Rheological features of a class of boundary layer flows: Shear thickening and shear thinning effects

Understanding the boundary layer flow of rheological fluids is a problem of great interest because of their industrial and technological importance. There are a large number of industrial applications of these fluids, be it inelastic or viscoelastic. Applications arise in such varied fields as polymer industry, biomedical engineering, and mineral processing industry involving molten polymers, drilling mud, oils, fluid suspensions, soap and food products, and cosmetics, among others. The stress tensor of such non-Newtonian fluids is known to have nonlinear relationship with the rate of deformation tensor, making mathematical analyses of these flows very complicated. In this project, our aim is to investigate certain aspects of boundary layer flows of inelastic fluids exhibiting either shear thickening or shear thinning behavior, in the presence of stationary or moving flat surfaces. We propose to use two specific inelastic fluid models corresponding to dilatancy and pseudoplasticity. The governing boundary layer PDEs of these fluids will be transformed to ODEs through similarity analyses. These resulting boundary value problems will be subjected to perturbation analyses followed by numerical integrations. One of the aims of this study is to assess the higher order effects in the perturbation expansions. The study will also focus on the effects of governing rheological parameters on the boundary layer velocity components as well as on the wall shear stress.