THE OMEGA-D-FLUID - GENERAL-THEORY WITH SPECIAL EMPHASIS ON STATIONARY 2-DIMENSIONAL FLOWS

In this paper a theory is presented in which the extra stress tensor t au is allowed to depend not only on the rate of strain tensor D but al so on the relative vorticity omega of the fluid, i.e. on the vorticity relative to the rate of rotation of the principal straining direction s. This theory has its origin in an expansion of tau in terms of kinem atic tensors in the limit of stationarity in a material sense (constan t stretch history flows). For two dimensional flows of an incompressib le fluid three tensors suffice to completely specify tau. The three ma terial functions which appear can depend only on two invariants, namel y the second invariant of D and on omega(2). Using the predictions of an Oldroyd 8 constant fluid in a homogeneous planar flow of constant s tretch history, the three material functions are studied in detail. Fo r the special case of a quasi-Newtonian fluid shear thinning and exten sion thickening can directly be accounted for in the ''viscosity'' fun ction.