Skip to main content
SpringerLink
Log in

Using surface-motions for locomotion of microscopic robots in viscous fluids

  • Research Paper
  • Published:
Journal of Micro-Bio Robotics Aims and scope Submit manuscript

Abstract

Microscopic robots could perform tasks with high spatial precision, such as acting in biological tissues on the scale of individual cells, provided they can reach precise locations. This paper evaluates the performance of in vivo locomotion for micron-size robots. Two appealing methods rely only on surface motions: steady tangential motion and small amplitude oscillations. These methods contrast with common microorganism propulsion based on flagella or cilia, which may lead to tangling and increased likelihood of fouling due to the large exposed surface areas. The power potentially available to such robots, as determined by previous studies, supports speeds ranging from one to hundreds of microns per second, over the range of viscosities found in biological tissue. We discuss design trade-offs among propulsion method, speed, power, shear forces and robot shape, and relate those choices to robot task requirements. This study shows that realizing such locomotion requires substantial improvements in fabrication capabilities and material properties over current technology.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  1. Abbott JJ et al. (2009) How should microrobots swim? Intl J Robot Res 28:1434–1447

    Article  Google Scholar 

  2. Alouges F et al. (2011) Numerical strategies for stroke optimization of axisymmetric microswimmers. Math Model Methods Appl Sci 21:361–387. doi:10.1142/S0218202511005088

    Article  MATH  MathSciNet  Google Scholar 

  3. Behkam B, Sitti M (2007) Bacterial flagella-based propulsion and on/off motion control of microscale objects. Appl Phys Lett 90:023–902. doi:10.1063/1.2431454

    Article  Google Scholar 

  4. Berg HC (1993) Random Walks in Biology, 2nd edn. Princeton Univ. Press

  5. Blake JR (1971) A spherical envelope approach to ciliary propulsion. J Fluid Mech 46:199–208. 10.1017/S002211207100048X

    Article  MATH  Google Scholar 

  6. Brennen C (1974) An oscillating-boundary-layer theory for ciliary propulsion. J Fluid Mech 65:799–824

    Article  MATH  Google Scholar 

  7. Brennen C, Winet H (1977) Fluid mechanics of propulsion by cilia and flagella. Ann Rev Fluid Mech 9: 339–398. doi:10.1146/annurev.fl.09.010177.002011

    Article  Google Scholar 

  8. Chan ML et al. (2011) Low friction liquid bearing mems micromotor. Proc of 24th IEEE Intl Conf Micro Electro Mech Syst (MEMS):1237–1240. doi:10.1109/MEMSYS.2011.5734656

  9. Chen BPC et al. (2001) DNA microarray analysis of gene expression in endothelial cells in response to 24-h shear stress. Physiol Genomics 7:55–63

    Article  Google Scholar 

  10. Davies PF (1995) Flow-mediated endothelial mechanotransduction. Physiol Rev 75:519–560

    Google Scholar 

  11. Discher DE, Janmey P, Wang Y (2005) Tissue cells feel and respond to the stiffness of their substrate. Sci 310:1139–1143

    Article  Google Scholar 

  12. Drexler KE (1992) Nanosystems: Molecular Machinery, Manufacturing, and Computation. John Wiley, NY

    Google Scholar 

  13. Dreyfus R et al. (2005) Microscopic artificial swimmers. Nat 437:862–865. doi:10.1038/nature04090

    Article  Google Scholar 

  14. Dusenbery DB (2009) Living at Micro Scale: The Unexpected Physics of Being Small. Harvard Univ. Press. Cambridge, MA

    Google Scholar 

  15. Ehlers K, Oster G (2012) On the mysterious propulsion of Synechococcus. PLoS ONE 7:e36–081. doi:10.1371/journal.pone.0036081

    Article  Google Scholar 

  16. Ehlers KM, Koiller J (2011) Could cell membranes produce acoustic streaming? Making the case for Synechococcus self-propulsion. Math Comput Model 53:1489–1504. doi:10.1016/j.mcm.2010.03.054

