ON THE FLOW PAST A SPHERE IN A CYLINDRICAL TUBE - LIMITING WEISSENBERG NUMBER

The paper is concerned with the steady flow generated by a sphere falling along the centreline of a cylindrical tube containing a viscoelastic fluid which is modelled by the Oldroyd-B constitutive relation. By exploiting the similarity solution in the neighbourhood of the centreline of the tube it is found that there is a limiting Weissenberg number above which no steady state axisymmetric solution can exist. The full numerical solution to the problem using a boundary element method is reported and compared with results obtained by other numerical methods. We find an overall agreement between different sets of results pointing to the existence of the limiting Weissenberg number. © 1990.