MOTION OF A SLIGHTLY DEFORMED SPHERE IN A VISCOELASTIC FLUID

To study the motion of an arbitrary near sphere immersed in a homogeneous shear flow of an incompressible viscoelastic fluid we impose the restriction that the flow is dynamically and rheologically slow. This allows us to derive an expression for the hydrodynamic force and couple, respectively, which are exerted upon the particle. With the exception of elongational flows marked differences to the behavior in a newtonian fluid show up: sedimentation in a quiescent fluid is accompanied by a rotation until a stable terminal orientation is attained. For prolate spheroids the symmetry axis thus ends up parallel to the direction of the external force and perpendicular to it if the spheroid is oblate. In simple shear the difference between prolate and oblate spheroids manifests itself in the direction in which the rotating symmetry axis drifts (orbit-drift): prolate spheroids drift towards the orbit C = 0 while for oblate ones the drift is towards C = 0. For deviations from the spheroidal shape (but still fore-aft symmetry) another orbit C* comes into play. Some particles drift towards C* while others towards C = 0 if initially C < C* and towards C = ∞ if initially C > C*. If no longer matters whether the particle is slender or not. Although this is perhaps the most interesting result obtained one should also mention the behavior of an ovoid in simple shear. If the symmetry axis is parallel to the vorticity vector the resulting translational slip velocity causes the particle to migrate out of the flow-shear plane in the direction of its pointed end. © 1979 Dr. Dietrich Steinkopff Verlag.