Stability analysis of a shear-thinning fluid injection into a boundary layer of Newtonian fluid #

Liam Escott, Paul Griffiths

11:50 Wednesday in 3E11.

Part of the Applied fluid dynamics session.

Abstract #

The study of boundary layer flows involving Newtonian fluids has been a subject of interest for researchers in fluid dynamics for more than a century. Amongst a large variety of studies, the investigation of a natural phenomenon observed in fish is of particular interest to us. Studies have shown that some species of fish can secrete a complex fluid onto their bodies, which results in a drag reduction during motion. This is of benefit for many reasons, not the least being faster escape in a predator-prey situation. 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, described by a non-Newtonian fluid being injected into a larger Newtonian boundary layer, itself subjected to a uniform translational flow. Our problem utilises the Carreau-Yasuda model to describe the injected fluid, which has shear-thinning properties. We find the base flow solutions with some interface location, which is discoverable, along with further perturbation-based analysis which facilitates our understanding of the stability in the system. Central to our research is the comparison of stability between different levels of shear-thinning behaviour, along with a reference to the Newtonian injection case.

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. Further, 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.