Covariant description of the colloidal dynamics on curved manifolds - Castro-Villarreal, Pavel; Solano-Cabrera, César O.; Castañeda-Priego, Ramón (Frontiers in Physics, 2023)
Brownian motion is a universal characteristic of colloidal particles embedded in a host medium, and it is the fingerprint of molecular transport or diffusion, a generic feature of relevance not only in Physics but also in several branches of Science and Engineering. Since its discovery, Brownian motion, also known as colloid dynamics, has been important in elucidating the connection between the molecular details of the diffusing macromolecule and the macroscopic information of the host medium. However, colloid dynamics is far from being completely understood. For redinstance, the diffusion of non-spherical colloids and the effects of redthe underlying geometry redof the host medium on the dynamics of either passive or active redparticles are a few representative cases that are part of the current challenges in Soft Matter Physics. In this contribution, we take a step forward to introduce a covariant description of the colloid dynamics in curved spaces. redWithout loss of generality, we consider the case where hydrodynamic interactions are neglected. This formalism will allow us to understand several phenomena, for instance, the redcurvature effects on the kinetics during spinodal decomposition and the thermodynamic properties of the colloidal dispersion, just to mention a few examples. This theoretical framework will also serve as the starting point to highlight the role of geometry on colloid dynamics, an aspect that is of paramount importance to understanding more complex transport phenomena, such as the diffusive mechanisms of proteins embedded in cell membranes.