    Article  Google Scholar 

  17. Ehlers KM, Koiller J (2011) Micro-swimming without flagella: Propulsion by internal structures. Regular and Chaotic Dynamics 16:623–652. doi:10.1134/S1560354711060050

    Article  MATH  MathSciNet  Google Scholar 

  18. Ehlers KM, Samuel ADT, Berg HC, Montgomery R (1996) Do cyanobacteria swim using traveling surface waves? Proc. Natl Acad Sci USA 93:8340–8343

    Article  Google Scholar 

  19. Fetter AL, Walecka JD (1980) Theoretical Mechanics of Particles and Continua. McGraw-Hill, New York

    MATH  Google Scholar 

  20. Freitas Jr. RA (1998) Exploratory design in medical nanotechnology: A mechanical artificial red cell. Artificial Cells. Blood Substit Immobil Biotechnol 26:411–430

    Article  Google Scholar 

  21. Freitas Jr. R ANanomedicine, vol. I: Basic Capabilities. Landes Bioscience, Georgetown, TX (1999). www.nanomedicine.com/NMI.htm

  22. Freitas Jr. R ANanomedicine, vol. IIA: Biocompatibility. Landes Bioscience, Georgetown, TX (2003). www.nanomedicine.com/NMIIA.htm

  23. Freitas Jr. RA (2006) Pharmacytes: An ideal vehicle for targeted drug delivery. J Nanosci Nanotechnol 6:2769–2775

    Article  Google Scholar 

  24. Freitas Jr. RA (2009) Computational tasks in medical nanorobotics. In: Eshaghian-Wilner M (ed) Bio-inspired and Nano-scale Integrated Computing, chap. 15. John Wiley, NY, pp 391–428

    Chapter  Google Scholar 

  25. Gao R et al. (2012) Outside looking in: Nanotube transistor intracellular sensors. Nano Lett 12:3329–3333

    Article  Google Scholar 

  26. Guasto JS, Rusconi R, Stocker R (2012) Fluid mechanics of planktonic microorganisms. Annu Rev Fluid Mech 44:373–400. doi:10.1146/annurev-fluid-120710-101156

    Article  MathSciNet  Google Scholar 

  27. Happel J, Brenner H (1983) Low Reynolds number hydrodynamics, 2nd edn. Kluwer. The Hague

  28. Hernandez-Ortiz JP, Stoltz CG, Graham MD (2005) Transport and collective dynamics in suspensions of confined swimming particles. Phys Rev Lett 95(204):501

    Google Scholar 

  29. Hill C, Amodeo A, Joseph JV, Patel HRH (2008) Nano- and microrobotics: how far is the reality? Expert Rev Anticancer Ther 8:1891–1897

    Article  Google Scholar 

  30. Hogg T, Freitas Jr. RA (2010) Chemical power for microscopic robots in capillaries. Nanomedicine: Nanotechnol Biol Med 6:298–317. doi:10.1016/j.nano.2009.10.002

    Article  Google Scholar 

  31. Hogg T, Freitas Jr. RA (2012) Acoustic communication for medical nanorobots. Nano Commun Netw 3:83–102. doi:10.1016/j.nancom.2012.02.002

    Article  Google Scholar 

  32. Huang H et al. (2004) Cell mechanics and mechanotransduction: pathways, probes, and physiology. Am J Physiol: Cell Physiol 287:C1–C11. doi:10.1152/ajpcell.00559.2003

    Article  Google Scholar 

  33. Ishikawa T, Pedley TJ (2008) Coherent structures in monolayers of swimming particles. Phys Rev Lett 100:088–103. doi:10.1103/PhysRevLett.100.088103

    Google Scholar 

  34. Ishiyama K, Sendoh M, Arai KI (2002) Magnetic micromachines for medical applications. J Magn Magn Mater 242-245:41–46

    Article  Google Scholar 

  35. Jahn TL, Votta JJ (1972) Locomotion of protozoa. Ann Rev Fluid Mech 4:93–116

    Article  Google Scholar 

  36. Kanevsky A, Shelley MJ, Tornberg AK (2010) Modeling simple locomotors in Stokes flow. J Comput Phys 229:958–977. doi:10.1016/j.jcp.2009.05.030

