Sobre el movimiento browniano: historia, modelamiento y simulación

Abstract

In this work, the aim is to broaden the understanding of one of the most important phenomena in statistical mechanics and thermodynamics, namely Brownian motion. Therefore, it seeks to highlight the importance of the kinetic-molecular theory of heat in the 19th and 20th centuries, considering the crucial role of debate in the development of science. Similarly, the intention is to detail the theoretical and experimental aspects that connect the Brownian motion phenomenon with the comprehension of atomic theory. Following the aforementioned, the following question arises: Is the theory established until the early 20th century adequate to accurately describe Brownian motion? Thus, the goal is to frame the Brownian motion theory from a historical, analytical, experimental, and computational perspective. This work is divided into four main parts. The first two parts focus on highlighting historical progress and analyzing in detail some of the most important articles of that time. The third part involves the execution of a scale experimental setup to confirm the ideas presented in the theory. Subsequently, a computational simulation is carried out modeling water molecules as triatomic structures instead of rigid spheres. As a result of this research, it is demonstrated that the chronological overview presented here allows for the analysis of the motion of small particles from different perspectives, within the framework of theoretical evolution. On the other hand, it is found that the mechanism proposed based on the concept described in Einstein's articles successfully replicates the random motion experienced by Brownian particles. Finally, the results obtained in the simulation demonstrate that there is no appreciable difference when modeling water molecules as rigid spheres or as triatomic structures.