The drainage of non-Newtonian fluids in the quasi-steady motion of a sphere towards a plane

Antoine Despeyroux (1) , Abdelhak Ambari (1)

1 LAMPA - Laboratoire Angevin de Mécanique, Procédés et InnovAtion

In the lubrication limit, the time needed for the drainage of the liquid film between two particles or between particles and walls is of industrial importance, because it controls the dynamics and aggregation of nondilute suspensions. This problem is also of fundamental interest in the application of the dynamic surface force apparatus to nanorheology. Even if this problem has an exact solution in Newtonian fluid when the sphere moves steadily and slowly towards or away from a plane wall, this problem remains, to our knowledge, without any exact analytical solution in non-Newtonian fluids with negligible viscoelastic components. But Rodin, using the method of asymptotic expansions, gives an asymptotic solution to this problem in the lateral unbounded power-law fluid. Therefore, in this study, we give a numerical result using the dynamic mesh technique and an asymptotic analytical formula valid in the lubrication regime, for a fluidity index 0.5

Mots clés: Dynamic surface force apparatus; Non-Newtonian fluids; Power-law fluids; Sphere towards a plane; Hydrodynamic interactions

Domaines: Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]

Antoine Despeyroux, Abdelhak Ambari. The drainage of non-Newtonian fluids in the quasi-steady motion of a sphere towards a plane. Microfluidics and Nanofluidics, 2012, 12 (1-4), pp.639-648. ⟨10.1007/s10404-011-0906-2⟩. ⟨hal-01061882⟩