Microswimmer: Advances in Miniature Propulsion Systems for Nanoengineering

Chapter 1: Microswimmer

The ability to move in a fluid environment is what distinguishes a microswimmer from other types of microscopic objects. In the natural world, natural microswimmers can be found everywhere as biological microorganisms. Some examples of natural microswimmers are bacteria, archaea, protists, sperm, and animals that are rather small. The production of synthetic and biohybrid microswimmers has garnered a growing amount of interest ever since the turn of the millennium. Despite the fact that they have only been around for twenty years, they have already demonstrated that they have the potential to be utilized in a variety of biomedical and environmental applications.

There is not currently an agreement in the literature regarding the nomenclature of the microscopic objects that are referred to as microswimmers in this article. This is understandable given the relatively new nature of the area. Microswimmers, microscale swimmers, micro/nanorobots, and micro/nanomotors are perhaps the names that are used the most commonly to refer to these kinds of objects, among the many other names that are written about them in the scientific literature. It is possible that other common names are more descriptive. These phrases may include information on the geometry of the object, such as microtube or microhelix, its components, such as biohybrid, spermbot, bacteriabot, or micro-bio-robot, or its behavior, such as microrocket, microbullet, microtool, or microroller. In addition, researchers have given their particular microswimmers names, such as medibots, hairbots, iMushbots, IRONSperm, teabots, biobots, T-budbots, or MOFBOTS.

Robert Brown, a British biologist, made the discovery that pollen has a constant jiggling motion in water in the year 1828. He wrote about his discovery in an article titled A Brief Account of Microscopical Observations..., which led to an extensive scholarly discussion concerning the cause of this motion. This mystery was not solved until 1905, when Albert Einstein published his renowned article entitled über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen. This was the turning point that brought about the resolution of this mystery. In a way, Einstein was the world's first microrheologist because he not only determined the diffusion of suspended particles in quiescent liquids, but he also indicated that these discoveries could be utilized to measure the size of particles.

Ever since Newton developed his equations of motion, the mystery of motion on the microscale has emerged regularly in the history of science. This is one of the most famous examples of this phenomenon, and it is illustrated by a couple of articles that should be quickly reviewed. Osborne Reynolds is credited for popularizing the idea that the relative importance of inertia and viscosity for the motion of a fluid is dependent on particular aspects of the system that is being considered. This is a fundamental notion. Utilizing a dimensionless ratio of characteristic inertial and viscous forces, the Reynolds number Re, which was named after him, provides a quantitative representation of this comparison:

In this context, the Greek letter ρ denotes the density of the fluid, while the letter u represents a distinctive velocity of the system (for example, the velocity of a swimming particle), the letter l indicates a characteristic length scale (for example, the size of the swimmer), and the Greek letter μ represents the viscosity of the fluid. By considering water as the suspending fluid and utilizing the values that have been empirically found for u, it is possible to ascertain that inertia plays a significant role in the motion of macroscopic swimmers such as fish (Re = 100), whereas viscosity is the dominant factor in the motion of microscale swimmers such as bacteria (Re = 10−4).

The overwhelming significance of viscosity for swimming at the micrometer scale has significant repercussions for the technique that an individual employs when swimming. E. has provided a memorable discussion on this topic. M. Purcell, who provided the reader with an interactive experience into the world of microbes and theoretically investigated the conditions under which they move. In the first place, the propulsion tactics of large-scale swimmers frequently entail transferring momentum to the fluid that is surrounding them in periodic discrete events, such as the shedding of vortices, and coasting between these events through the use of inertia. The inertial coasting time of a micron-sized particle is on the order of one microsecond, which means that this method cannot be efficient for microscale swimmers such as bacteria. This is because of the high viscous damping they experience. It is estimated that a microbe traveling at a typical speed will travel around 0.1 angstroms (Å) in its coasting distance. Purcell came to the conclusion that the only forces that contribute to the propulsion of a microscale body are those that are exerted in the present moment on the body. As a result, a mechanism that converts energy in a consistent manner is needed.

The metabolism of microorganisms has been designed for continuous energy production, whereas the microswimmers (microrobots) that are totally artificial must receive energy from the environment because their on-board storage capacity is extremely restricted. As an additional consequence of the continual waste of energy, biological and artificial microswimmers do not obey the principles of equilibrium statistical physics. Instead, they require a description that is based on non-equilibrium dynamics. Purcell investigated the ramifications of a low Reynolds number from a mathematical standpoint by using the Navier-Stokes equation and removing the inertial terms:

where the vector {bold u} represents the velocity of the fluid and the vector {bold nabla p} represents the gradient of the pressure. As pointed out by Purcell, the equation that was produced as a result, known as the Stokes equation, does not include any explicit time dependence. This has a number of significant repercussions associated with the manner in which a suspended entity, such as a bacterium, is able to swim by periodic mechanical motions or deformations, such as those of a flagellum. Changing the rate of motion will affect the scale of the velocities of the fluid and of the microswimmer, but it will not change the pattern of fluid flow. This is the first point to make. The rate of motion is almost irrelevant for the motion of the microswimmer and the fluid that is surrounding it. Second, reversing the direction of motion in a mechanical system will simply result in the reversal of all velocities inside the system. Because of these features of the Stokes equation, the variety of swimming tactics that are currently possible is severely limited.

