Helical motion can be observed on all length scales, which affects a variety of life processes, including biological reproduction, foraging, locating favorable environments and detecting nutrient gradients. The development of artificial swimmers that can perform helical motions not only has a wide range of applications and improves our understanding of the laws and mechanisms of biological swimmers' motions, but also contributes to the design of novel robots and improves the efficiency of robotic motions. In this paper, we first summarize artificial swimmers that can perform helical motions in artificial systems designed by using the rotation and flapping of microbial flagella/cilia as an inspiration source. Then diverse artificial swimmers that perform helical motions in recent years are introduced by different sources of driving force. Finally, the unresolved questions and prospect are tentatively presented in this field.
Contents
1 Introduction
2 Helical motion and bionic design of biological swimmers
2.1 Flagella-driven swimmers
2.2 Cilia-driven swimmers
3 Driving forces and motion control of helical motion of artificial swimmers
3.1 Helical motion driven by external physical fields
3.2 Helical motion driven by interfacial/surface tension force
Active Matter can spontaneously convert its own internal or environmental energy into mechanical force and motion through nonlinear action far from equilibrium[1]. Self-propelled swimmers are one of the main forms of active matter, which move autonomously in fluid environments in various forms of motion, such as sliding, jetting and spiral swimming[2][3][4]. Self-propelled swimmers cover a wide range, from prokaryotic cells, eukaryotic cells (such as bacteria, algae, leukocytes, etc.) To various artificial swimmers, and the motion mode of swimmers is generally reflected in two-dimensional (2D) and three-dimensional (3D) spiral trajectories[5,6].
In biological systems, spiral motion is the mode of motion adopted by many microorganisms, because the interaction between individual organisms and the environment is dominated by viscous forces at low Reynolds numbers.At this time, the directional movement of microswimmers should follow the Scallops Principle, in which the directional movement of most microswimmers is realized by the accumulation of multi-cycle micro-spiral Non-reciprocal trajectories[7][8]. The velocity of a biological swimmer can be generally decomposed into a rotational velocity vector and a translational velocity vector. When the individual velocity is constant, if the rotation velocity vector is parallel or perpendicular to the translation velocity vector, the swimming trajectory is a straight line or a circle, respectively. Otherwise its trajectory is a spiral path with its central axis parallel to the direction of net displacement of the body[9]. From the above kinematic analysis, it can be seen that spiral trajectory is a ubiquitous biological motion mode. The non-reciprocity of spiral motion endows spiral motion with efficient motion ability, which is helpful for biological swimmers to locate environmental stimuli and quickly adjust their direction of advance in complex environments so as to seek advantages and avoid disadvantages, and is essential for many biological functions such as population distribution, nutrient gradient detection, predator avoidance and so on[10][11⇓~13].
The design of artificial swimmers with helical motion patterns in abiotic systems is an important direction in the research field of chemistry and materials science. Generally speaking, the successful preparation of "swimming body" by artificial methods depends on its ability to spontaneously convert environmental or internal stimuli (energy) into driving force. Although the biological swimmer and the artificial swimmer are similar in morphology, their propulsion mechanisms have many types. The classification, induction and discussion of various propulsion mechanisms can inspire the proposal of new mechanisms for the directional motion of the bionic swimmer and expand the research ideas of motion control. The controlled spiral motion of artificial swimmers has important applications in targeted drug delivery, bioengineering, environmental monitoring, and remediation[14,15].
In this paper, we first summarize the motion modes and phenomenological laws of various artificial swimmers based on biological swimmers, and then introduce various driving forces such as external physical fields, interface/surface tension, and chemical forces to discuss their driving principles and their respective advantages and limitations. Finally, the difficulties, challenges and future research directions of spiral motion design and motion mechanism of artificial swimmers are summarized and prospected.
2 Spiral Motion and Biomimetic Design of Biological Swimmer
In 1901, Jennings proposed that the rotation of organisms on the long axis and the resulting spiral path are of great biological significance[16]. Any geometrically irregular organism can produce net motion along the axial direction through its chirality[17,18]. Most of the biological swimmers are propelled by their chiral appendages (such as flagella, cilia, etc.) To swim along the spiral trajectory. Biologists have put forward the preliminary theory of biological spiral motion through the study of related driving mechanisms, which has promoted the research progress of microbial spiral chemotaxis, search and orientation[19].
In recent years, researchers have carried out extensive studies on the characteristics and functions of ciliated/flagellated motility of biological swimmers in nature, and their motility mainly depends on the propulsion of helical flagella or cilia.It is of great significance to prepare biomimetic micro-swimmers with simple process, efficient propulsion and precise navigation by analogy in the directional transportation of drugs and environmental repair[20]. This section will introduce the swimmer body, which is inspired by the flagellar and ciliary structures.
