Instabilities in the thin film flows effect of odd viscosity

Abstract

Thin film flows are very widely observed in nature encompassing scenarios such as rain droplets sliding down a windowpane, lava flows, mud flows, and snow avalanches in geophysical set- tings. These flows have diverse applications, including cooling systems, heat exchangers, biomedical applications, and film coatings. Mathematical modelling of such thin film phe- nomena involves expressing them as partial differential equations (PDEs). Investigating the stability and dynamics by solving these PDEs is crucial for understanding how various physical parameters affect the stability and dynamics of liquid film flows. newline newlineIn most day-to-day liquids, time-reversal symmetry is maintained, and a single coefficient of viscosity, known as even viscosity or simply known as viscosity, prevails. However, certain liquids exhibit a broken time-reversal symmetry, either due to external forces or spontaneously, leading to the presence of an additional non-dissipative viscosity known as odd viscosity. This study delves into the impact of odd viscosity on the stability of liquid film flows in various scenarios. In the introductory chapter, the thin films flows are defined, a discussion of their characteristics, and applications is presented which is followed by the description of the equa- tions and boundary conditions that govern such flows. Further the discussion delves into fluids featuring odd viscosity, exploring both their physical and mathematical definitions, along with their applications. Additionally, an overview of the current state of research development in this field is provided. The thesis is primarily organized into three main parts. newline newline