**Uma Balakrishnan**

**Afilliation:**Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania

**Title:**Nanoparticle thermal motion in a Newtonian fluid using fluctuating hydrodynamics

**Abstract:**Brownian motion of nanoparticles in an incompressible Newtonian fluid is critical to the use of nanoparticles for targeted drug delivery. Nanoparticles allow more precise and successful infiltration of drugs to target cells. In general, nanoparticle drug-delivery systems have been shown to enhance the solubility of compounds, and to reduce the impact of drugs on non-target tissue, thereby eliminating unwanted and dangerous side effects. In order to more broadly integrate this technology into medicine, a precise understanding of how to guide the nanoparticle to the target site is necessary. We employ a direct numerical simulation adopting an arbitrary Lagrangian-Eulerian based finite element method to simulate the Brownian motion of a nanoparticle in an incompressible Newtonian fluid contained in a horizontal micron sized circular tube. Thermal fluctuations from the fluid are implemented using a fluctuating hydrodynamics approach. The formalism considers situations where both the Brownian motion as well as the hydrodynamic interactions are important. The instantaneous flow description around the particle and the motion of the particle are fully resolved. Different sized carriers with various densities have been investigated. The results for thermal equilibrium between the particle and the surrounding incompressible Newtonian fluid are evaluated and compared with analytical results, where available. Our numerical results show that (i) the calculated temperature of the Brownian particle in a quiescent fluid satisfies the equipartition theorem; (ii) velocity distribution of the particle follows Maxwell-Boltzmann distribution; (iii) the translational and rotational decay of the velocity autocorrelation functions capture algebraic tails, over long time; (iv) the translational and rotational mean square displacement of the particle obeys Stokes-Einstein and Stokes-Einstein-Debye relations, respectively.

**Slides:**BalakrishnanUma.pdf