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

The 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.

► We study the drag undergone by a sphere approaching a plane in a non-Newtonian fluid. ► We give a numerical and asymptotic solution of this geometrically unsteady problem. ► We study the effect of the lateral confinement on the frontal correction of the drag. ► The comparison of asymptotic and numerical results mutually confirms their validity. ► These results apply to the dynamics of aggregation of concentrated dispersions.