Design, Implementation, and Force Modeling of Quadrupole Magnetic Tweezers

This paper presents the design, implementation, and force modeling of quadrupole magnetic tweezers, which are capable of exerting magnetic forces in arbitrary 2-D directions on magnetic particles in the workspace. A lumped-parameter model based on magnetic monopole approximation is employed to describe the magnetic field generated by the quadrupole magnetic tweezers in the workspace. In this model, the magnetic field generated by each magnetic pole is approximated by the field of a point magnetic charge associated with the magnetic pole, and the total magnetic field produced by the system is obtained by applying the principle of superposition. An analytical force model considering the interaction between a magnetic particle and the magnetic field is then developed. The derived force model accurately characterizes the nonlinearity of the magnetic force exerting on the magnetic particle with respect to the applied currents to the coils and the position dependency of the magnetic force in the workspace. The directionality as well as the force generation anisotropy of the designed system is then explored using the force model. The model also facilitates the implementation of a feedback control law to stabilize and control the motion of a magnetic particle. Experimental results in terms of the magnetic force in relation to stable motion control of a magnetic particle are used to validate the force model.