An exact solution for tube and slit flow of a FENE-P fluid

Abstract

A fully analytical solution is derived for rectilinear flow of a nonlinear viscoelastic fluid obeying the constitutive FENE-P model, under fully developed conditions. Both the plane case (slit flow) and the axisymmetric case (tube flow) are considered. Physical interpretation of the results is provided. The normal stress profile is found to vary in a non-monotone way with the dimensionless parameter characterizing viscoelasticity, the Deborah number (De). For Deborah numbers below a critical value (dependent on the extensibility parameter of the model L 2) the normal stress raises with elasticity, but this trend is reversed for values above the critical one. This effect is due to the competing influence of elasticity and shear thinning. Also, as a consequence of shear thinning the velocity profile becomes flatter as De increases and L2 decreases, leading to higher flow rates for the same pressure drop.