Microscopic artificial swimmers

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Original entry: Naveen Sinha, APPHY 226, Spring 2009

Second Entry: Xu Zhang, AP225 Fall 2009

Third Entry: Hsin-I Lu, AP225 Fall 2009

Microscopic artificial swimmers

Rémi Dreyfus, Jean Baudry, Marcus L. Roper, Marc Fermigier, Howard A. Stone & Jérôme Bibette Nature 437, 862-865 (6 October 2005). Keywords:

Summary

The authors constructed a micro-scale swimming robot based on the behavior of swimming micro-ogranisms. Bacteria tend to use helical tail-like structures known as flagella that rotate in order to move through liquids, whereas eukaryotic cells tend to use flagella that undergo an oscillatory beating motion. The authors made their device from micron-size magnetic colloidal particles that were bound together using 100nm-long segments of DNA. This artificial flagella was used to propel a red-blood cell. To power this artificial swimmer, the researchers applied two magnetic fields: a steady magnetic field to lengthen the flegella and an oscillatory transverse field to cause the beating motion. A diagram is shown below:

Figure1.jpg

The crucial aspect of this technique was ensuring that the motion was cyclic, but no time-reversible. A symmetric motion would cause the device to simply oscillate back and forth due to the dominance of viscosity at such small length scales. When observed under a microscope, the authors saw the device move uni-directionally as planned, but with the tail first. They suspect this is due to whether the disturbances in the flagella propagate from the head to the free end (as in most natural cases) or in the opposite direction (which occurred in this case).

Soft Matter aspects

Although we have typically studied stationary, non-living systems in this course, novel behavior in complex fluids could be created by applying magnetic fields to specially constructed systems. One possibility would be to have magnetic beads dispersed throughout a polymer network.


Additional Entry: Xu Zhang, AP225 Fall 2009

Reference

Re´mi Dreyfus, Jean Baudry, Marcus L. Roper, Marc Fermigier, Howard A. Stone & Je´roˆme Bibette,Microscopic artificial swimmers, Nature, Vol 437, 862-865, |6 October 2005

Keywords

flagellum, Sperm number, magnetic field

Summary

Figure 1: Schematic representation of a flexible magnetic filament.
Figure 2: Beating pattern of the motion of a magnetic flexible filament attached to a red blood cell.

This paper shows that a linear chain of colloidal magnetic particles linked by DNA and attached to a red blood cell can act as a flexible artificial flagellum. The filament aligns with an external uniform magnetic field and is readily actuated by oscillating a transverse field. It is found that the actuation induces a beating pattern that propels the structure, and that the external fields can be adjusted to control the velocity and the direction of motion.

The microscopic device consists of two parts: a magnetically activated 'flagellum' that provides propulsion, and a second part, a red blood cell to be transported. The flagellum is made of superparamagnetic 1-<math>\mu m</math>-diameter colloids linked by several 107-nm-long (315 base pairs, bp) double-stranded DNA linkers(Fig.1). Two magnetic fields are used to generate motion in a controlled direction and with a controlled speed: one homogeneous static field B<math>_x=B_x</math>x and a sinusoidal field B<math>_y=B_ysin(2\pi ft)</math>y perpendicular to B<math>_x</math>. These two fields have comparable amplitude so that the resulting field B<math>_e</math> oscillates around the x axis. A fast camera is used to record the dynamics of a microstructure formed by a red blood cell specifically bound to one end of a 30-<math>\mu</math>m-long filament(Fig.2). The wave propagation, which is responsible for the non reversible displacements of the filament, is visible in Fig.3 indicated by the arrows.

Figure 3: Sequence of deformation of the end of a free filament.

Soft Matter Connection

It is so fresh to see engineered flagellum using colloidal particles and DNA linkers. The use of magnetic field to propel linked magnetic particles is a brilliant idea. It comes to my mind that we can also make use of other effects to propel the filament.Instead of using uniform colloidal particles, we can Janus particles which have different physical characteristics on two sides. For example, we can use half coated gold particles and put the filaments in a polymer solution. By applying expanded laser light, we can get a temperature gradient on two sides the particles resulted from the different absorption on two sides. Due to Soret effect, the polymers around the particles will have asymmetrical distribution thus pushing the particles on one direction. As a result, the filament might be propelled either in a translational way or in a more complicated way depending on different designs.



Third Entry by Hsin-I Lu, AP225 Fall 2009

Keywords

Microorganism, flagella, viscous coefficient, magnetic colloids

Summary

The authors used linear chain of colloidal magnetic particles linked by DNA and attached to a red blood cell to study the motion of flagellum. With the externally applied magnetic field, energy can be injected and transferred into this artificial flagellum. They found that the actuation of time varying magnetic field induces a beating pattern that propels the structure, and that the external fields can be adjusted to control the velocity and the direction of motion.

Soft Matter

Fig. 1
Fig. 2: Escherichia coli cells, from Ref. [1]
Fig. 3
Fig. 4
  • Structure of artificial flagellum:

The flagellum is made of micrometre-scale magnetic colloids attached together by short flexible joints. More specifically, it consists of superparamagnetic 1-mm-diameter colloids linked by several 107-nm-long (315 base pairs, bp) double-stranded DNAs (See Fig. 1). This flagellum is attached to a red blood cell and provides propulsion.


  • How artificial flagellum moves:

Naturally, a flagellum is a tail-like projection that protrudes from the cell body of certain prokaryotic and eukaryotic cells, and functions in locomotion [1]. Fig. 2 shows an example of Escherichia coli cells propelling themselves with flagella that rotate counter-clockwise, generating torque to rotate the bacterium clockwise. To make artificial flagellum move, external forces are necessary. In this paper, one static magnetic field along x axis and one time varying magnetic field along y axis are used to generate locomotion. Since the particles are superparamagnetic, they acquire a magnetic dipole when subjected to a magnetic field. As the beads are known to have a preferred magnetization direction, there are two different contributions to the magnetic torque exerted upon the filament: the first contribution is due to the dipolar interactions between the beads, and the second contribution is due to the interaction between the dipole and the external field. The motion generated due to mangetic dipolar interactio is easy to understand. Since magnetic dipolar interaction is anisotropic, the magnetic fields generated from nearby beads have magnetic field gradient and only field gradient can induce force. The authors also point out two conditions need to be fulfilled to achieve controlled motion or swimming of manmade microstructures. First, energy should be injected and transferred into a mechanical deformation of the device. Second, the sequence of deformations must be cyclic and not timereversible. I think the second point can be understood from motion of simple harmonic oscillator (SHM). SHM is periodic and timereversible, but there is no net motion. The existence of fluid in this experiment is essential since fluid dynamics at the micrometre scale is dominated by viscous rather than inertial terms. The use of time varying magnetic field fulfills the first requirement since static magnetic field can not change the system energy with time. Fig. 3 shows the beating pattern of the motion of a magnetic flexible filament attached to a red blood cell. Fig. 4 shows sequence of deformation of the end of a free filament.

Finally, I think this method can be generalized to colloids with electric dipole moments and time varying electric field can be used to generate locomotion. The advantage of using electric dipole moments is electric dipolar interaction is much stronger than magnetic dipolar interaciton. Therefore, length of flexible joints can be increased to simulate the motion of more flexible flagellum without losing the interaction strength.

References

[1] http://en.wikipedia.org/wiki/Flagellum