2.1 Biomimetic flagellum driven swimmer
Many tiny biological swimmers drive their own movement by rotating their spiral flagella, which push or pull microbial cells in a form similar to propellers, and can achieve efficient and precise movement of organisms themselves[21].
The morphology and number of flagella can regulate the motor function of organisms, and cells with single flagella control the direction of swimming by changing the rotational chirality of flagella. Counterclockwise (CCW) rotation of the flagellum pushes the cell forward; Clockwise (CW) rotation of the flagellum pulls the cell backward (Figure 1A)[22].
Most monoflagellar swimmer flagella flap roughly in the same plane, but euglena gracilis has a unique "rotating lasso" non-planar flagellar flapping pattern (Fig. 1b)[23,24]. When the flagellum is twisted into a double ring and distributed on both sides, the euglena moves forward. When the flagellum is twisted into a single ring extending in front, the Euglena performs a rotational movement[21]. Because the rotating flagellum has a non-reciprocal driving force to drive the organism to rotate and translate at the same time, the rotation of the flagellum along the main axis of the cell body enables the cell to optimize the direction of progress and locate a favorable living environment[25].
Escherichia coli and Salmonella belong to bacteria with 4 to 8 flagella, each of which is connected to a molecular motor that can rotate independently[26]. When the flagellar motor makes a CCW rotation, the flagellum forms a bundle and pushes the bacteria forward in a spiral. When one or more motors perform CW rotation, the swimmer will change the swimming direction in the form of "tumbling" in a short time (Figure 1C)[27].
Unlike the "tumbling" mode used by E. coli and others, V. alginolyticus uses a three-step cyclic (forward-backward-flick) swimming mode. As shown in Fig. 1 d, when the bacteria swim forward, the individual can randomly choose a new swimming direction by shaking the flagellum. The unique flicking motion in this process "guides" the cell to a new direction, effectively achieving a random change in bacterial swimming direction[28]. Compared with the "rolling" mode of bacteria, the "flicking" mode responds faster and can achieve rapid chemotactic movement behavior. This repositioning mechanism is very beneficial to the life of marine microorganisms in the transient environment of the ocean[27][29].
Inspired by the spiral Bacterial Flagellum, Nelson et al. Reported the spiral forward movement of an Artificial Bacterial Flagellum (ABF) in 2009[30]. They consist of a helical tail and a thin soft magnetic "head", similar in shape to the biological swimmer, as shown in Figure 2a. The external magnetic field can rotate the magnetic head or the magnetic flagellum, and the hydrodynamic interaction between the helical tail and the fluid converts the rotational motion into a motional driving force, and the ABF forward and backward motion mode is changed by reversing the direction of the magnetic field. These small spiral swimmers use a motion method similar to the biological swimming method, and can be widely used in the medical and biological fields as a wireless manipulation microrobot[31].
Another type of swim-type robot is inspired by the oscillatory propulsion of sperm, relying on asymmetric shape deformation to drive the net displacement of the system. For example, Ghosh and Fischer prepared a nanohelix structure coated with ferromagnetic materials by vapor deposition, and designed a magnetic-field-driven artificial swimmer with navigation accuracy of micron level (Fig. 2b)[32]. Bibette et al. Prepared artificial flagella with magnetically driven linear colloidal particle chains, which could drive and activate the "flagella" to promote the movement of red blood cells by controlling the external magnetic field[33]. Zhang et al. Used Spirulina as a template to prepare a magnetic helical microswimmer with enhanced propulsion speed, which has excellent swimming performance at low Reynolds number (Fig. 2C)[34].
Sitti et al. Reported a magnetic microswimmer with a soft double tail, using a uniform magnetic field parallel to the direction of motion and a sinusoidally varying orthogonal component to drive and manipulate the planar waves of two soft flagella to swim forward and backward (Figure 2D)[35]. Recently, researchers have directly used biological motors as the main component or modification basis of functional swimming bodies through bio-artificial composite methods to push swimming bodies to produce motion[36].
When biological-artificial swimmers move, they can be controlled not only by the external field strength, but also by the cells and microorganisms themselves, and they can sense and respond to changes in the external environment[37]. For example, flagellum-driven bacteria asymmetrically attached to colloidal beads can generate propulsion[38]. Bio-artificial composite swimmers driven by the flagella of sperm or attached artificial spiral flagella (Fig. 2 e ∼ G) can be autonomously oriented by biological interactions with the surrounding environment and other cells, or externally controlled and monitored by artificial sensors and actuators[39,40].
