Numerical simulation of dyebath and the influence of dispersion factor on dye transport

In order to model the mass transfer in a fluid, a "dispersion" model is frequently used. When the flow behavior does not drastically deviate from plug flow, the model performs well. The dispersive flow properties of liquids within fibrous textile assemblies however, have not been fully explored. In the mass transfer model, the dispersive flow is assumed to reduce the concentration gradient of dye liquor flowing through the package. This paper illustrates the influence of dispersion term on dye transport based on numerical simulation of dyebath. The transfer of dye through the package is described by a set of time-dependent partial differential equations, which govern convection, dispersion, and adsorption of dyes in the dyebath and across the yarn package. The simulation results prove, theoretically, that the inclusion of the dispersion term in the dyeing model improves the results of the dyeing process in terms of dye uptake and levelness.