The immersed molecular finite element method

In this paper, we present the framework of the immersed molecular finite element method (IMFEM). The framework incorporates Brownian motion dynamics, a molecular phenomenon predominantly present at the nanoscale, into the previously developed immersed finite element method, thus referred to as the immersed molecular finite element method. The thermal fluctuations are embedded in the fluid equations via fluctuating stress terms that are constructed at each timestep in accordance to the fluctuation dissipation theorem. The coupling between the immersed objects and the surrounding fluctuating fluid is accomplished via the hydrodynamic forces that are naturally introduced in the fluid–structure interaction term. A three-dimensional implementation of the framework is presented and verified with an example problem where a comparison is made with the analytic solution. Incorporating a molecular-type force field superimposed with a Coulomb potential between the immersed objects allows us to use the IMFEM to comprehensively model self-assembly of nanoscale structures. Our preliminary investigations suggest that this integrated simulation package will assist in achieving a fundamental understanding of nanodiamond self-assembly process, which represents an important component in the advancement of therapeutic and diagnostic applications.