Unsteady shear-stress-driven rivulets flow of Newtonian and non-Newtonian power-law fluids with strong surface-tension effect / Aina Sharina Muhammad Badrollddin

Studying thin-film flow provides several significant advantages in both scientific and practical contexts. Understanding the behaviour of thin-films under various conditions is crucial for optimising a wide range of industrial processes. This research investigates the thin-film flow of rivulets for both Newtonian and non-Newtonian power-law fluids on an inclined plane, emphasising the role of shear stress at the free surface in driving the flow under strong surface tension effects. The study investigates the dynamics of rivulets under different parameters of fluid viscosity, power-law indices, and shear stress through a combination of theoretical modelling and numerical simulations. The lubrication approximation is used to solve the continuity equation and the Navier- Stokes equations. A fourth-order governing partial differential equation is obtained by applying these equations to the kinematic condition, the no-slip and no-penetration boundary conditions, and the balances of normal and tangential stress. The similarity transformation method is then used to reduce the governing equation to an ordinary differential equation. The governing fourth-order ODE was solved numerically using the Runge-Kutta-Fehlberg Fourth Fifth (RKF45) in Maple.