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This paper addresses the mixed Couette-Poiseuille problem, that is the flow between two parallel plates, in the presence of simultaneous pressure gradient and wall motion. Instead of the wall-normal coordinate y, we use the local shear stress as our primary variable and rewrite the corresponding formulae for the velocity profile, flow rate, etc. This gives rise to a graphical technique for solving the problem in the case of arbitrary (possibly measured) generalized Newtonian fluid rheology. We demonstrate the use of the proposed technique on two problems: (a) Bingham fluid and (b) a non-Newtonian fluid with general, nonmonotonous viscosity function.

Recently, the increasingly strict safety and emission regulations in the automotive industry drove the interest towards automatic length compensating devices, e.g., hydraulic lash adjusters (lower emission) and slack adjuster in brake systems (faster brake response). These devices have two crucial requirements: (a) be stiff during high load, while (b) be flexible in the released state to compensate for environmental effects such as wear and temperature difference. This study aims to use the advantageous properties of shear thickening fluids to develop a less complicated, cost-efficient design. The proposed design is modeled by a system of ordinary differential equations in which the effect of the non-Newtonian fluid flow is taken into account with a novel, simplified, semi-analytical flow rate-pressure drop relationship suitable for handling arbitrary rheology. The adjuster’s dimensions are determined with a multi-objective genetic algorithm based on the coupled solid-fluid mechanical model for six different shear thickening rheologies. The accuracy of the simplified flow model is verified by means of steady-state and transient CFD simulations for the optimal candidates. We have found that the dominating parameters of such devices are (a) the shear thickening region of the fluid rheology and (b) the gap sizes, while the piston diameters and the zero viscosity or the critical shear rate of the fluid have less effect. Based on the results, we give guidelines to design similar-length compensating devices.