Slow motion of a sphere towards a plane through confined non-Newtonian fluid

Abstract

is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. a b s t r a c tThe time needed for the contact of two spheres or a sphere with a rigid plane is mainly controlled by the hydrodynamic drainage of the film located in the gap as long as its thickness is out of range of the Van der Waals interactions. In fact, this time controls the dynamics of aggregation of concentrated dispersions. This fundamental problem has an exact solution in Newtonian fluid which has been used to confirm the validity of the numerical dynamic mesh method employed in this geometrically unsteady problem. Following this validation, we applied it to calculate the correction factor of the drag undergone by a sphere approaching a plane, at constant Reynolds number, in a cylindrical tube filled with a non-Newtonian fluid having negligible viscoelastic component and roughly behaving as a power-law fluid. After a justification for using this useful model, we studied the influence of the lateral confinement on the frontal correction factor of the drag. In the lubrication limit, we recall the asymptotic solution of Rodin to this problem in lateral unbounded power law fluid. The comparison of both asymptotical and numerical results confirms their validity. The results obtained in this study may find an application to Dynamic Surface Force Apparatus for nanorheology.

Effect of solid boundaries on swimming dynamics of microorganisms in a viscoelastic fluid

“…On the contrary, the significance of the solid boundaries is well received in the context of particulate viscoelastic flows. Several computational (Ardekani et al 2007; D’Avino et al 2009; Despeyroux and Ambari 2012; Padhy et al 2013) and experimental (Tatum et al 2007; Ardekani et al 2009; Eisenberg et al 2013) investigations have been carried out to shed light on the dynamical behavior of rigid particles moving in close proximity of a solid surface in non-Newtonian fluids. In particular, it is found (Ardekani et al 2007) that in the second-order fluids, a strong attraction force is developed which draws a solid sphere towards the corresponding wall.…”

Motion of a sphere in a viscous fluid towards a wall confined versus unconfined conditions

“…It is worth mentioning the efforts of studying spheres settling in pipes [10,23], spheres in conical containers [24], sphero-cylindrical particles in cylindrical containers [25]. Moreover, Despeyroux et al investigated the settling of spheres confined in a cylindrical container using a non-newtonian fluid [26].…”