Optimization of pathway pattern size for programmable biomolecule actuation

We generalize a method for optimization of pattern size for an programmable actuation of magnetic beads, as biomolecule carriers, by analytically formulating the governing forces in terms of bead and pattern sizes. There is a good agreement between analytically calculated and numerically obtained forces, giving a validity of the analytical actuation force for the optimization of pattern size. The maximum actuation force is given at the phase angle of π/4 between the direction of magnetic field and the bead position, and the optimum radius of disk pattern is in the range of 2-5 times of bead radius, depending on the magnetization of the disk pattern under an external magnetic field.