Poiseuille flow of nonlocal microstructured fluid

• Analytical solutions nonlocal viscoplastic fluids in the Poiseuille flow geometry.
• Hypergeometric functions are used to compute the velocity profiles.
• A plug flow zone can be exhibited within this nonlocal concept for viscous fluids.

In this paper, an Eringen's type nonlocal flow law is developed to account for the microstructured effects in modelling the behaviour of heterogeneous fluids. The axisymmetrical Poiseuille flow of Newtonian and non-Newtonian fluids is studied using the nonlocal mechanics, and some original analytical results are obtained for this geometrical configuration. It is shown that the nonlocal Newtonian fluid exhibits a kind of pseudo plastic behaviour because a plug flow zone exists within the concept of nonlocal mechanics. Furthermore, the shear rate profile shows some nonlinearity for the nonlocal Newtonian fluid, a property which cannot be accounted for with the so-called local theory. Viscoplastic fluids, modelled by Herschel–Bulkley or Bingham laws, are also investigated using this nonlocal generalization. Hypergeometric functions are used to compute velocity profiles. A general parametric study illustrates the nonlocal specificities of the viscoplastic flow for such heterogeneous materials. Finally, the Newtonian nonlocal model is calibrated using a discrete layered axisymmetrical Poiseuille flow.