Normal Stress Differences in Polymers During Shear Flow

Steady-shear flows are characterized by three material functions—the viscosity and the first and second normal stress coefficients; the latter are commonly represented by their corresponding normal stress differences, defined in the first chapter. The viscosity behavior of polymeric fluids was considered in detail in the third and fourth chapters. In this chapter we examine the first and second normal stress differences, N 1 and N 2 . These are nonzero only for polymeric fluids, and they arise because polymer molecules tend to stretch under the influence of a velocity gradient and also align with the flow field; this makes the fluid properties anisotropic. Phenomena such as rod climbing and die swell are manifestations of N 1 , while secondary flows in non-circular channels result from the presence of N 2 . These are called elastic effects, and, as with viscosity, they are useful for material characterization, quality control, equipment design, product shape, and process simulation and optimization. Measurement of N 1 is done routinely using rotational viscometers, but this is possible only at relatively low shear rates. N 1 is a positive quantity whose magnitude depends on the shear rate, the polymer molecular weight, molecular weight distribution, long-chain branching, and temperature. For solutions, concentration is another variable. At high shear rates, special techniques have to be used to measure N 1 . By contrast, a measurement of N 2 , even at low shear rates, remains a challenge. It is found that N 2 is much smaller in magnitude as compared to N 1 , and it has a negative sign.