One example that can be used to illustrate this concept is a mathematical scallop, which is made up of two rigid components that are linked by a hinge. Is it possible for the scallop to swim if the hinge is opened and closed at regular intervals? That is not the case: the scallop will always return to its beginning location at the conclusion of the cycle, regardless of how the cycle of opening and shutting is dependent on the passage of time. This is the place where the famous remark Fast or slow, it exactly retraces its trajectory and it's back where it started was first uttered. Taking into consideration the scallop theorem, Purcell created many methods that can be utilized to manufacture artificial motion on a micro scale. This publication continues to be a source of inspiration for current scientific discussion. For instance, recent research conducted by the Fischer group at the Max Planck Institute for Intelligent Systems has experimentally proved that the scallop principle is only applicable to Newtonian fluids.

The motion of microswimmers is regulated by viscosity, which means that the motion is almost entirely driven by drag. This was covered in the part that came before this one. Additionally, the scallop theorem reveals that microswimmers are unable to rely on time-dependence for movement, which necessitates that they have more than one degree of freedom. Derivations for the parallel and normal components of drag on simple geometries in creeping flow can be found in recorded media and in published works, most notably in spheres: {upper F Subscript s p h e r e Baseline equals 6 pi mu u r} and spheroids with major and minor axis a, b: {upper F Subscript p a r a l l e l Baseline equals 6 pi left parenthesis StartFraction 4 plus a divided by b Over 5 EndFraction right parenthesis} {upper F Subscript p e r p e n d i c u l a r Baseline equals 6 pi left parenthesis StartFraction 3 plus 2 a divided by b Over 5 EndFraction right parenthesis} Due to the linear nature of the governing fluid equations, the superposition principle can be used to model more complex geometries, such as corkscrews, as a result of the analysis conducted by Purcell and possibly other researchers. As an illustration, the following shows the drag and torque that are associated with the helical coil:

{StartBinomialOrMatrix upper F Choose upper T EndBinomialOrMatrix equals Start 2 By 2 Matrix 1st Row 1st Column a 2nd Column b 2nd Row 1st Column b 2nd Column c EndMatrix StartBinomialOrMatrix u Choose omega EndBinomialOrMatrix}

{a equals 2 pi n sigma left parenthesis StartFraction xi Subscript parallel to Baseline cosine squared left parenthesis theta right parenthesis plus xi Subscript up tack Baseline sine squared left parenthesis theta right parenthesis Over sine left parenthesis theta right parenthesis EndFraction right parenthesis}

{b equals 2 pi n sigma squared left parenthesis xi Subscript parallel to Baseline minus xi Subscript up tack Baseline right parenthesis cosine left parenthesis alpha right parenthesis}

{c equals 2 pi n sigma cubed left parenthesis StartFraction xi Subscript parallel to Baseline sine squared left parenthesis theta right parenthesis plus xi Subscript up tack Baseline cosine squared left parenthesis theta right parenthesis Over sine left parenthesis theta right parenthesis EndFraction right parenthesis}

{xi Subscript parallel to Baseline equals StartStartFraction 2 pi mu OverOver ln left parenthesis StartFraction 0.36 pi sigma Over r sine left parenthesis theta right parenthesis EndFraction right parenthesis EndEndFraction comma xi Subscript up tack Baseline equals StartStartFraction 4 pi mu OverOver ln left parenthesis StartFraction 0.36 pi sigma Over r sine left parenthesis theta right parenthesis plus 0.5 EndFraction right parenthesis EndEndFraction}?

It is arctan {bold nabla p}0. While the scallop theorem necessitates the existence of more than one degree of freedom, it is essential to keep in mind that the motion of a straightforward corkscrew can be achieved through the application of external forces, such as magnetic forces.

Microswimmers come in a variety of distinct varieties, each of which is driven and actuated in a unique way. The swimming techniques of individual microswimmers as well as those of swarms of microswimmers have been investigated over the course of many years. Generally speaking, microswimmers are dependent on either external power sources, as is the case with magnetic, optical, or acoustic control, or they make use of the fuel that is present in their surroundings, as is the case with biohybrid or catalytic microswimmers. Typically, magnetic and acoustic actuation are compatible with in vivo microswimmer manipulation. Catalytic microswimmers can be specifically constructed to use in vivo fuels, and they can also be used to manipulate in vivo microswimmers. There have been some fascinating examples displayed, despite the fact that the application of optical forces in biological fluids or in vivo is a more difficult