    Article  MATH  MathSciNet  Google Scholar 

  37. Keeley A, Soldati D (2004) The glideosome: a molecular machine powering motility and host-cell invasion by Apicomplexa. Trends Cell Biol 14:528–532. doi:10.1016/j.tcb.2004.08.002

    Article  Google Scholar 

  38. Keller SR, Wu TY (1977) A porous prolate-spheroidal model for ciliated micro-organisms. J Fluid Mech 80:259–278

    Article  MATH  Google Scholar 

  39. Kim S, Karrila SJ (2005) Microhydrodynamics. Dover

  40. Krim J (2002) Surface science and the atomic-scale origins of friction. Surf Sci 500:741–758

    Article  Google Scholar 

  41. Lai SK, Wang YY, Hanes J (2009) Mucus-penetrating nanoparticles for drug and gene delivery to mucosal tissues. Adv Drug Deliv Rev 61:158–171. doi:10.1016/j.addr.2008.11.002

    Article  Google Scholar 

  42. Lauga E (2009) Powers, T.R.: The hydrodynamics of swimming microorganisms. Rep Prog Phys 72:096–601. doi:10.1088/0034-4885/72/9/096601

    Article  MathSciNet  Google Scholar 

  43. Lee C et al. (2008) Measurement of the elastic properties and intrinsic strength of monolayer graphene. Sci 321:385–388. doi:10.1126/science.1157996

    Article  Google Scholar 

  44. Leshansky AM, article (2007) A frictionless microswimmer. New J Phys 9:145. doi:10.1088/1367-2630/9/5/145

    Article  Google Scholar 

  45. Lighthill J (1978) Acoustic streaming. J Sound Vib 61:391–418

    Article  MATH  Google Scholar 

  46. Lighthill MJ (1952) On the squirming motion of nearly spherical deformable bodies through liquids at very small reynolds numbers. Commun Pur Appl Math 5:109–118. doi:10.1002/cpa.3160050201

    Article  MATH  MathSciNet  Google Scholar 

  47. Loheac J et al. (2013) Controllability and time optimal control for low Reynolds numbers swimmers. Acta Applicandae Math 123:175–200

    Article  MATH  MathSciNet  Google Scholar 

  48. Martel S (2007) The coming invasion of the medical nanorobots. Nanotechno Perceptions 3:165–173

    MathSciNet  Google Scholar 

  49. Martel S et al. (2007) Automatic navigation of an untethered device in the artery of a living animal using a conventional clinical magnetic resonance imaging system. Appl Phys Lett 90(114):105

    Google Scholar 

  50. Martel S et al. (2008) Flagellated bacterial nanorobots for medical interventions in the human body. In: Meldrum D, Khatib O (eds) Proc. of 2nd IEEE Conf. on Biomedical Robotics and Biomechatronics, pp 264–269

  51. Menard R (2001) Gliding motility and cell invasion by Apicomplexa: insights from the Plasmodium sporozoite. Cell Microbiol 3:63–73

    Article  Google Scholar 

  52. Michelin S, Lauga E (2010) Efficiency optimization and symmetry-breaking in a model of ciliary locomotion. Fluid Dyn 22:111–901. doi:10.1063/1.3507951

    Google Scholar 

  53. Nelson P (2008) Biological Physics: Energy, Information, Life. W. H. Freeman, NY

    Google Scholar 

  54. Olamaei N, Cheriet F, Beaudoin G, Martel S (2010) MRI visualization of a single 15 μm navigable imaging agent and future microrobot In: Proc. of the 2010 Conf. on Engineering in Medicine and Biology Society, pp. 4355–4358. IEEE

  55. Oliver FWJ et al. (2010) NIST Handbook of Mathematical Functions. Cambridge Univ. Press

  56. Osterman N, Vilfan A (2011) Finding the ciliary beating pattern with optimal efficiency. Proc Natl Acad Sci USA 108:15,727–15,732. doi:10.1073/pnas.1107889108

