Eur. Phys. J. E (2019) 42: 81
https://doi.org/10.1140/epje/i2019-11843-6

Topical Review

Lattice Boltzmann methods and active fluids

¹ Dipartimento di Fisica, Università degli Studi di Bari, and INFN Sezione di Bari, Via Amendola 173, 70126, Bari, Italy
² Istituto Applicazioni Calcolo, CNR, Via Amendola 122/D, 70126, Bari, Italy
³ Center for Life Nano Science@La Sapienza, Istituto Italiano di Tecnologia, 00161, Roma, Italy

^* e-mail: Giuseppe.Gonnella@ba.infn.it

Received: 28 January 2019
Accepted: 24 May 2019
Published online: 28 June 2019

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.