A significant advantage of using biological motors is that it integrates various functions and motility of organisms into artificial systems, so that the complex system has many functions such as movement and metabolism of biological motors[41]. Bio-artificial composite swimmer not only has the ability of autonomous perception and navigation, but also can self-repair and self-assemble in complex environments, and is more suitable for movement in living organisms, making full use of the sensing and driving capabilities of biological cells[42].
Although the addition of biological motors provides artificial swimmers with more complex and powerful motor accessories, it can play an advantage in the biological environment. However, the stability of these accessories is relatively poor, the duration of continuous movement is relatively short, the operation in the practical application process is more complex, and the synthesis technology is not mature enough, which limits their development and application[40].
2.2 Biomimetic cilium driven swimmer
In bacteria and other microorganisms, cilia are essential for locomotion, and cilia can perform many biological functions through beating, such as liquid transport (such as the clearance of mucus in animal trachea) and self-propulsion of microorganisms[43]. Cilia are short hair-like nanostructures wrapped around the cell body, and by flapping thousands of cilia on the cell body, ciliates can achieve spiral swimming in water. Unlike the undulating motion of the flagellum, the cilium exhibits a bending motion with a characteristic power stroke and recovery stroke that drive fluid flow[44].
A single cilium generates a net propulsive force by generating an asymmetric waveform, and the periodic flapping movement of a large number of cilia can emerge the collective behavior of cilia (ciliary wave) on the body surface, which can better drive the overall movement of the fluid around the individual, thus pushing back the rapid movement of the organism. Ishikawa et al. Used fluid mechanics to prove that the collective motion behavior of cilia can achieve the best propulsion efficiency[45]. Under the stimulation of Ca2+, tetrahymena can show different spiral swimming patterns, including backward swimming along the right-handed spiral path and forward swimming along the left-handed spiral path, which are determined by the flapping pattern of cilia (Fig. 3A)[46].
In 2016, Choi et al. Proposed an artificial ciliated micro-robot (Fig. 3B) that simulates the beating of Paramecium cilia through non-interactive driving. The ciliated structure is a two-photon polymerization structure using nickel deposition.The power stroke and recovery stroke are programmed by gradually changing the magnetic field direction and strength, and when driven by the magnetic field, the cilia move in a non-reversible manner, resulting in a net propulsive force[47]. The mode of motion is controlled by the shape parameters of the cilia (e.g., cilia length and cilia angle), as well as the field strength and field angle, through which the position and orientation of the microrobot can be precisely controlled.
The research on biomimetic artificial cilia motion is of great significance in the field of bioengineering and robotics[48]. However, due to the instability of these hair-like appendages in fluid propulsion, the functional research directions of bionic ciliated robots at this stage are mainly divided into material mixing, particle transport and fluid pumping, and the motion ability is very limited, so it is very important to improve the motion efficiency of micro robots[49].
The bionic swimmer can be driven to produce spiral motion with good orientation, strong penetration and low invasion by the synergistic effect of external physical field and fluid mechanics[50,51]. However, the motion mechanism of bionic swimming body is essentially different from that of biology, especially the adaptive mediation ability is weak. The motion of bionic swimming body depends on the driving force provided by the biochemical reaction network in vivo.Biochemical reaction networks enable biological swimmers to sense the environment and communicate with each other so that they have strong adaptive ability and complex motor functions (such as escape and hunting).
3 Driving Force and Motion Control of Spiral Motion of Artificial Swimming Body
The efficient biological motors created by nature can move in complex environments, and the complex motion mechanisms of real organisms can provide inspiration and design methods for the development of artificial swimmers and controllable devices. Bibette et al. Proposed two conditions to realize the controllable swimming or motion of an artificial swimmer: first, the supply of energy and its conversion into the mechanical motion of the system[33]; Second, the sequence of transformations must be cyclic and not time-reversible. In recent years, researchers have prepared many artificial swimmers that can imitate the trajectory of biological motion, and proposed a variety of actuation methods in the design and motion behavior control of artificial swimmers.
In this paper, the driving force is divided into three categories according to the energy source of the spiral motion of the artificial swimmer: one is the external differential physical field force, including AC electric field, magnetic field, light and ultrasound; The second type is interfacial/surface tension; The third category is driven by chemical force, such as chemo-mechanical effect.
3.1 Helical motion driven by external physical field
Without considering the shape and Brownian motion of the artificial swimmer, the swimmer can only move forward or backward in a constant physical field, and will not show a complex trajectory. However, when there are differences in the physical field of the environment, swimmers will adjust their motion parameters (speed and direction, etc.) According to the intensity or direction of the physical field to adapt to changes in the environment, so their motion behavior will become rich.
