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

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).

On the dynamics of a spherical scaffold in rotating bioreactors.

We analyze the dynamics of a spherical scaffold in rotating bioreactors (or clinostats). The idealized clinostat environment consists of a purely rotational flow that is perpendicular to a gravitational field. We confirm through a detailed analytical study that lift effects considerably alter the position of the equilibrium point reached by the scaffolds in the (vertical) direction collinear to the gravitational field. This result holds for small particle and shear Reynolds numbers. Our analysis shows that the inertial lift effect is negligible in the horizontal direction. We show that for all rotations of practical interest, and for the range of particle Reynolds number smaller than unity, the vertical coordinate of the equilibrium point is strongly affected by consideration of lift effects. For light (heavy) particles, inclusion of lift in the formation forces the equilibrium position to be below (above) the horizontal plane that contains the axis of rotation. The equilibrium point for light particles is stable and therefore is observable experimentally. The equilibrium point for heavy particles is unstable. We also estimate the stress level applied to the scaffold and derive an algebraic expression that indicates that the stress level acting on the scaffold decreases with increasing shear Reynolds number.