11.016","article-title":"Laundry detergents and detergent residue after rinsing directly disrupt tight junction barrier integrity in human bronchial epithelial cells","volume":"143","author":"Wang","year":"2019","journal-title":"J. Allergy Clin. Immunol."},{"key":"2021120106451949800_ref6","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1080\/07373930601160940","article-title":"Experimental validation of the heat and mass transfer model for convective drying","volume":"25","author":"Kowalski","year":"2007","journal-title":"Dry. Technol."},{"key":"2021120106451949800_ref7","doi-asserted-by":"crossref","first-page":"778","DOI":"10.2136\/sssaj1968.03615995003200060024x","article-title":"The drying through the top surface of a vertical porous column","volume":"32","author":"Heller","year":"1968","journal-title":"Soil Sci. Soc. Amer. Proc."},{"key":"2021120106451949800_ref8","volume-title":"Dynamics of Fluids in Porous Media","author":"Bear","year":"1988"},{"key":"2021120106451949800_ref9","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780195126051.001.0001","volume-title":"Soil Water Dynamics","author":"Warrick","year":"2003"},{"key":"2021120106451949800_ref10","doi-asserted-by":"crossref","first-page":"495","DOI":"10.1016\/S0309-1708(98)00024-4","article-title":"Calculation of humidity during evaporation from soils","volume":"22","author":"Stewart","year":"1999","journal-title":"Adv. Water Res."},{"key":"2021120106451949800_ref11","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1029\/WR024i001p00155","article-title":"Constant rate rainfall infiltration: a versatile non-linear model. 2. Applications of solutions","volume":"24","author":"White","year":"1988","journal-title":"Water Resour. Res."},{"key":"2021120106451949800_ref12","doi-asserted-by":"crossref","first-page":"959","DOI":"10.1590\/0104-6632.20140314s00002685","article-title":"Mathematical modeling of a convective textile drying process","volume":"31","author":"Johann","year":"2014","journal-title":"Brazilian J. Chem. Eng."},{"key":"2021120106451949800_ref13","doi-asserted-by":"crossref","first-page":"430","DOI":"10.1017\/S0334270000007153","article-title":"Exact nonlinear solutions for constant-rate expression from material of finite thickness","volume":"33","author":"Broadbridge","year":"1992","journal-title":"J. Austral. Math. Soc. Ser. B"},{"key":"2021120106451949800_ref14","doi-asserted-by":"crossref","first-page":"844","DOI":"10.1103\/PhysRevLett.49.1844","article-title":"Method for the exact solution of a nonlinear diffusion-convection equation","volume":"49","author":"Rosen","year":"1982","journal-title":"Phys. Rev. Lett."},{"key":"2021120106451949800_ref15","doi-asserted-by":"crossref","DOI":"10.1016\/B978-0-12-391927-4.10019-2","article-title":"Thermodynamic principles of self-assembly","volume-title":"Intermolecular and Surface Forces","author":"Israelachvili","year":"2011"},{"key":"2021120106451949800_ref16","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1007\/s11242-004-6799-8","article-title":"Symmetry solutions for transient solute transport in unsaturated soils with realistic water profile","volume":"61","author":"Moitsheki","year":"2005","journal-title":"Trans. Porous Media"},{"key":"2021120106451949800_ref17","doi-asserted-by":"crossref","DOI":"10.6028\/NBS.NSRDS.36","article-title":"Critical Micelle Concentration of Aqueous Surfactant Systems","author":"Mukerjee","year":"1971"},{"key":"2021120106451949800_ref18","article-title":"Applied surfactants","volume-title":"Principles and Applications","author":"Tadros","year":"2006"},{"key":"2021120106451949800_ref19","doi-asserted-by":"crossref","first-page":"214","DOI":"10.1021\/je950234b","article-title":"Mutual diffusion coefficients and resistance coefficients for aqueous solutions of sodium alkanoate surfactants","volume":"41","author":"Deng","year":"1996","journal-title":"J. Chem. Eng. Data"},{"key":"2021120106451949800_ref20","doi-asserted-by":"crossref","first-page":"184","DOI":"10.1016\/0021-9797(83)90397-1","article-title":"Surfactant diffusion: new results and interpretations","volume":"93","author":"Evans","year":"1983","journal-title":"J. Colloid Interface Sci."