3.1.1 Electric field driven swimmer
As an external energy source, the environmental electric field can not only drive the artificial swimmer to move through a variety of mechanisms, but also control the position of the swimmer. There are usually two propulsion mechanisms for the motion of Janus particles driven by alternating current, namely self-dielectrophoresis (sDEP) and induced charge electrophoresis (ICEP)[52]. Their basic principles are to realize asymmetric electrostatic force or to produce asymmetric fluid flowing locally around an electromagnet by constructing a local electric field gradient, respectively. Miloh et al. Proposed that sDEP propulsion generally occurs in a high-frequency AC electric field environment, that is, the localized electric gradient caused by the asymmetric dielectric constant of the two hemispheres of the Janus particle tends to interact with the induced dipole moment, resulting in a net electrostatic force to drive the Janus particle forward[53]. ICEP is induced by induced charge electroosmosis (ICEO) flow in a low frequency AC electric field environment[54]. Compared with sDEP, ICEP can control the movement route of Janus particles more precisely and make the particles move along the set route.
In 2019, Bharti et al. prepared a spherical micro-swimmer (as shown in Figure 4A), the surface of which is covered with metal patches of different shapes and sizes, and the swimmer can move between two electrodes by controlling the direction of the AC electric field[7]; Every time the microswimmer moves towards the electrode, it shows a spiral trajectory motion, and the asymmetry of the metal patch of the particle determines the direction of the particle motion[7,55]. They described the particle motion according to the kinematic equation of spiral trajectory, where the radius is R, the angular velocity is , the linear velocity is u, and the positive and negative values of the angular frequency and linear velocity will lead to four different trajectories of the particle in the experiment. For example, when > 0 and U > 0, the particle moves along a right spiral trajectory in the positive direction.
Recent work by Bharti et al. Has found that the geometry of the spiral trajectory of this spherical particle can be determined by the geometry of the patch and the particle[56]. There is a clear control law between the geometry of the metal coverage on the ellipsoid (Fig. 4 B) and the behavior of the active particle, such as linear, circular, and spiral motion. The results show that the pitch and diameter of the spiral trajectory of the ellipsoidal particle are related to the characteristics of the metal patch with asymmetric longitudinal and transverse axes of the particle: with the increase of the longitudinal symmetry of the patch, the pitch of the spiral generally decreases; As the transverse symmetry increases, the helix diameter decreases.
As shown in Fig. 5, Li et al. Proposed a new type of electroswimmer with asymmetric shape and controllable sDEP and ICEP motion behavior in different frequency ranges[52]. The electrodynamic swimmer generates a local asymmetric field gradient through an artificially set spatial asymmetric topological defect, which can drive the electrodynamic swimmer to rotate and spiral in three-dimensional space. Compared with the work of Bharti et al., the swimmer designed by shape defects can overcome the limitations of materials and synthetic molds, which provides a novel idea for the structural design of new electrodynamic swimmers and is of great significance for the motion control of electrodynamic swimmers[53].
3.1.2 Magnetic field driven swimmer
Magnetic field is widely used as the driving force of artificial swimmers because of its non-invasive, high penetration and strong controllability. The behavior of swimmers can be controlled by controlling the field strength and direction[57]. In the bionic design of biological swimmers, we introduce a variety of magnetic field-driven bionic swimmers with spiral or flexible structures, which can adjust their tails or heads at any time to respond to changes in the magnetic field and thus propel forward. In addition, in the field of micro-robots, researchers have also fabricated a variety of magnetically driven spiral motion robots.
Neeves et al. Explored a motion mechanism of rotating coupling of colloidal microwheels driven by a planar rotating magnetic field[58]. By changing the phase angle of the applied magnetic field, the direction of motion of the microwheel can be quickly and simply controlled, making motion control immediate and precise (Figure 6A). The experimental results show that the targeting and obstacle breaking function of the spiral motion generated by the micro-wheel controlled by the rotating magnetic field are better than those of the linear motion. Since both the assembly and translation of the microwheel are manipulated by a weak, nanoscale external magnetic field that does not decay in the tissue, it can be used for drug delivery in occluded vessels away from the external surface of the body.
In most previous studies, artificial swimmers lacked the ability to actively twist their magnetic anisotropy as they moved. Therefore, these swimmers can change their direction of motion only if they change the direction of the applied magnetic field, which limits their autonomy and ability to adapt to the environment. Gracias et al. Designed a new class of microswimmers with heterogeneity in shape and composition (Fig. 6 B), with the ability to swim forward and backward in a precessing magnetic field, which can achieve multiple modes of motion[59]. The asymmetric swimmer can change the direction of motion without changing the direction of rotation of the magnetic field, and this phenomenon occurs regardless of the direction and frequency of rotation of the applied magnetic field. The main advantage of magnetic field propelled swimmer is its high degree of control and long time operation, but this method has limitations in small range operation and special driving devices[60].
