A simple and fast numerical method is developed capable of accurately determining the 3D rotational dynamics of a magnetic particle chain in an infinite fluid domain. The focus is to control the alternating breakup and reformation of the bead chain which we believe is essential to achieve effective fluid mixing at small scales. The numerical scheme makes use of magnetic dipole moments and extended forms of the Oseen-Burgers tensor to account for both the magnetic and hydrodynamic interactions between the particles. It is shown that the inclusion of hydrodynamic interaction between the particles is crucial to obtain a good description of the particle dynamics. Only a small error of deviation is observed when benchmarking the numerical scheme against a more computationally intensive method, the direct simulation method. The numerical results are compared with experiments and the simulated rotational dynamics correspond well with those obtained from video-microscopy experiments qualitatively and quantitatively. In addition, a dimensionless number (RT) is derived as the sole control parameter for the rotational bead chain dynamics. Numerically and experimentally, RT$\approx${} 1 is the boundary between rigid ``rod'' and dynamic ``breaking and reformation'' behaviors.

Chaotic mixing, induced by breakup and reformation of a magnetic chain under the influence of a rotating magnetic field, is studied. A direct simulation method combining the Maxwell stress tensor and a fictitious domain method is employed to solve flows with suspended magnetic particles. The motion of the chain is significantly dependent on the Mason number (Ma), the ratio of viscous force to magnetic force. The degree of chaos is characterized by the maximum Lyapunov exponents. We also track the interface of two fluids in time and calculate the rate of stretching as it is affected by the Mason number. The progress of mixing is visualized via a tracer particle-tracking method and is characterized by the discrete intensity of segregation. Within a limited range of Mason number, a magnetic chain rotates and breaks into smaller chains, and the detached chains connect again to form a single chain. The repeating topological changes of the chain lead to the most efficient way of chaotic mixing by stretching at chain breakup and folding due to rotational flows.

A simple synthetic strategy has been developed for accessing internally functionalized dendrimers. The key feature of this approach is the use of two orthogonal and efficient reactions—‘epoxy–amine’ and ‘thiol–ene’ coupling—for rapid growth of the dendritic scaffold. This sequence of reactions allows for the introduction of reactive hydroxyl groups at each dendritic layer.