The ellipsoid-dipole model. Theoretical fundamentals and applications†

We report the fundamental theoretical framework of the ellipsoid-dipole model and its applicability in quantifying the pairwise dipolar energy between ellipsoids with different sizes, aspect ratios, and magnetic properties. Additionally, we discuss the limitations of the model and its potential for describing interacting ellipsoids under various field conditions for both established and emerging applications. We analyze the dipolar interaction energy of suspensions composed of different pairs of magnetic ellipsoids, including permanently magnetized ellipsoids, paramagnetic ellipsoids, diamagnetic ellipsoids, and mixtures of them. We validate the results of the ellipsoid-dipole model and the corresponding pairwise dipolar interaction energy against those produced by the point-dipole approximation. Furthermore, we quantify the relative equilibrium positions and orientations of different ellipsoid pairs in a uniform magnetic field. The article shows that the ellipsoid-dipole model offers a wide range of possibilities for predicting and engineering colloidal suspensions composed of binary ellipsoids and for enhancing current applications.