Phase separation in active matter : from schematic to realistic models

• Main Author: Nie, Pin
• Other Authors: Pica Ciamarra Massimo
• Format: Thesis-Doctor of Philosophy
• Language: English
• Published: Nanyang Technological University 2020
• Subjects: Science::Physics::Atomic physics::Statistical physics; Science::Biological sciences::Biophysics
• Online Access: https://hdl.handle.net/10356/136759
• Institution: Nanyang Technological University

Large density fluctuations are commonly observed in biological systems of self- propelling particles. Examples we are all familiar with include fish schools, bird flocks, herds of animals. These density fluctuations are frequently interpreted as the manifestation of phase separation, despite the underlying system being out of thermal equilibrium. The active elements consume energy to self-propel. Due to the absence of a thermodynamic description, a question of great interest concerns the identification of the microscopic processes that induce these density fluctuations, as well as to develop of a non-equilibrium theory to predict the phase diagram of these systems. Research in this direction follows two paths. On one side, we might assume these density fluctuations originate from underlying physical processes that are universal across different biological systems. Hence, to rationalize the microscopic origin of these fluctuations, one might devise simple models which are able to reproduce them and then investigate these models in detail. On the other side, one might acknowledge that different biological systems are different, and hence try to under- stand a particular system. In my research work, I have followed both approaches to some extent. The most significant part of my research work, and hence of this thesis, focused on the investigation of a prototypical schematic model of the active particle, known as Active Brownian Particles (ABPs). This model describes a collection of particles interacting via short-range repulsive forces, experiencing thermal noise and self- propelling force. The self-propulsion results from an active force acting on each particle, which differs across particles, whose directions are persistent on nature. This active force induces a velocity, known as the active velocity of the particles. At high enough particle density and high enough active velocity, ABPs undergo a transition from a homogeneous to a phase-separated state. How does this happen? How it is possible that, in the absence of attractive forces, a group of particles condense? The ABPs model is by-far the most investigated model of active particles. And indeed, when I started my thesis, I assumed the microscopic origin of its motility- induced phase separation to be clear. It was not the case. In literature, there are two competing theoretical approaches, one based on a kinetic description and the other on a hydrodynamic-like formulation. Apart from being in contradiction regarding to the identification of underlying physical processes driving the phase separation, these models are unable to make accurate quantitative predictions. In this line of research, my main contribution has been in developing a theoretical model to predict the limit of stability of ABPs, as a function of the density of the particles and the motility strength. I have then numerically validated my theoretical model, in both two and three spatial dimensions, and as a function of different control parameters involved. My theoretical model results from a novel understanding of the underlying mechanism which is missed by the community before. In particular, I have identified a previously unreported physical process that promotes the destruction of the density fluctuations and formalizes its dependence on the different control parameters. In the kinetic description of ABPs, the decay of the density fluctuation has been associated to the diffusivity of the self-propelling direction. In the continuum approach, it was attributed to the particle diffusivity. I have shown that the motility also induces the decay of the density fluctuations. This novel motility-induced physical process is fundamental to correctly predict the spinodal line, which results from the balance of physical processes promoting and suppressing density fluctuations. As an extension of this project and partially motivated by the desire of understand- ing the phase separation occurring in systems of self-propelled colloidal particles, I have investigated how friction affects the motility induced phase separation. In- deed, friction is certainly present in dry experiments of active matter, and might also be relevant in wet experiments, where the active particles are suspended in a fluid. Recent experiments on colloidal suspensions under shear have indeed demon- strated the unexpected relevance of frictional forces. I have numerically demon- strated and theoretically rationalized, how friction affects the different physical mechanisms promoting and suppressing density fluctuations in active Brownian particles. As a consequence, I have streamlined the physical origin of the qualita- tively marked differences between the phase diagram of frictionless and frictional particles. Another line of research, I have developed during my Ph.D. concerned the physics of a specific biological system of active particles: microbial biofilms. This is a research activity carried out in collaboration with SCELSE, the Singapore Centre for Environmental Life Sciences Engineering. The goal has been that of ratio- nalizing all of the relevant processes influencing the early-stage biofilm formation, to develop a particle-resolved numerical model with that would help investigate the underlying physics. This is, therefore, a more interdisciplinary project, which required some understanding of the biological processes occurring in biofilms. In literature, there are just a few numerical models describing this process, and all of them seem to neglect what appears to be key biofilm features. In this line of research, my main contribution has been the identification of all the relevant physical processes, and the developing of a numerical model able to describe the early stage biofilm formation. This has been a very complicated task, as bacteria move, grow and divide, leave a trail as they move and interact with it, like ants. In addition, they extrude polymers, known as extracellular polymeric substances, to which they may bond and ends up to be embedded in a protective gel-like polymeric matrix. The level of complexity is enormous, when compared to the schematic ABPs model. After developing the model, tailoring the many free parameters using available experimental data on the pathogen Pseudomonas Aeruginosa, I have investigated a few aspects of particular interests. My numerical results well compare with experimental data, which however are scarce, and shed light on the role and of the interplay of different parameters. For instance, I have demonstrated competition between the typical velocity of the bacteria and their reproduction rate, as well as the possibility of an auto-limited growth induced by the production of extracellular polymeric substances. Summarizing, in my thesis, I fully rationalized the physic of the most studied schematic model of active particles, the active Brownian particles model. Also, I have developed a more realistic model to describe the early stage formation of biofilm, using it to investigate how different parameters affect the forming of a biofilm.