Motion of a spherical solid particle in Couette flow: exact solution vs. homotopy perturbation approximation with and without Pade approximants

TL;DR

This paper compares the exact solution and homotopy perturbation approximation (with and without Pade approximants) for the motion of a spherical particle in Couette flow, highlighting the simplicity of the exact solution.

Contribution

It provides a comparative analysis of exact and approximate solutions for particle motion in Couette flow, emphasizing the efficiency of the exact solution.

Findings

Exact solution is simple and sufficient for the problem.

Homotopy perturbation approximation is unnecessary for this linear problem.

Pade approximants do not significantly improve the approximation.

Abstract

The motion of a spherical solid particle in plane Couette flow is governed by a linear problem that has a simple exact solution. As such, there is no need for an approximate analytical representation of the solution; specially when it is tedious, complicated, and requires hairy terms to give accurate results only at small or moderate values of the time.