Microswimmer
A microswimmer is a microscopic object with the ability to move in a fluid environment. [|Natural microswimmers] are found everywhere in the natural world as biological microorganisms, such as bacteria, archaea, protists, sperm, and microanimals. Since the turn of the millennium, there has been increasing interest in manufacturing [|synthetic] and [|biohybrid microswimmers]. Although only two decades have passed since their emergence, they have already shown promise for various biomedical and environmental applications.
Given the recent nature of the field, there is yet no consensus in the literature for the nomenclature of the microscopic objects this article refers to as "microswimmers". Among the many alternative names such objects are given in the literature, microswimmers, microscale swimmers, micro/nanorobots and micro/nanomotors are likely the most frequently encountered. Other common terms may be more descriptive, including information about the object shape, e.g., microtube or microhelix, its components, e.g., biohybrid, spermbot, bacteriabot, or micro-bio-robot, or behavior, e.g., microrocket, microbullet, microtool or microroller. Researchers have also named their specific microswimmers e.g., medibots, hairbots, iMushbots, IRONSperm, teabots, biobots, T-budbots, or MOFBOTS.
Background
In 1828, the British biologist Robert Brown discovered the incessant jiggling motion of pollen in water and described his finding in his article "A Brief Account of Microscopical Observations…", leading to extended scientific discussion about the origin of this motion. This enigma was resolved only in 1905, when Albert Einstein published his celebrated essay Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen. Einstein not only deduced the diffusion of suspended particles in quiescent liquids, but also suggested these findings could be used to determine particle size — in a sense, he was the world's first microrheologist.Ever since Newton established his equations of motion, the mystery of motion on the microscale has emerged frequently in scientific history, as famously demonstrated by a couple of articles that should be discussed briefly. First, an essential concept, popularized by Osborne Reynolds, is that the relative importance of inertia and viscosity for the motion of a fluid depends on certain details of the system under consideration. The Reynolds number, named in his honor, quantifies this comparison as a dimensionless ratio of characteristic inertial and viscous forces:
Here, represents the density of the fluid; is a characteristic velocity of the system ; is a characteristic length scale ; and is the viscosity of the fluid. Taking the suspending fluid to be water, and using experimentally observed values for, one can determine that inertia is important for macroscopic swimmers like fish, while viscosity dominates the motion of microscale swimmers like bacteria.
The overwhelming importance of viscosity for swimming at the micrometer scale has profound implications for swimming strategy. This has been discussed memorably by E. M. Purcell, who invited the reader into the world of microorganisms and theoretically studied the conditions of their motion. In the first place, propulsion strategies of large scale swimmers often involve imparting momentum to the surrounding fluid in periodic discrete events, such as vortex shedding, and coasting between these events through inertia. This cannot be effective for microscale swimmers like bacteria: due to the large viscous damping, the inertial coasting time of a micron-sized object is on the order of 1 μs. The coasting distance of a microorganism moving at a typical speed is about 0.1 angstroms. Purcell concluded that only forces that are exerted in the present moment on a microscale body contribute to its propulsion, so a constant energy conversion method is essential.
Microorganisms have optimized their metabolism for continuous energy production, while purely artificial microswimmers must obtain energy from the environment, since their on-board-storage-capacity is very limited. As a further consequence of the continuous dissipation of energy, biological and artificial microswimmers do not obey the laws of equilibrium statistical physics, and need to be described by non-equilibrium dynamics. Mathematically, Purcell explored the implications of low Reynolds number by taking the Navier-Stokes equation and eliminating the inertial terms:
where is the velocity of the fluid and is the gradient of the pressure. As Purcell noted, the resulting equation — the Stokes equation — contains no explicit time dependence. This has some important consequences for how a suspended body can swim through periodic mechanical motions or deformations. First, the rate of motion is practically irrelevant for the motion of the microswimmer and of the surrounding fluid: changing the rate of motion will change the scale of the velocities of the fluid and of the microswimmer, but it will not change the pattern of fluid flow. Secondly, reversing the direction of mechanical motion will simply reverse all velocities in the system. These properties of the Stokes equation severely restrict the range of feasible swimming strategies.
