  Exact, fully explicit, purely real analytical expressions for the material
functions describing steady, startup, and cessation regimes of shear flows and
of planar, uniaxial, and biaxial extensional flows of full linear
Phan-Thien--Tanner fluids are obtained. These expressions, which have no
analogs in the literature, are formulated in compact, beautiful forms,
partially due to the unique scaling procedure reducing the number of the model
parameters from four to one. The properties of the material functions are
investigated in detail. For steady extensional flows, the possible shapes of
the extensional viscosity curves are described and the conditions for these
shapes to occur are determined. For startup flows, it is found when exactly the
stress dynamics is oscillatory, and, in this case, a detailed characterization
of oscillations is given, which includes expressions for the position and
magnitude of stress overshoots and undershoots.

Fluid Dynamics