},{"key":"2021120106451949800_ref21","doi-asserted-by":"crossref","first-page":"2260","DOI":"10.1021\/jp993917x","article-title":"Salt induced growth of normal sodium alkyl sulphate micelles well above their critical micelle concentrations","volume":"104","author":"Ranganathan","year":"2000","journal-title":"J. Phys. Chem. B"},{"key":"2021120106451949800_ref22","doi-asserted-by":"crossref","first-page":"230","DOI":"10.1021\/je0503498","article-title":"Solubility and partitioning behavior of surfactants and additives used in bioprocesses","volume":"51","author":"Pollard","year":"2006","journal-title":"J. Chem. Eng. Data"},{"key":"2021120106451949800_ref23","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1016\/S0167-7322(02)00069-7","article-title":"Diffusion coefficients of sodium dodecylsulfate in aqueous solutions and in aqueous solutions of $\\upbeta $-cyclodextrin","volume":"102","author":"Ribeiro","year":"2003","journal-title":"J. Molec. Liquids"},{"key":"2021120106451949800_ref24","doi-asserted-by":"crossref","first-page":"1071","DOI":"10.1029\/92WR02595","article-title":"The influence of solute size, pore water velocity, and intraparticle porosity on solute dispersion and transport in soil","volume":"29","author":"brusseau","year":"1993","journal-title":"Water Resour. Res."},{"key":"2021120106451949800_ref25","doi-asserted-by":"crossref","first-page":"1943","DOI":"10.1002\/wrcr.20152","article-title":"Saturation-dependent solute dispersivity in porous media: pore-scale processes","volume":"49","author":"Raoof","year":"2013","journal-title":"Water Resour. Res."},{"key":"2021120106451949800_ref26","doi-asserted-by":"crossref","first-page":"703","DOI":"10.2136\/sssaj2003.0703","article-title":"Hydrodynamic dispersion in an unsaturated dune sand","volume":"67","author":"Toride","year":"2003","journal-title":"Soil Sci. Soc. Amer. J."},{"key":"2021120106451949800_ref27","doi-asserted-by":"crossref","first-page":"1","DOI":"10.2136\/vzj2014.08.0105","article-title":"Water flow and solute transport in unsaturated sand\u2014a comprehensive experimental approach","volume":"14","author":"Kumahor","year":"2015","journal-title":"Vadose Zone J."},{"key":"2021120106451949800_ref28","first-page":"215","article-title":"Diffusion in absorbing media","volume":"171","author":"Henry","year":"1939","journal-title":"Proc. Royal Soc. London A"},{"key":"2021120106451949800_ref29","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1080\/00405000701556061","article-title":"Sorption isotherms for textile fabrics and foam used in the indoor environment","volume":"99","author":"Svennberg","year":"2008","journal-title":"J. Textile Inst."},{"key":"2021120106451949800_ref30","doi-asserted-by":"crossref","first-page":"2804","DOI":"10.1016\/j.compscitech.2008.06.010","article-title":"Permeability of textile reinforcements: simulation, influence of shear and validation","volume":"68","author":"Verleye","year":"2008","journal-title":"Composites Sci. Tech."},{"key":"2021120106451949800_ref31","doi-asserted-by":"crossref","DOI":"10.1029\/2020WR027332","article-title":"Influence of radiation on evaporation rates: a numerical analysis","volume":"56","author":"Heck","year":"2020","journal-title":"Water Resour. Res."},{"key":"2021120106451949800_ref32","first-page":"147","article-title":"Moisture movement in porous materials under temperature gradients","volume":"38","author":"Philip","year":"1957","journal-title":"EOS"}],"container-title":["Mathematical Medicine and Biology: A Journal of the IMA"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/imammb\/article-pdf\/38\/4\/474\/41324985\/dqab014.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/imammb\/article-pdf\/38\/4\/474\/41324985\/dqab014.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,10]],"date-time":"2023-11-10T13:45:54Z","timestamp":1699623954000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/imammb\/article\/38\/4\/474\/6410104"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,10,25]]},"references-count":32,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2021,10,25]]},"published-print":{"date-parts":[[2021,12,15]]}},"URL":"https:\/\/doi.org\/10.1093\/imammb\/dqab014","relation":{},"ISSN":["1477-8599","1477-8602"],"issn-type":[{"value":"1477-8599","type":"print"},{"value":"1477-8602","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2021,12]]},"published":{"date-parts":[[2021,10,25]]}}}