# Lattice Boltzmann Methods and Active Fluids

## TL;DR

This paper reviews the use of Lattice Boltzmann Methods in modeling active fluids, covering thermodynamics, implementation, and recent advances in phenomena like active turbulence and self-propelled droplets.

## Contribution

It provides a comprehensive overview of how LBM can be applied to simulate complex active fluid systems and recent developments in the field.

## Key findings

- LBM can accurately simulate active fluid hydrodynamics.
- Recent studies have explored phenomena like active turbulence and self-propelled droplets.
- Chapman-Enskog expansion links LBM to continuous active fluid equations.

## Abstract

We review the state of the art of active fluids with particular attention to hydrodynamic continuous models and to the use of Lattice Boltzmann Methods (LBM) in this field. We present the thermodynamics of active fluids, in terms of liquid crystals modelling adapted to describe large-scale organization of active systems, as well as other effective phenomenological models. We discuss how LBM can be implemented to solve the hydrodynamics of active matter, starting from the case of a simple fluid, for which we explicitly recover the continuous equations by means of Chapman-Enskog expansion. Going beyond this simple case, we summarize how LBM can be used to treat complex and active fluids. We then review recent developments concerning some relevant topics in active matter that have been studied by means of LBM: spontaneous flow, self-propelled droplets, active emulsions, rheology, active turbulence, and active colloids.