During dyeing, dispersive flow is assumed to reduce the concentration gradient of dye liquor flowing through a yarn package, resulting in a more even distribution of dye in the liquor within the package. However, little is known about the degree of significance of dispersive transport, as a proportion of the total transport of dye. This study investigates the influence of dispersion on dye transport during dyeing, based on a finite element method approach utilised in a mathematical model. The model has been applied to establish the influence of several parameters during the course of the dyeing process. This study theoretically discusses the role of dispersion on the rate of dyeing and the uniformity of dye distribution. © 2006 The Authors. Journal compilation © 2006 Society of Dyers and Colourists.