3.1.3 Optically driven swimmer
As one of the control force sources of the artificial swimming body, the light is easy to obtain and control, and the precise motion control and speed adjustment of the swimming body can be remotely carried out by turning on/off the light source or adjusting the light intensity without any physical connection with the swimming body[61]. Efficient motion of a swimmer under light activation can be achieved indirectly by changing its immediate environment or by directly inducing an asymmetric gradient in the photoactive particle itself[62].
Wang et al. developed a photosensitive AgCl-Janus swimmer. Under strong light irradiation, ion diffusion electrophoresis near the AgCl particle pushes the Janus particle to move away from the reaction (AgCl) side, and the light can induce the Janus particle to move away from the gravity axis in a spiral manner (Fig. 7A)[63]. However, this kind of AgCl micromotor has the disadvantages of short life and long response time. With the passage of time, its active chemical substance (AgCl) is continuously consumed, so it can not be reused or used continuously.
Santer et al. Proposed a mechanism of light-induced self-propelled motion of porous silica particles[64]. Under blue light conditions, when porous silica particles are immersed in an aqueous solution containing a photosensitive surfactant, a photoisomerization reaction occurs within the particles, and the hydrophilic cis-isomer formed within the pores expels the liquid from the colloid, resulting in a local light-induced diffusion-infiltration (LDDO) flow around the pores, which pushes the colloidal particles to move (Fig. 7B). This mechanism can simply control the motion mode by the intensity and wavelength of external light, thus realizing a variety of motion trajectories.
3.1.4 Ultrasonically driven swimmer
Recently, researchers have become interested in using ultrasound as a driving energy source for artificial swimmers, which is non-invasive, precisely tunable, and easy to operate[61]. Since the motion of micro- and nano-particles propelled by the acoustic field is insensitive to the chemical composition of the environmental medium, it can be widely used in biological environments with high ionic strength. As an external energy source for propulsion, the motion of the swimmer can be manipulated by adjusting the frequency/direction of the ultrasound or by on-off control of the ultrasound source[65].
Bishop et al. Reported a method to remotely control the motion behavior of chiral colloidal swimmers by ultrasound[66]. They designed and fabricated colloidal particles with a distorted star structure (Figure 8 a), studying their motion behavior in the plane of a uniform acoustic field at megahertz frequencies. In the experiment, it is observed that the swimmer can make a stable spiral motion under the action of the acoustic field, and the direction of rotation is closely related to the chiral shape of the colloid. The experimental results can be explained by steady flow and ultrasound-actuated hydrodynamic models. This study presents a method to control the complex motion trajectory of a swimmer through the combination of the system shape and the ultrasonic field vector.
Wang et al. Studied the motion behavior and rotation dynamics of metallic microrods in in-plane orbits in megahertz ultrasound[67]. The experimental results show that these metallic microrods can move along the tight helical trajectory near the resonant ultrasonic frequency. The possible reason for the rotational motion behavior is that the inhomogeneity of the metal microrod leads to the uneven distribution of force and torque on the nodal surface of the metal rod, thus rotating in the plane (Fig. 8 B). The results of this study lay the foundation for the design and development of swimmers with biocompatible energy sources and controllable motion.
The existing research work on ultrasonic propulsion of swimming body has designed a variety of motion modes, but there are still some shortcomings, for example, the motion mechanism of the swimming body propelled by the acoustic field can not be accurately explained, and the behavior of the swimming body in practice is difficult to predict, which hinders the wide application of the acoustic propulsion of swimming body[66,67].
A lot of basic work has been done on the use of physical fields (electric field, ultrasound, etc.) To drive the swimmer to spiral motion, which has important guiding significance for the design of micro-robots sailing in complex environments. However, there are the following problems: the preparation process of artificial swimming body is complex, the preparation process requirements are high, the special shape and composition usually need to be accurately controlled, the lack of a simple and reliable manufacturing technology, the inability to move autonomously without continuous external energy supply, the lack of controllability and remote interaction in practical applications, and so on. Considering the complexity of physical and chemical conditions in the real environment, there are some difficulties in the initiation and termination of swimming body movement and real-time position tracking.
