Flow Characteristics Around a Stationary Solid Sphere and Falling Fluid Droplet

Abstract

This paper investigates two fundamental fluid dynamics problems: the flow of a Newtonian fluid past a stationary solid sphere and the motion of a fluid droplet falling through a surrounding Newtonian fluid. For the flow past a sphere, various quantities such as normalized tangential velocity, pressure difference, and shear stress are plotted as functions of normalized distance from the sphere's center. The locations of maximum fluid pressure and maximum shear stress are determined. The second part of the paper employs the stream function approach to solve for the velocity field around the falling droplet. Assumptions are made regarding fluid behavior and boundary conditions are derived. The total drags on the droplet, including form drag and viscous drag, is evaluated. The plausibility of the results is tested, and the state of the fluid inside the droplet is determined. Additionally, an estimation of the total drags on a gas bubble rising in a liquid is provided. This analysis provides insights into complex fluid flow phenomena with implications for various engineering and scientific applications.