Wall Effects for Dilute Polymer Solutions in Arbitrary Unidirectional Flows

General rheological results for a dilute solution of dumbbell model macromolecules in general unidirectional flows in the presence of plane walls $\mathrm{(z=\pm d)}$ are obtained. Quite generally, we show that all three normal stresses are unequal and that the second normal stress is independent of transverse position z. For simple shear flow a shear viscosity and a first normal stress coefficient result, which are independent of the strength of the flow. For channel flow within a narrow channel a first normal stress coefficient cannot be defined, the reason being that a nonzero flow‐induced first normal stress prevails at the channel axis, where the local shear rate is zero. The results are valid no matter what $\text{v(0),}$ the actual center line velocity, is. This implies that, as in the shear flow case, the thickness of wall layers is independent of the strengths of the flow field.