Analytical solution for channel flow of a Giesekus fluid with non-zero solvent viscosity

A semi analytical solution is obtained here for the fully developed plane Poiseuille flow of a Giesekus fluid with a Newtonian solvent. The fluid behaviour is described using the Deborah number, the mobility factor and an appropriate ratio of fluid viscosity to total viscosity as parameters. The given solution shows that the velocity increases significantly with rising the polymer concentration, confirming that dilution of the solution produces the same effect as an increase in resistance. The analysis demonstrates that there are limiting values of Deborah number related to the mobility parameter.