Modelling and Analysis of the Dispersal of a Polymeric Pollutant Injected into a Channel Flow of a Newtonian Liquid

Abstract

The transient dynamics of nonlinear dispersion of a polymeric pollutant ejected by an external source into a laminar flow of a Newtonian liquid flowing through a rectangular channel is investigated. The Boussinesq approximation is assumed for the density variation with pollutant concentration. The governing equations of mass and momentum conservation are coupled to the pollutant concentration equation as well as to the viscoelastic constitutive model for the polymer stresses. The Oldroyd-B viscoelastic constitutive model is employed to model the deformation and characteristics of the polymer stresses. The coupled system of nonlinear partial differential equations is solved numerically using robust and efficient semi-implicit finite difference methods (FDM). Solutions are presented in graphical form for various parameter values. The model can be a useful tool in understanding the dynamics of domestic and industrial pollution situations that may arise from improper discharge of long-chain hydrocarbon products into, say, water drainage systems. The novelty of this investigation is in the modelling of the long-chain hydrocarbon-product pollutants via appropriate viscoelastic (polymeric) constitutive equations. In general, it is observed that parameters which increase (decrease) the flow velocity correspondingly increase (respectively decrease) the wall shear stress. Similarly, it is observed that parameters which increase (decrease) the polymer concentration correspondingly increase (respectively decrease) the mass transfer rates. The wall shear stress and mass transfer are measurable quantities. In this respect, our work offers such measurements as predictive tools to detect the scale of contamination.