The study of boundary layer flows involving Newtonian fluids, with or without suction or injection, has been a subject of interest for researchers in fluid dynamics for more than a century. The aim of our study is to extend traditional boundary layer-type analyses to consider a natural phenomenon that has been observed in some species of fish. Studies have shown that certain fish secrete a small amount of fluid with complex properties, which has the potential to reduce their drag in water. Our research aims to model the behaviour exhibited by these fish via a modified boundary layer analysis.

We investigate the flow profiles of a two-tier system with a non-Newtonian fluid being injected into a larger Newtonian boundary layer, itself subjected to a uniform translational flow. We use a variety of models to capture the non-Newtonian behaviour of these fish slimes and, given each choice of constitutive model, present the differing behaviour of the system. In particular, we evaluate the boundary location between our two fluid layers as well as the velocity, viscosity and shear profiles which change significantly both under the variation of key modelling parameters and the choice of model itself.

Self-similar solutions are present for a specific choice of incline angle of the flat plate, and we present these flow profiles for a variety of constitutive constants. Previous studies have shown, that under certain parameter regimes, the onset of instability in a non-Newtonian boundary layer flow is delayed when compared to its Newtonian counterpart. The relevant stability analysis is therefore conducted to assess if we can predict similar behaviour in the self-similar regime. Furthermore, we provide flow profiles in the fully two-dimensional case, under zero angle of inclination. An analysis of the stability in this flow system is the next natural progression in our work.