As a concrete illustration, consider a mathematical scallop that consists of two rigid pieces connected by a hinge. Can the "scallop" swim by periodically opening and closing the hinge? No: regardless of how the cycle of opening and closing depends on time, the scallop will always return to its starting point at the end of the cycle. Here originated the striking quote: "Fast or slow, it exactly retraces its trajectory and it's back where it started". In light of this scallop theorem, Purcell developed approaches concerning how artificial motion at the micro scale can be generated. This paper continues to inspire ongoing scientific discussion; for example, recent work by the Fischer group from the Max Planck Institute for Intelligent Systems experimentally confirmed that the scallop principle is only valid for Newtonian fluids.
Physics
As discussed in the previous section, the motion of microswimmers is controlled by viscosity, meaning the motion is drag-dominant. In addition, the scallop theorem demonstrates microswimmers are unable to rely on time-dependence for movement, requiring them to 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 literature, and recorded media, notably in spheres:and spheroids with major and minor axis a, b:
Due to the linear nature of the governing fluid equations, the superposition principle may be used to model more complex geometries, such as corkscrews, following the analysis of Purcell and others. For example, the drag and torque on the helical coil is as follows:
Where. It is important to note that while the scallop theorem requires more than one degree of freedom, external forcing allows for the motion of a simple corkscrew.
Types
Different types of microswimmers are powered and actuated in different ways. Swimming strategies for individual microswimmers as well as swarms of microswimmers have been examined down through the years. Typically, microswimmers rely either on external power sources, as it is the case for magnetic, optic, or acoustic control, or employ the fuel available in their surroundings, as is the case with biohybrid or catalytic microswimmers. Magnetic and acoustic actuation are typically compatible with in vivo microswimmer manipulation and catalytic microswimmers can be specifically engineered to employ in vivo fuels. The use of optical forces in biological fluids or in vivo is more challenging, but interesting examples have nevertheless been demonstrated.Often, researchers choose to take inspiration from nature, either for the entire microswimmer design, or for achieving a desired propulsion type. For example, one of the first bioinspired microswimmers consisted of human red blood cells modified with a flagellum-like artificial component made of filaments of magnetic particles bonded via biotin–streptavidin interactions. More recently, biomimetic swimming inspired by worm-like travelling wave features, shrimp locomotion, and bacterial run-and-tumble motion, was demonstrated by using shaped light.
A different nature-inspired approach is the use of biohybrid microswimmers. These comprise a living component and a synthetic one. Biohybrids most often take advantage of the microscale motion of various biological systems and can also make use of other behaviours characterising the living component. For magnetic bioinspired and biohybrid microswimmers, typical model organisms are bacteria, sperm cells and magnetotactic cells. In addition to the use of magnetic forces, actuation of bioinspired microswimmers was also demonstrated using e.g., acoustic excitation or optical forces. Another nature-inspired behavior related to optical forces is that of phototaxis, which can be exploited by e.g., cargo-carrying microorganisms, synthetic microswimmers or biohybrid microswimmers. A number of recent review papers are focused on explaining or comparing existing propulsion and control strategies used in microswimmer actuation. Magnetic actuation is most often included for controlled in vivo guiding, even for microswimmers which rely on a different type of propulsion. In 2020, Koleoso et al. reviewed the use of magnetic small scale robots for biomedical applications and provide details about the various magnetic fields and actuation systems developed for such purposes.
Strategies for the fabrication of microswimmers include two-photon polymerisation 3D printing, photolithography, template-assisted electrodeposition, or bonding of a living component to an inanimate one by exploiting different strategies. More recent approaches exploit 4D printing, which is the 3D printing of stimuli-responsive materials. Further functionalization is often required, either to enable a certain type of actuation, e.g., metal coating for magnetic control or thermoplasmonic responses, or as part of the application, if certain characteristics are required for e.g., sensing, cargo transport, controlled interactions with the environment, or biodegradation.
Microswimmers can also be categorized by their propulsion methods, and two primary methods are used: self-propulsion and external-field propulsion. In self-propulsion, a chemical fuel is coated over the robot that reacts with the liquid environment to create bubbles that propel the robot. External-field propulsion offers more variety, using optical, magnetic, acoustic, or electric fields. External field is better suited for biological applications as it will not need chemical fuels that produce pollutants that may be harmful to the host that the microswimmers are servicing including films and chemicals that may be biocompatible. This propulsive method also provides higher spatial resolution and more controllability, with recent advancements enabling three-dimensional movement enhancing the flexibility and functionality of microswimmers.