Self Propulsion

Self propulsion breaks equilibrium by locally generating forces, driving the swimmer. Important is that the drive is coupled to the particle, and not an external field. Thus a swimming sperm cell is a microswimmer, a sedimenting polymer is not. Sometimes, the activity due to swimming can be mapped to an elevated effective temperature, but more often than not, the activity manifests itself in phenomena inexplicable in equilibrium physics. Often however, equilibrium concepts and analogies can be used to depict what is going on. For example, collections of self-propelled disks spontaneously "phase separate", motile tissues undergo "glass-like arrest" as density or adhesion increases, or non-equilibrium surface accumulation occurs. The living matter group studies microswimmers in many different forms, ranging from generic self-propelled particles and filaments to hydrodynamic symulations of sperm and ciliated microswimmers.

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Further reading:

Physics of microswimmers—single particle motion and collective behavior: a review

Self Propelled Filaments
J. Elgeti, IBI-5

Adding flexibility to self-propelled particles leads to a new degree of freedom for the particle to explore. Self-propelled semiflexible fillaments can serve as a minimal model for flexible self-propelled particles. By themselvs, the fillaments show an interesting coiling transition at high propulsive strength, where the fillament coils up into a spiral shape. When a rigid load is attached to the front of the filament an even richer phasediagram is observed, with filaments beating, rotating, and pushing the load through the fluid.

Further reading:

Self-propelled worm-like filaments: spontaneous spiral formation, structure, and dynamics

Dynamics of self-propelled filaments pushing a load

Emergence of Metachronal Waves in Cilia Arrays

Propulsion by cilia is a fascinating and universal mechanism in biological organisms to generate fluid motion on the cellular level. Cilia are hair-like organelles, which are found in many different tissues and many uni- and multi-cellular organisms.  Assembled in large fields, cilia beat neither randomly nor completely synchronously  -- instead they display self-organization in the form of metachronal waves (MCWs). The main questions are how the individual cilia interact with the flow field generated by their neighbours and synchronize their beats for the metachronal wave to emerge, and how the properties of the metachronal wave are determined by the geometrical arrangement of the cilia, i.e. cilia spacing and beat direction. 

We address these issues by using large-scale computer simulations of a mesoscopic model of two-dimensional cilia arrays in a three-dimensional fluid medium.We show that hydrodynamic interactions are indeed sufficient to explain the self-organization of MCWs, and study beat patterns, stability, energy expenditure and transport properties. We find that MCW strongly increase both propulsion velocity and efficiency -- compared to cilia all beating in phase. This can be a vital advantage for ciliated organisms, and may be interesting to guide biological experiments as well as the design of efficient microfluidic devices and artificial microswimmers.

Further reading:

Emergence of metachronal waves in cilia arrays

Sperm Hydrodynamics near Surfaces

The sperm cell is probably the best-known example of a microscopic swimmer. Motion is generated by a snake-like motion of its tail, called the flagellum, which pushes the head (containing the genetic material) forward. This motion is essential for the sperm to reach the egg. Sperm fall into the general class of microswimmers called "pushers", because the forward force is generated in the rear part of the swimmer.

In confinement, sperm are found to accumulate at the walls and to swim in circles. Mesoscale hydrodynamics simulations can unravel the physical mechanism of this behavior. The reason for the attraction to the wall is the hydrodynamic flow field generated by the beating tail. The circling motion can be traced back to the chiral shape of sperm.

Further reading:

Hydrodynamics of Sperm Cells near Surfaces

Self-Propelled Nanorods near Surfaces

Self-propelled rods can also be seen as a generic model for a large class of self-propelled elongated particles, in case the details of the propulsion mechanism are not important. Passive elongated particles are repelled from a planar wall due to reduced entropy. Does this also apply to rod-like swimmers?

Computer simulations show that self-propelled rods actually align with and accumulate at the wall. This effect increases with increasing swimming velocity and with increasing rod length. It can be traced back to the difficulty of an aligned particle to wiggle itself free from the wall. There is an interesting analogy of the swimming trajectories with the conformations of semi-flexible polymers.

Further reading:

Microswimmers near surfaces

Self-propelled rods near surfaces

Cooperation of sperm in two dimensions

Sperm motility is important for the reproduction of animals. Sperm cells are propelled in a fluid by a snake-like beating of their tails. The sperm motion occurs in the regime of low Reynolds numbers, where inertia effects are negligible. The beating tails not only propel the sperm through the fluid, but also create flow fields through which sperm interact with each other. We study the hydrodynamic interaction and cooperation of sperm embedded in a two-dimensional fluid by using multi-particle collision dynamics (MPC), a particle-based mesoscopic simulation technique. Two effects of hydrodynamic interaction are found, synchronization and attraction. With these hydrodynamic effects, cooperating sperm clusters are formed in system at high concentrations. A dynamic balance between cluster formation and break-up results in a stable cluster-size distribution, which depends on the number density of sperm and on the distribution of beating frequencies of the individual sperm. The average cluster size shows a power-law dependence on the width of the frequency distribution.

Last Modified: 25.01.2023