Developing Bingham Fluid Flow in the Entrance Region Between Parallel Plates

Bingham fluids, also called Bingham plastics, are used in different industries including the production of food, pharmaceuticals, household products, construction and oil and gas drilling. The behavior of Bingham fluids is viscous above a critical shear stress and rigid-body below the threshold stress value. Knowledge of the size of the entrance region has several applications including hemodynamics and microfluidics. A model for steady Bingham fluid flow in the entrance region between parallel plates is developed using the inlet-filled region concept. A boundary layer model is used to solve the fluid flow dynamics in the inlet region up to the point where the critical shear stress is reached at the edge of the boundary layer. Beyond that point, the boundary layer does not grow, while the velocity profile keeps readjusting in the filled region to asymptotically reach the fully developed flow. The results include boundary layer thickness profiles, dimensionless pressure drop, centerline velocity, friction factor and inlet and entrance region sizes as functions of the Bingham number. The results are validated against the results for the Newtonian fluid case (Bingham fluid yield stress equal to zero) and CFD results, using the finite element method, for nonzero Bingham numbers. In addition, the results are found to asymptotically reach the fully developed flow values for the general Bingham fluid flow case. The effects of the Bingham number are addressed and compared with the literature. The present model is largely analytical, requiring minor numerical tasks.