MODELING OF OSCILLATORY FLOW OF A RHEOLOGICALLY COMPLEX LIQUID IN A FLAT CHANNEL

Abstract

This research presents a detailed investigation into the laminar oscillatory flow of rheologically complex fluids within a flat channel. Such flows are characteristic of various industrial and technological processes involving polymer solutions, turbid water mixtures, and high-viscosity petroleum products. The study is grounded in the necessity to understand how the rheological properties of these fluids lead to unconventional hydrodynamic phenomena that differ from standard Newtonian behavior. The mathematical modeling is conducted using a simplified system of differential equations based on the generalized Maxwell model to account for the elastic-viscous properties of the medium. By employing periodic time functions, the research bypasses the need for initial conditions, focusing instead on stabilized oscillatory states. The study specifically analyzes the relationship between wall shear stress and the average velocity over the channel cross-section, deriving a transfer function known as the amplitude-spatial frequency characteristic (AFC). Numerical analysis reveals that at small oscillation frequencies, significant deviations in wall stress occur compared to Newtonian fluids. A key finding is the identification of a spatial phase shift in wall shear stress relative to the average velocity. Furthermore, the research demonstrates that under certain conditions—particularly with high relaxation times and specific fluid acceleration parameters—unusual effects such as reverse flow can occur within the channel. These results provide critical insights for the diagnosis and treatment of biological flows (such as blood) and the optimization of microfluidic devices.