Chemistry Reference
In-Depth Information
Chapter 7
Interacting Droplets: Collective Dynamics
The statistics and dynamics of the interactions of squirmers with
each other, with passive tracer particles, with walls and in
confinement are investigated.
7.1 Introduction
Interacting self propelled particles (SPPs) have implications in a broad range of
systems. Living matter exhibits pattern formation due to interacting self propelled
units at various scales, from human crowds, herds, bird flocks, and fish schools [
1
-
3
]
to bacterial swarms [
4
], and even down to a molecular level in the dynamics of actin
and tubulin filaments [
5
]. At a theoretical level, several qualitative approaches have
been made to incorporate the diverse collective behaviors of such different systems in
a common framework [
6
-
8
]. Broadly, there have been three categories of theoretical
approaches to study and understand the interactions:
1. analysis of the flow induced by an individual or pair of swimmers moving in a
viscous liquid [
9
-
12
]
2. including nonequilibrium terms in the well studied hydrodynamics of liquid crys-
tals, where active particles are likened to liquid crystals exhibiting orientational
order because of their elongated shapes [
13
-
15
]
3. derivation of continuumhydrodynamic equations from specificmicroscopicmod-
els (e.g. rule based Vicsek model) of the dynamics [
16
-
18
].
Each approach has different merits and disadvantages, with some being too
detailed to incorporate more than a few elements at once, and others being too
