## Introduction to hydrodynamic interactions For particles in the fluid, like the colloidal systems, the motion of particles would induce long range flow to the fluid, and the motion of the fluid will in turn act on the particles and affect the motion of these particles. By generating and reacting to the motion of the fluid, the particles experience this hydrodynamic interaction. Although such interaction has long be recognized, but the studies on it is restricted and the phenomena are not fully understood. Partially because the coupling itself is very complicated, also the investigation from experiments are limited. Scattering - the traditional way of studying soft materials can hardly give reasonable results for local interactions in the length scale where hydrodynamic force is significant, since these techniques (x-ray, neutron scattering) generates data in reciprocal space, and interpretation are intrinsically carried out for a much larger sample size. In recent years, confocal microscope started to be an emerging tools for analyze motion and behaviors of colloidal system in real space by directly imaging. With the aid of fast scanning rate, three-dimensional, high time-resolved data could be obtained. Beside experiments aspects, theories (based on Stokeslet analysis and Faxén's law, etc) and simulations on hydrodynamic effects has been developed during recent year. Brownian Dynamics (BD), Fluid Particle Dynamics (DPF), and more recently applied, long range hydrodynamic interactions approximated by RPY tensor combining with BD simulation were suggested in last 30 years. These simulation, as claimed by the authors, nicely show some of the behaviors. In this page, a brief but comprehensive review will be presented, introduction would be given from the early works like stokeslet analysis, to recent simulation works based on RPY potential like [[The hydrodynamics of colloidal gelation]], and observation using Rheoconfocal like [[Ultrafast imaging of soft materials during shear flow]]. >[!Notice] >It is worth noting here, in the [[Project_sotmat]], we say viscosity is the source of *hydrodynamic effect*, which is an reasonable expression. The term *hydrodynamic interaction* is more like an phenomenology interpretation of, some kind of, solid-liquid coupling. It is called interaction, but difficult to attribute certain observable effect directly to such interaction. ### Stokeslet analysis >[!Info] >See more on: >https://physics.nyu.edu/grierlab/leshouches2/leshouches2.html, This page is the lecture note given by David G. Grier, he is also the developer of those commonly applied particles tracking algorithms.