Computational study of the emergent behavior of micro-swimmer suspensions

Abstract

It is known that active particles induce emerging patterns as a result of their dynamic interactions, giving rise to amazing collective motions, such as swarming or clustering. Here we present a systematic numerical study of self-propelling particles; our main goal is to characterize the collective behavior of suspensions of active particles as a result of the competition among their propulsion

activity and the intensity of an attractive pair potential. Active particles are modeled using the squirmer model. Due to its hydrodynamic nature, we are able to classify the squirmer swimmer activity in terms of the stress it generates (referred to as pullers or pushers). We show that these active stresses play a central role in the emergence of collective motion. We have found that hydrodynamics drive the coherent swimming between swimmers while the swimmer direct interactions, modeled by a Lennard-Jones potential, contributes to the swimmers' cohesion. This competition gives rise to two different regimes where giant density fluctuations (GDF) emerge. These two regimes are differentiated by the suspension alignment; one regime has GDF in aligned suspensions whereas the other regime has GDF of suspensions with an isotropic orientated state. All the simulated squirmer suspensions shown in this study were characterized by a thorough analysis of global properties of the squirmer suspensions as well as a complementary cluster analysis.

Active matter refers generically to systems composed of self-driven units, active particles, each capable of converting stored or ambient free energy into systematic movement. Examples of active systems are found at all length scales and could be classified in living and nonliving systems such as microorganisms, tissues and organisms, animal groups, self- propelled colloids and artificial nanoswimmers. Specifically, at the micro and nano scale we find an enormous range of interesting systems both biological and artificial; e.g. spermatozoa that fuse with the ovum during fertilization, the bacteria that inhabit our guts, the protozoa in our ponds, the algae in the ocean; these are but a few examples of a wide biological spectrum. In the artificial world we have self- healing colloidal crystals and membranes as well as self- assembled microswimmers and robots. Experiments in this field are now developing at a very rapid pace and new theoretical ideas are needed to bring unity to the field and identify "universal" behavior in these internally driven systems.

One important feature of active matter is that their elements can develop emergent, coordinated behavior; collective motion constitutes one of the most common and spectacular example. Collective motion is ubiquitous and at every scale, from herds of large mammals to amoeba and bacteria colonies, down to the cooperative behavior of molecular motors in the cell. The behavior of large fish schools and the dance of starling flocks at dusk are among the most spectacular examples. From a physical perspective collective motion emerges from a spontaneous symmetry breaking that allows for long-range orientational orden The different mechanisms responsible for such symmetry breaking are still not completely understood. We have performed a systematic numerical study of interactive micro-swimmer suspensions building on the squirmer model, introduced by Lighthill. Since the squirmer identifies systematically the hydrodynamic origin of self-propulsion and stress generation it provides a natural scheme to scrutinize the impact that the different features associated to self-propulsion in a liquid medium have in the collective dynamics of squirmer suspensions. In this abstract we describe the simulation scheme and how squirmers are modeled, then some of the main results are discussed and finally we conclude emphasizing the main implications of the results obtained.

Los sistemas activos se definen como materiales fuera del equilibrio termodinámico compuestos por muchas unidades interactuantes que individualmente consumen energía y colectivamente generan movimiento o estreses mecánicos. Ejemplos se pueden encontrar en un enorme rango de escalas de longitud, desde el mundo biológico hasta artificial, incluyendo organismos unicelulares, tejidos y organismos pluricelulares, grupos de animales, coloides auto-propulsados y nano-nadadores artificiales. Actualmente se están desarrollando experimentos en este campo a un ritmo muy veloz, en consecuencia son necesarias nuevas ideas teóricas para traer unidad al campo de estudio e identificar comportamientos “universales” en estos sistemas propulsados internamente.

El objetivo de esta tesis es el estudiar mediante simulaciones numéricas, el comportamiento colectivo de un modelo de micro-nadadores. En particular, el modelo de squirmers, donde el movimiento del fluido es axi-simétrico. Existen estructuras coherentes que emergen de estos sistemas así que, el entender si las estructuras coherentes son generadas por la firma hidrodinámica intrínseca de los squirmers individuales o por un efecto de tamaño finito se vuelve algo de primordial importancia. Nosotros también estudiamos la influencia que tiene la geometría en la aparición de estructuras coherentes, la interacción directa entre las partículas, la concentración, etc.