Optimal design of non‐Newtonian, micro‐scale viscous pumps for biomedical devices

Abstract

The present paper addresses the numerical optimization of geometrical parameters of non-Newtonian micro-scale viscous pumps for biomedical devices. The objective is to maximize the mass flow rate per unit of shaft power consumed by the rotor when an external pressure load is applied along the channel that houses the rotor. Two geometric parameters are considered in the optimization process: (i) the height of the channel that houses the rotor (H) and (ii), the eccentricity (epsilon) of the rotor. Three different micro-scale viscous pump configurations were tested: a straight-housed pump (I-shaped housing) and two curved housed pumps (L- and U-shaped housings). The stress-strain constitutive law is modeled by a power-law relation. The results show that the geometric optimization of micro-scale viscous pumps is critical since the mass flow rate propelled by the rotor is highly dependent on epsilon and H. Numerical simulations indicate that mass flow rate is maximized when epsilon approximately 0, namely when the rotor is placed at a distance of 0.05 radii from the lower wall. The results also show that micro-scale viscous pumps with curved housing provide higher mass flow rate per unit of shaft power consumed when compared with straight-housed pumps. The results are presented in terms optimized dimensions of all three configurations (i.e., H(opt) and epsilon(opt)) and for values of the power-law index varying between 0.5 (shear thinning fluids) and 1.5 (shear-thickening fluids).