Determination of Wall Correction Factors for Small Particles of Different Shapes Moving in a Cylindrical Channel

Abstract

Motion of small particles of different size and shape plays an important role in many applications of engineering and scientific significance. A finite element model, consisting of Navier–Stokes and continuity equations in the arbitrary Lagrangian Eulerian (ALE) framework has been presented to determine flow field in a channel and track the movement of a particle through the channel. The hydrodynamic retardation effect for the particle due to the presence of bounding walls has been quantified in terms of wall correction factors. Wall correction factors for particles of different shapes e.g. cylindrical, elliptical, capsule and dumb-bell shapes moving in a fluid-filled cylindrical channel of uniform cross-section in the Stokes flow region have been calculated for two flow cases: (i) moving particle in stationary fluid, and (ii) stationary particle in moving fluid. Lag factors of the particles are then obtained for flow case (iii) moving particle in moving fluid, by employing linear superposition of case (i) and case (ii). The model was validated by calculating the wall correction factors for a spherical particle and comparing the results with various published analytical and numerical results. The wall correction factors for non-spherical particles were compared for same volume and same radial height considering different particle to channel radii ratio, λ=0.3-0.9 and Reynolds numbers, Re<1. The results show that the drag of cylindrical particle is significantly higher than the other shapes whereas the elliptical shape experiences the least drag in comparison to the capsule and cylindrical shapes. The increase of length of the particle increases the drag of the particle except the dumb-bell shaped particle. The drag of dumb-bell shaped particle varies in a different way.