    Article  Google Scholar 

  57. Papaioannou TG, Stefanadis C (2005) Vascular wall shear stress: Basic principles and methods. Hell J Cardiol 46:9–15

    Google Scholar 

  58. Purcell EM (1977) Life at low Reynolds number. Am J Phys 45:3–11

    Article  Google Scholar 

  59. Riedel IH et al. (2005) A self-organized vortex array of hydrodynamically entrained sperm cells. Sci 309:300–303

    Article  Google Scholar 

  60. Setter E, Bucher I (2010) Elastic travelling waves in multi-dimensional structures with application to self propulsion. In: Sas P, Bergen B (eds) Proc. of Intl. Conf. on Noise and Vibration Engineering (ISMA2010), pp 3785–3800

  61. Shapere A, Wilczek F (1989) Efficiencies of self-propulsion at low Reynolds number. J Fluid Mech 198:587–599. doi:10.1017/S0022112089000261

    Article  MATH  MathSciNet  Google Scholar 

  62. Shapere A, Wilczek F (1989) Geometry of self-propulsion at low Reynolds number. J Fluid Mech 198:557–585

    Article  MATH  MathSciNet  Google Scholar 

  63. Soong RK et al. (2000) Powering an inorganic nanodevice with a biomolecular motor. Sci 290:1555–1558

    Article  Google Scholar 

  64. Spagnolie SE, Lauga E (2012) Jet propulsion without inertia. Phys Fluids 22(081):902

    Google Scholar 

  65. Stone HA, Samuel A (1996) Propulsion of microorganisms by surface distortions. Phys Rev Lett 77:4102–4104

    Article  Google Scholar 

  66. Tobias PA, Trindade DC (1986) Applied Reliability. Van Nostrand Reinhold. NY

  67. Trouilloud R et al. (2008) Soft swimming: Exploiting deformable interfaces for low Reynolds number locomotion. Phys Rev Lett 101(048):102. doi:10.1103/PhysRevLett.101.048102

    Google Scholar 

  68. Vanossi A et al. (2013) Modeling friction: From nanoscale to mesoscale. Rev Mod Phys 85:529–552. doi:10.1103/RevModPhys.85.529

    Article  Google Scholar 

  69. Vogel V, Sheetz M (2006) Local force and geometry sensing regulate cell functions. Nat Rev: Mol Cell Biol 7:265–275. doi:10.1038/nrm1890

    Article  Google Scholar 

  70. Wang B., Kral P. (2007) Chemically tunable nanoscale propellers of liquids. Phys Rev Lett 98(266):102

    Google Scholar 

  71. Wang X et al. (2007) Direct-current nanogenerator driven by ultrasonic waves. Sci 316:102–105

    Article  Google Scholar 

  72. Xie X et al. (2013) Nanostraw-electroporation system for highly efficient intracellular delivery and transfection. ACS Nano 7:4351–4358. doi:10.1021/nn400874a

    Article  Google Scholar 

  73. Yang J et al. (2013) Observation of high-speed microscale superlubricity in graphite. Phys Rev Lett 110(255):504. doi:10.1103/PhysRevLett.110.255504

    Google Scholar 

  74. Zhang L. et al. (2009) Artificial bacterial flagella: Fabrication and magnetic control. Appl Phys Lett 94(064):107

    Google Scholar 

  75. Zhou Z, Liu Z (2008) Biomimetic cilia based on MEMS technology. J Bionic Eng 5:358–365. doi:10.1016/S1672-6529(08)60181-X

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute for Molecular Manufacturing, 555 Bryant St., Palo Alto, CA, USA

    Tad Hogg

Authors
  1. Tad Hogg
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tad Hogg.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hogg, T. Using surface-motions for locomotion of microscopic robots in viscous fluids. J Micro-Bio Robot 9, 61–77 (2014). https://doi.org/10.1007/s12213-014-0074-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12213-014-0074-z

Keywords

Search

Navigation