Herschel-Bulkley fluid flow through narrow tubes

The present paper deals with a two-fluid model for the flow of Jeffrey fluid in tubes of small diameters. It is assumed that the core region consists of Jeffrey fluid and Newtonian fluid in the peripheral region. Analytical expressions for velocity, effective viscosity, core hematocrit and mean hematocrit have been derived. The effects of various parameters, namely, Jeffrey parameter ({\lambda}1), tube hematocrit (H0) and tube radius (a) on effective viscosity, core hematocrit and mean hematocrit have been studied. It is found that the effective viscosity decreases as the Jeffrey parameter increases but increases with tube hematocrit and tube radius. Further, the core hematocrit decreases with Jeffrey parameter, tube hematocrit and tube radius. It is also noticed that the flow exhibits the anomalous Fahraeus-Lindquist effect.