Normal stresses on the surface of a rigid body in an Oldroyd-B fluid.

Abstract

In this note we show that the normal stresses on the surface of a rigid body in an incompressible Oldroyd-B fluid are zero. ________________________________________________________________________ A proof showing that normal stresses on the surface of a rigid body in an incompressible Oldroyd-B fluid are zero was first briefly proposed by Huang, Hu and Joseph [1]. In this note we present a similar proof but unlike the original version is based on the property of frame indifference of the constitutive equation of an Oldroyd-B fluid. It was deemed appropriate to present the proof in this note since no such details are available in literature. Consider a rigid body moving with some translational velocity V and angular velocity Ω in an incompressible Oldroyd-B fluid at time t. Stress σ at a point in the fluid is given by TI +− = pσ (1) where p is the pressure, I is the identity tensor and T is the extra-stress. For an Oldroyd-B fluid the extra-stress is given by the following constitutive equatio