An analytical study of unsteady motion of non-spherical particle in plane of Couette flow

An analytical solution of the unsteady two dimensional motion of a non-spherical particle in the plane of Couette flow was acquired using the finite parameter optimal homotopy analysis method. To achieve the best accuracy and ensure the convergence of the results, the averaged residual errors were obtained and minimized. The effects of different initial guesses and the number of convergence-control parameter (k) on the accuracy and efficiency of the problem were studied in detail. It was shown that the current method gives completely reliable results and there is no need to compare the results to those of similar numerical or experimental techniques. Furthermore, the effects of different parameters including sphericity and the proportionality constant on three different base fluids namely: water, ethylene-glycol, and glycerin were investigated. Based on the analytical results, it was shown that non-spherical particles are slower to settle rather than spherical particles and the settling velocity of the particles in the glycerin is much lower than that in the ethylene-glycol and the water base fluids.