The interpretation of a long-standing rheological flow problem using computational rheology and a PTT constitutive model

•The rotation of a solid sphere in an non-Newtonian elastic liquid is considered.•Under some conditions a secondary flow is predicted with the Giesekus model.•Moving away from the restriction of slow flow, the inertial vortex flow can be also predicted by the PTT model. Modern computational rheology techniques are used to interpret an experimental observation, which has remained unresolved for over four decades. The simple flow in question involved the rotation of a solid sphere in an infinite expanse of non-Newtonian elastic liquid. Under some conditions, Giesekus observed an interesting secondary flow. This added an ‘inertial’ secondary flow near the rotating sphere to the well-understood ‘slow-flow’ features observed and predicted by others in the 1960s. By employing a Phan-Thien/Tanner (PTT) constitutive model and moving away from the restriction of ‘slow-flow’, we show that it is possible to predict numerically the inertial vortex observed by Giesekus.