Experimental Verification for the Application Feasibility of Buckingham Pi Theorem in Designing a Scaled Model of Flagellated Swimmer with Traditional Resistive Force Theory
The microstructure of bacterial is an important reference to design
underwater swimmers. Applying Buckingham Pi Theorem is a possible method to
build a scaled model based on a theoretical flagellum designed with traditional
Resistive Force Theory. By making a scaled model, the forward velocity could be
obtained to verify the application feasibility of Buckingham Pi Theorem in such
designs. The optimal value of the model’s pitch angle can be calculated with
the traditional RFT as well as the forward velocity. Comparing the experimental
results with the results of theoretical calculations, it is found that the
experimental and calculated results are consistent, which means Buckingham Pi
Theorem works well in such design of underwater swimmer.
References
[1]
Jian, F. and Sung, K.C. (2014) Mini and Micro Propulsion for Medical Swimmers. Micromachines, 5, 97-113. https://doi.org/10.3390/mi5010097
[2]
Mohamed, K.T., Ata, A.A. and El-Souhily, B.M. (2011) Dynamic Analysis Algorithm for a Micro-Robot for Surgical Applications. International Journal of Mechanics and Materials in Design, 7, 17-28.
https://doi.org/10.1007/s10999-010-9146-y
[3]
Editorial Department (2014) Micro Medical Robot for Targeted Drug Delivery. Shanghai of Biomedical Engineering, No. 2, 118.
[4]
Purcell, E.M. (1977) Life at Low Reynolds Number. American Journal of Physics, 45, 3-11. https://doi.org/10.1119/1.10903
[5]
Holwill, M.E.J. and Burge, R.E. (1963) A Hydrodynamic Study of the Motility of Flagellated Bacteria. Archives of Biochemistry and Biophysics, 101, 249-260.
https://doi.org/10.1016/S0003-9861(63)80010-7
[6]
Buckingham, E. (1914) On Physically Similar Systems; Illustrations of the Use of Dimensional Equations. Physical Review, 4, 345.
https://doi.org/10.1103/PhysRev.4.345
[7]
Magariyama, Y. and Kudo, S. (2002) A Mathematical Explanation of an Increase in Bacterial Swimming Speed with Viscosity in Linear-Polymer Solutions. Biophysical Journal, 83, 733-739. https://doi.org/10.1016/S0006-3495(02)75204-1
[8]
Happel, J. and Brenner, H. (1973) Low Reynolds Number Hydrodynamics. Kluwer Academic Publishers, Dordrecht.
[9]
Magariyama, Y., Sugiyama, S., Muramoto, K., Kawagishi, I., Imae, Y. and Kudo, S. (1995) Simultaneous Measurement of Bacterial Flagellar Rotation Rate and Swimming Speed. Biophysical Journal, 69, 2154-2162.
https://doi.org/10.1016/S0006-3495(95)80089-5
[10]
Lighthill, J. (1996) Helical Distributions of Stokeslets. Journal of Engineering Mathematics, 30, 35-78. https://doi.org/10.1007/978-94-009-0225-1_4
[11]
Chwang, A.T. and Wu, T.Y.T. (1975) Hydromechanics of Low-Reynolds-Number Flow. Part 2. Singularity Method for Stokes Flows. Journal of Fluid Mechanics, 67, 787-815. https://doi.org/10.1017/S0022112075000614
[12]
Lauga, E. and Thomas, R. (2008) The Hydrodynamics of Swimming Microorganisms, Powers, 10.1088/0034-4885/72/9/096601.
[13]
Fan, W.L. and Zhang, B.A. (2008) Viscosity Research on Three Kinds of Liquid Detergents. China Surfactant Soap and Detergent Industries, No. 4, 73-74.
[14]
Su, H.K. and Zhao, J.T. (2018) Study on the Influence of Temperature on the Viscosity and Density of Vegetable Oil. Cereal & Food Industry, 25, 29-32.
