An Advanced Study on Developed Numerical Simulation of Falling and Moving Objects in Viscous Fluids under the Action of a Reynolds Lubrication Theory and Low Reynolds Numbers

Abstract

The development work focuses on the numerical simulations of free body movement in viscous fluid. In many areas of science and engineering, the flow of viscous fluids at low Reynolds number plays an important role, especially in applied areas of lubrication theory and micro- organism locomotion. The aim is to make the simulation of very slow motion of the small body in viscous fluid. We developed bodies’ immersed dynamics simulations in viscous fluid by seeking numerical solutions for appropriate field variables. We developed the methods for vertically and spherically cylindrical objects’ motions, the forces on bodies close to a plane stationary wall are computed from the velocity and pressure fields using the Stokes equation through COMSOL Multiphysics finite element software. The Navier-Stokes equation is reduced to Stokes equation there is independence of time which means object will have an effect only on the motion and the slightly compressible flow assumption is made in order to obtain smooth solution numerically. The forces on an object in slightly compressible Stokes flow have been exerted on the falling objects. The resulting forces have compared with analytical results from the Reynolds Lubrication Theory, and achieved significant results from the development method in Matlab and achieved significant numerical simulations in COMSOL. In addition, an investigation has been made to an object swimming at low Reynolds number. At low Reynolds number moving is possible when object scale is small and flow pattern is slow and sticky. We have developed a system for a thin two-dimensional (2D) worm-like object wiggle that is passing a wave along its centreline and its motion has simulated by the Ordinary Differential Equations (ODE) system and by the Arbitrary Lagrangian-Eulerian (ALE) moving mesh technology. The development method result shows that it is possible for the small object to have a motion from one position to another through small amplitudes and wavelengths in viscous fluid. The development methods in COMSOL 3.5 Multiphysics with Matlab has worked sufficiently well in getting a good enough solution as required in our study.