Active turbulence and active shell models for microswimmer suspensions

Abstract

[eng] This doctoral thesis deals with the study of the collective behavior of active particles using computacional simulations of semi-dilute solutions of microswimmers. Results are obtained for the polar order parameter, the diffusion and the energy spectrum among others as a function of the concentration and the degree of orientation of the particles. Our main interest is to improve the understanding of the relation between energy flows through the scales of the system and the characteristic collective movements that occur spontaneously and that can be easily recognized in a wide range of situations in different fields (banks of fish, flocks of birds, bacterial cultures, polymer solutions, etc) into a regime that we can refer to as soft active turbulence. Shell models are deterministic dynamical systems that reduce the complexity of the full field equations, though retaining some of their essential features. Originally introduced as a proxy of the Navier-Stokes equations, and therefore characterized by a quadratic nonlinearity and the same inviscid invariants (energy and helicity). Since GOY-model is the original shell model that reproduces aspects of inertial turbulence through a modeling of the system as a sort of Fourier amplitudes of velocity fluctuations over a length scale with associated wavenumber kn, our main aim is to propose a new generalized shell model that can capture some basic properties of the active turbulence dynamics but not trajectories or any other geometric aspect. In the bibliography one can find an improved version of GOY called SABRA-model and other variations of the original idea, although all performed the interaction of shells on a single field. For this reason, our goal is to perform simulations with a generalized SABRA- model developed from the interaction and self-action of two fields. The nature of these fields as well as the form of the model equations places the theoretical framework in the field of active matter and this is the reason why we refer to the proposed model as SabrActive-model. In this sense, several simulations have been carried out with a specific code to quantify the impact of the variations of the main parameters of the model: the concentration and orientation of the active particles (squirmers). On the other hand, with the intention of knowing better the collective behavior of the active matter and, to a certain extent, to validate the results obtained

with the shell model, several computational simulations have been carried out with Ludwig code, which is an open source code based on the Lattice-Boltzmann method for simulating complex three-dimensional fluids. With this code it is possible to configure multiple models with different values of free energy and other parameters. The program allows for the creation of periodic boundary conditions, interaction between suspended colloids, liquid crystals and binary fluids. Therefore, there are two very well differentiated parts in this work, which is structured in six chapters.

Chapter 1 is a topic introduction that defines what are the active systems and the theoretical framework.

Chapter 2 explains the numerical methodology that we use to simulate the fluid that interact with active particles.

Chapter 3 shows some results of massive hydrodynamic simulations of suspensions of resolved model microswimmers using the Lattice- Boltzmann method.

In Chapter 4 the same simulation results from the previous chapter are used to calculate the mean and normalized energy spectrum.

In Chapter 5, starting from two vector fields, one of velocities and the other of individual orientations of the particles, a set of differential equations that include different terms with the interaction and self-action between the fields are proposed as generators of the system dynamics.

Finally in Chapter 6 the conclusions and future directions of the research.

[spa] El objetivo de esta tesis es estudiar el comportamiento colectivo de la materia activa mediante simulaciones numéricas, específicamente la dinámica de micronadadores en una suspensión semidiluida. Queremos explorar las capacidades de los ingredientes físicos básicos para generar estructuras emergentes en escalas mucho mayores que las de los agentes individuales. El objetivo es mejorar la comprensión del fenómeno de la turbulencia activa como un ejemplo paradigmático y fascinante de movimiento autoorganizado a gran escala en materia activa. Se presentan algunas simulaciones hidrodinámicas masivas de suspensiones de micronadadores, utilizando un código fuente abierto basado en los métodos Lattice-Boltzmann (LBM). Medimos el espectro de energía cinética estudiando los flujos de energía a través de las diferentes escalas en las que se descompone el sistema y también calculamos el desplazamiento cuadrático medio y el orden polar del sistema, demostrando que existen diferencias significativas en el comportamiento de los llamados pullers y pushers. Además, proponemos un modelo dinámico determinista para turbulencia activa, inspirado en modelos de turbulencia clásica. Se han realizado varias simulaciones computacionales utilizando la implementación de este modelo en un código específico, cuyo estudio numérico y analítico confirma la ley de potencia espectral predicha por la teoría y observada en las simulaciones LBM.