An exact solution for laminar, unidirectional flow of Houska thixotropic fluids in a circular pipe

Laminar flow of an incompressible thixotropic liquid which obeys the Houska model as its constitutive equation is investigated theoretically in a circular pipe under equilibrium (steady) conditions. Having derived the single differential equation governing fully-developed, unidirectional, pipe flow of this fluid model, it is shown that an analytical solution is possible for the linear case of the Houska model. The existence and uniqueness of the analytical solution so-obtained is examined theoretically. For the more general nonlinear case of the Houska model, the trust region algorithm is used to obtain numerical results for the flow characteristics. The effects of thixotropic parameters such as breakdown-to-rebuild ratio, viscosity ratio, and Bingham number are investigated on the structural parameter and velocity profiles. As a special case, pipe flow of a thixotropic fluid obeying the Moore model is addressed and a correct boundary condition is proposed at the pipe centerline for this particular fluid model.

► An analytical solution is obtained for steady Poiseuille flow of Houska fluid.
► The breakdown-to-buildup ratio is shown to affect the velocity profiles.
► The viscosity and yield stress ratios are all shown to affect velocity profiles.