Analytical Description of the Flow Behavior of Extended Herschel-Bulkley Fluids with Regard to Gel Propellants

Kurzfassung

Gel propellants are shear-thinning fluids, which have in many cases a distinct yield stress at low shear rates and/or a constant viscosity at high shear rates. Their viscosity behavior can be described by an extended formulation of the Herschel-Bulkley equation with an additional term containing the theoretical constant viscosity value of the high shear rate range. In this paper the general equations of the flow behavior of fluids with an exponential factor n=0.5 are analytically derived for steady, fully developed and laminar flows through constant area tubes. Velocity profiles and shear rate distributions are shown for different fluids and boundary conditions also in comparison to the common Herschel-Bulkley approach. The shape of this Extended Herschel-Bulkley velocity profile depends upon a derived dimensionless number k_HBE and the ratio of the yield stress to wall shear stress.