An alternative way to propel the motion of a swimmer in an artificial system with constant or no external field is by changing only the asymmetry of the swimmer geometry or the interaction of the swimmer with the fluid surface,The motion of a swimmer is driven by the coupling of the fluid flow and the local field gradient, which can be achieved by changing the physical or chemical asymmetry of the swimmer in general[68]. The symmetry breaking of the surface physical field caused by the Marangoni effect and the solute effect can push the artificial swimmer to move in a variety of modes, such as straight lines, curves, and spirals. In this subsection, we focus on the spiral motion behavior of the swimmer.
3.2.1 Marangoni effect driven swimmer
The shear force generated by the Marangoni effect in the interface action is the most common to push the swimmer to spiral motion. The asymmetry in the shape of the swimmer leads to translation-rotation coupling in the hydrodynamic sense or anisotropy in the propulsion mechanism[69].
In 1997, Yoshikawa et al. Observed that some camphor sheets could produce translational and rotational motion on the water surface in the autonomous motion experiment of camphor sheets (Fig. 9)[41]. The asymmetry in the shape of the camphor sheet determines the change in the direction of rotation of the motion from clockwise to counterclockwise. They believe that the driving force of the translation and rotation of the camphor sheet is the Marangoni effect induced by the change of the surface tension of the interface composed of "air-solvent-high concentration liquid phase around the camphor sheet", but the complexity of the flow field environment interferes with the control and real-time tracking of the swimming body's motion behavior[70].
Maass et al. Have shown that the trajectory of an artificial swimmer in a system without chiral elements can be controlled simply by changing the temperature of its environment[71]. The nematic order and surface flow interaction within each droplet can produce a rotational torque, resulting in a two-dimensional circular motion of the droplet. When the liquid crystal droplet is heated to 35 ℃, the molecules inside the droplet become disordered, resulting in the disappearance of the rotational torque, and the droplet returns to the swimming state. As shown in Fig. 10, this transition of motion pattern can be systematically and reversibly regulated with temperature.
Sano et al. first reported an artificial microswimmer with controllable helical motion chirality under uniform external field conditions in the study of chiral dynamics of swimming droplet motion (Fig. 11)[72]. They prepared photoresponsive cholesteric liquid crystals (CLC) by doping chiral molecular motors in achiral nematic liquid crystals. By encoding the number of helical turns of the chiral dopant, the number of CLC droplet rotations can be controlled, and then the directional swimming direction of the droplet can be changed. The CLC droplet exhibits helical motion due to the chiral coupling between the rotation of the chiral motor and the Marangoni flow at the liquid-liquid interface, which induces the translation-rotation motion of the droplet through the helical handedness inside the CLC droplet. The method of motional modulation of symmetric artificial molecular system by asymmetric molecular doping is one of the new methods of active motional control[73,74].
They used the phenomenological model of CLC droplet helical swimming to study the mechanism of helical swimming motion. The model does not take into account the concentration field degrees of freedom, and the dynamics is modeled by describing isotropic self-propelled CLC droplets driven by Marangoni flow, with the following equations[75,76].
By analyzing the bifurcation behavior between the chiral motions, it is found that the velocity-angular velocity chiral coupling term, the CLC droplet structure anisotropy and the nonlinear term in the model equation play an important role in the CLC droplet helical motion behavior, and the model is also applicable to describe other types of chiral self-propulsion.
The moving distance of a swimmer driven by Marangoni force is hundreds of times of its diameter in the effective moving time range, which is the most widely used driving method[77]. However, the speed driven by Marangoni force is uncontrollable, and the time and space range of motion are also limited by fuel[78]. The above non-persistent propulsion and uncontrollable mobility not only make the motion system unstable, but also greatly limit the expansion and development of the motion function of this kind of artificial swimming body, which is one of the main scientific challenges facing the research work of this kind of system.
3.2.2 Interface solute effect driven swimmer
In 2013, Bechinger et al. Studied the motion of asymmetric self-propelled particles (L-type) in viscous liquid by using solute effect (Fig. 12)[79]. By heating the metal layer covering the surface of the L-shaped particle with light, the solvent can be partially delaminated, so that the asymmetric swimmer is subjected to a velocity-dependent torque to push the particle into a spiral trajectory (Fig. 12A), so that the radius of curvature of its trajectory is independent of the propulsion force and depends only on the chiral shape of the swimmer[17,18][80]. In 2014, they studied the motion of a swimmer in a gravitational field based on a surface diffusiophoresis mechanism that induces a local surface chemical gradient in the solvent around the L-shaped swimmer (Fig. 12b)[13]. The results show that the anisotropy of the swimmer shape alone is sufficient to cause the spiral trajectory motion, and this mechanism only exists in chiral anisotropic particles.
