Diffusion of dermatological irritant in drying laundered cloth

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.