A REMARK ON THE GIESEKUS VISCOELASTIC FLUID

Steady planar shear flow is considered as a solution of a boundary value problem for the equation of a Giesekus fluid for various values of the mobility parameter. It is shown that if the mobility parameter is greater than 1/2 then such a solution either does not exist or is not realizable for large values of the shear rate (if there is no solvent viscosity contribution) or for an entire finite range of shear rates (if there is a small contribution from the solvent viscosity). If the mobility parameter does not exceed 1/2 then the solution exists and is realizable for all values of the shear rate. The conclusions follow from a one-dimensional linear stability analysis of the appropriate boundary value problem and from an admissibility criterion that stems from restrictions imposed on the configuration tensor which arises from the molecular model description of the polymer liquid. We consider a solution realizable if it is stable and admissible. Thus a clearly distinct behavior of the Giesekus model is observed for values of the mobility parameter between 0 and 1/2 as opposed to values between 1/2 and 1. This may have implications on the suitability of the model with values of the mobility parameter exceeding 1/2.