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Updated: Mar 18, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
111 years of Brownian motion
Xin Bian1, Changho Kim, George Em Karniadakis
1Division of Applied Mathematics, Brown University, Providence, RI 02912, USA. xin_bian@brown.edu changhokim@lbl.gov george_karniadakis@brown.edu.
Abstract:
We consider the Brownian motion of a particle and present a tutorial review over the last 111 years since Einstein's paper in 1905. We describe Einstein's model, Langevin's model and the hydrodynamic models, with increasing sophistication on the hydrodynamic interactions between the particle and the fluid. In recent years, the effects of interfaces on the nearby Brownian motion have been the focus of several investigations. We summarize various results and discuss some of the controversies associated with new findings about the changes in Brownian motion induced by the interface.
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