3.3 Screw motion driven by chemical force
In 2004, Crespi et al. Proposed a synthetic swimmer driven by chemical reaction and able to move autonomously, and they found that bimetallic nanorods could move autonomously in hydrogen peroxide solution[81]. This work has promoted the driving of artificial swimmers by chemical forces to become a research hotspot.
Active colloidal particles are a class of microparticles that "swim" through a fluid by breaking the symmetry of their surface force distribution[82⇓~84]. By encoding the required forces and torques at the individual particle level, active colloidal particles can be made to move along complex trajectories in three dimensions,Their motion involves a change in the symmetry of the surface properties caused by the local chemical reaction, and the driving force comes from the asymmetric interfacial force generated by the chemical reaction between the colloidal particle surface and the solution environment (Fig. 13).
In 2017, Ebbens et al. studied the motion trajectory of spherical Janus particles with asymmetric distribution on the catalyst surface in three-dimensional space (3D). The Janus particles were covered with platinum metal catalyst material on a hemispherical surface (Fig. 13A). Pt catalyzed the decomposition of aqueous hydrogen peroxide into oxygen and water to produce bubbles, and the ejection of bubbles transferred momentum to the swimmer to push the Janus particles to move[85]. Due to the difference of the thickness of the platinum coating and the size of the colloid, the Janus particles move in a spiral direction.
Self-electrophoretically driven Janus particle motion is due to the asymmetry of the electrochemical reaction around the particle, which allows the charged particle to move in the self-generated electric field. The Au-Pt double-segment self-electrophoretic nanorod developed by Mallouk et al. Can produce directional motion behavior toward the Pt end at a speed of about 10 μm/s (Fig. 13b)[86].
Zhang et al. Synthesized asymmetric ZnO/Au Janus nanorods that can perform multiple modes of motion (Fig. 13C)[87]. With the increase of H2O2 concentration or UV light intensity, the trajectory of ZnO/Au rods transits from ballistic motion to continuous rotation. By adjusting the angle of the incident light, the motion trajectory of the ZnO/Au rod can be reversibly transformed between linear translation, spiral motion, and circular motion.
Based on the mechanical instability caused by the structural asymmetry of Janus particles, the triggered active rotation can be designed without the need for built-in chiral shape or chiral chemical activity. However, the motion of Janus particles has the following limitations: the use of catalytic decomposition of hydrogen peroxide to achieve propulsion usually leads to unstable motion; The rotational degree of freedom of the particle is lack of controllability[88]; The gradual consumption of fuel during the reaction can lead to the reduction of the motility of the swimmer. How to realize the controllable motion of Janus particles and continuous energy supply will be the focus of future research.
Recent studies have shown that the asymmetry of the swimmer shape is not a necessary condition for the rotational motion, and the swimming droplet will spontaneously spiral in the non-equilibrium state even without the asymmetry of the swimmer shape. When a droplet is able to produce chemical molecules from within, the coupling between chemical reaction and motion spontaneously breaks the symmetry, leading to directed motion of the droplet. Surface tension plays an important role in this kind of system. It can also be used as a chemo-mechanical sensor, where the uneven concentration of chemical molecules can be converted into mechanical differences on the surface of the droplet to achieve the detection process[89].
The interfacial tension of the solution system corresponding to the oxidized state of the catalyst iron is higher than that of the solution system corresponding to the reduced state when the chemical oscillation reaction is carried out inside the BZ reaction droplet. As the chemical oscillation reaction in the droplet continues, the surface tension of the droplet will change periodically. When there is a periodic chemical wave propagating inside the droplet, the directional flow of the fluid can be induced, thus driving the motion of the BZ droplet. Sumino et al. Studied the motion of BZ droplets driven by spiral waves[90]. When the spiral wave is spontaneously generated inside the BZ droplet, the interfacial tension gradient is driven to rotate by the spiral wave, and the rotational convection generates and induces the rotational motion according to the gradient (Fig. 14). It is observed that the motion of BZ droplets is short-range, random and uncontrollable, because there is no mature experimental technology to excite and control chemical waves that can propagate directionally and stably for a long time in BZ droplets.
Belousov-Zhabotinsky self-oscillating gel is an active soft substance first synthesized by Yoshida et al. In the 1990s, which can autonomously and continuously convert chemical energy into mechanical energy without external stimulation[91⇓~93]. Due to these unique self-oscillation properties, many biomimetic behaviors similar to heartbeat and biorhythm can be obtained[94⇓~96]. In addition, chemical wave-driven locomotion has the same dynamic mechanism as nerve-driven muscle locomotion, so BZ gel can produce various forms of locomotion, such as antiwave and syn-wave locomotion, phototactic and photophobic locomotions, spiral wave-driven angular movement, periodic migration, group movement pattern transformation, and many other biomimetic movement behaviors[97][98][99][100][101].
