A magnetically actuated ball valve applicable for small-scale fluid flows

We present three possible designs for magnetically actuated ball valves that can be scaled down to nanometer length scales. Analytical expressions are presented for the hydraulic resistance of the ball valve as a function of geometric parameters and the state of the valve, and we also present analytical expressions for the hydrodynamic force on the magnetic bead that functions as the ball in the valve. We verify these expressions numerically and calculate the magnetic forces that can be exerted on the magnetic bead using the proposed structures. Finally, for typical parameters we show that these structures will be able to withstand a back pressure between 3 and 30 kPa regardless of the size of the bead/ball.