Tangential Flow Analysis of Giesekus Model in Concentric Annulus with Both Cylinders Rotation

Abstract

Giesekus viscoelastic fluid is solved analytically for purely tangential flow in a concentric annulus at laminar and steady state conditions. Flow is created by a relative rotational motion between the cylinders. The analytical expressions for yield dimensionless velocity profile, pressure distribution, (f and Re are Fanning friction factor and Reynolds number) and material functions (viscosity, first and second normal stress difference coefficients) are obtained in cylindrical coordinates. Results show that difference between the values of lower as well as upper critical limits of the velocity ratio (where the minimum velocity happens) with their corresponding Newtonian values increase when mobility factor and Deborah number increase. The results also show that viscometric functions decrease by increasing elasticity because the viscoelastic fluid shows the shear thinning behavior which is strengthened by increasing elasticity. It is found that, for all values, profiles are symmetrical around (  and k are velocity ratio and radius ratio) because no relative motion exists.

Keywords

• Giesekus model; Deborah number; Elasticity; Velocity ratio; Material functions.