Modelling the reflectivity of oily coatings on textile substrates

This paper simulates the optics of oily coatings on textiles and proposes ways of minimising their visual perception. The simulation allows the design of formulations that incorporate oily benefit agents for fabrics with no perceptible stain marks. The prime optical factor in stain visibility is reduction in the reflection of light from the coated surface. We model the reflectivity of fabrics using the geometric model which Tsoutseos and Nobbs developed for colour appearance of textiles. We then modify this approach to deal with textiles of different thickness and coatings of different refractive indices, n. The use of Mie light scattering with an extended version of the geometric model enables us to simulate the effect of the coating microstructure on substrates. The model predicts that for thick substrates reflectivity is much less sensitive to the refractive index of the staining material compared to thinner substrates in which the loss in reflectivity is monotonous with the oil refractive index. However, beyond a threshold value of n the thicker fabrics also show a precipitous loss of reflection. The model shows that the reflectivity can be increased to make the stain invisible by modification of a fraction of the oil deposits into particulate form, by crystallisation for example. Fabric softener compositions for tumble dryer applications illustrate the model calculations.