In 2021, Gao et al. Proposed a spiral motion mode driven by an active self-oscillating BZ gel, which can drive the active gel to produce a spiral motion trajectory only through the asymmetry of the internal chemical wave signal under the condition that the external environment is uniform and the material itself and the boundary are symmetrical[102]. It was found that the phototactic and photophobic motion of BZ gel driven by chemical waves in a one-dimensional glass tube was similar to the forward and backward motion of Euglena gracilis enclosed in a one-dimensional glass tube[98][103]. In a two-dimensional solution environment, the spiral wave/pulse wave in a rectangular BZ self-oscillating gel propagates in the x-y two-dimensional space, and the direction of the driving force will deviate from the normal direction of the wave front. The gel alternately moves forward and backward along the normal and tangential motion vectors with phase difference, forming a spiral motion trajectory (Fig. 15). In contrast to the motion of a BZ droplet (interfacial tension driven), the helical motion of a rectangular BZ gel can occur without external interactions, i.e., it is internally driven. This movement pattern, direction, and speed of the BZ gel can be controlled by external control parameters such as light intensity, temperature, and substrate concentration of the BZ solution.
This work demonstrates that the helical motion of an artificial swimmer can be driven solely by internally propagating signals, without the need for built-in chiral shape or chiral chemical activity, or any external asymmetric environment. The range of the spiral motion can also be controlled by controlling external conditions, such as the shape of the BZ gel, the position of the chemical wave on the BZ gel, and other factors. However, the motion speed of this kind of soft robot driven by internal signals is far from that of biological swimmers. How to improve the motion speed, motion stability and chemical-mechanical energy conversion performance of BZ gel is a key issue for future development[104].
To sum up, the motion method of using chemical force to drive the swimmer enriches the "fuel" selection of the artificial swimmer. The driving property of chemical reaction network endows this kind of system with bionic functions such as directivity, stability and adaptability, and has characteristics and great development potential in bionic multi-mode intelligent motion. At present, the widely used fuel molecules such as H2O2 and BZ solution can provide energy for the movement system, but they can not be used in organisms. Therefore, the development of biocompatible fuel molecules is an important direction for the future research and development of artificial swimmers.
4 Conclusion and prospect
The excellent motility and functionality of biological swimmers inspire scientists to constantly imitate and create artificial swimmers with biological functions. This review mainly discusses the classification and principles of the motion of biological and artificial swimming bodies that perform spiral motion. The methods and mechanisms for propelling the spiral motion of an artificial swimmer using external differential physical fields, interfacial/surface tension and chemical forces are clarified and outlined.
Although a lot of substantial progress has been made in the field of artificial swimmer motion research in recent years, this kind of system still lacks biological efficiency and functionality (motion controllability, sustainability and environmental adaptability, etc.), which is quite different from biological swimmers[38,105]. In addition, due to the complex structure of the biological swimming body, the complex function of the biological swimming body cannot be completely realized by a synthesis method at present[106]; Several fuel-free propulsion and artificial fuel-driven systems proposed in existing research, which rely on electric field, magnetic field, acoustic field, interfacial tension and chemical reaction as the source of propulsion force for motion, are difficult to meet the requirements of ideal energy sources for future applications, especially in the biomedical field.
Based on the summary of the previous research on the spiral motion behavior of artificial swimmers, we propose the future development direction of this field as follows:
(1) At present, researchers have analyzed and explained the causes of spiral motion in artificial swimming from the theoretical research of machinery, material science, chemistry, physics, biology, control science and other disciplines. It is urgent to summarize the design methods and motion mechanisms of different disciplines into a universal spiral motion model and make theoretical analysis.
(2) Microorganisms can perform multi-mode spiral motion and perform complex functions in viscous and complex fluids, while the current research on artificial swimmers mainly focuses on the motion mode and mechanism. The development of bionic function is one of the important directions for the development of artificial spiral swimming body. How to improve the orientation, autonomy, material transport and release, and group ability of spiral swimming body needs further exploration[60].
(3) At present, the artificial swimming body lacks adaptability to the external environment.In the future, how to develop an intelligent swimmer that can sense external sensor signals and transmit the signals to the control system to form a closed-loop feedback to drive the actuator and achieve the corresponding motion through material science and chemical methods in artificial systems is an important research direction. Swimming body driven by chemical energy has unique advantages, but how to improve the stability and persistence of its driving performance is a challenge.
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