Near wall motion of undulatory swimmers in non-Newtonian fluids

Authors

  • Gaojin Li School of Mechanical Engineering, Purdue University,West Lafayette, IN, USA
  • Arezoo M. Ardekani School of Mechanical Engineering, Purdue University,West Lafayette, IN, USA

Keywords:

Viscoelastic fluid, low Reynolds number swimming, undulatory motion

Abstract

We investigate the near-wall motion of an undulatory swimmer in both Newtonian and non-Newtonian fluids using a twodimensional direct numerical simulation. Our results show that the undulatory swimmer has three types of swimming mode depending on its undulation amplitude. The swimmer can be strongly attracted to the wall and swim in close proximity of the wall, be weakly attracted to the wall with a relatively large distance away from the wall, or escape from the wall. The scattering angle of the swimmer and its hydrodynamic interaction with the wall are important in describing the nearwall swimming motion. The shear-thinning viscosity is found to increase the swimming speed and to slightly enhance the wall attraction by reducing the swimmer’s scattering angle. The fluid elasticity, however, leads to strong attraction of swimmer’s head towards the wall, reducing the swimming speed. The combined shear-thinning effect and fluid elasticity results in an enhanced swimming speed along the wall.

Downloads

Download data is not yet available.

References

Ardekani, A., Dabiri, S., & Rangel, R. (2008). Collision of multi-particle and general shape

objects in a viscous fluid. Journal of Computational Physics, 227, 10094–10107.

Ardekani, A., Joseph, D., Dunn-Rankin, D., & Rangel, R. (2009). Particle-wall collision in a

viscoelastic fluid. Journal of Fluid Mechanics, 633, 475–483.

Ardekani, A., Rangel, R., & Joseph, D. (2007). Motion of a sphere normal to a wall in a

second-order fluid. Journal of Fluid Mechanics, 587, 163–172.

Berke, A. P.,Turner, L., Berg, H. C.,&Lauga, E. (2008). Hydrodynamic attraction of swimming

microorganisms by surfaces. Physical Review Letters, 101, 038102-1–038102-4.

Bird, R. B., Armstrong, R. C. & Hassager, O. (1987). Dynamics of polymeric liquids. Vol. 1:

Fluid mechanics. NewYork, NY: JohnWiley and Sons Inc.

Carreau, P. J., De Kee, D., & Chhabra, R. P. (1997). Rheology of polymeric systems: Principles

and applications. Munich: Hanser Publishers.

Chrispell, J., Fauci, L., & Shelley, M. (2013). An actuated elastic sheet interacting with passive

and active structures in a viscoelastic fluid. Physics of Fluids, 25, 013103-1–013103-16.

Curtis, M., Kirkman-Brown, J., Connolly, T., & Gaffney, E. (2012). Modelling a tethered

mammalian sperm cell undergoing hyperactivation. Journal of Theoretical Biology, 309,

–10.

Dabiri, S., & Bhuvankar, P. (2016). Scaling law for bubbles rising near vertical walls. Physics

of Fluids, 28, 062101-1–062101-13.

Dabiri, S., Doostmohammadi, A., Bayareh, M., & Ardekani, A. (2015). Rising motion of a

swarm of drops in a linearly stratified fluid. International Journal of Multiphase Flow, 69,

–17.

Dabiri, S., Lu, J., & Tryggvason, G. (2013). Transition between regimes of a vertical channel

bubbly upflow due to bubble deformability. Physics of Fluids, 25, 102110-1–102110-12.

Dabiri, S.,&Tryggvason,G. (2015). Heat transfer in turbulent bubbly flowin vertical channels.

Chemical Engineering Science, 122, 106–113.

Datt, C., Zhu, L., Elfring, G. J., & Pak, O. S. (2015). Squirming through shear-thinning fluids.

Journal of Fluid Mechanics, 784, R1-1–R1-11.

Drescher, K., Dunkel, J., Cisneros, L. H., Ganguly, S., & Goldstein, R. E. (2011). Fluid

dynamics and noise in bacterial cell-cell and cell-surface scattering. Proceedings of the

National Academy of Sciences of the United States of America, 108, 10940–10945.

Elgeti, J., Kaupp, U. B., & Gompper, G. (2010). Hydrodynamics of sperm cells near surfaces.

Biophysical Journal, 99, 1018–1026.

Elgeti, J., Winkler, R. G., & Gompper, G. (2015). Physics of microswimmerssingle particle

motion and collective behavior: A review. Reports on Progress in Physics, 78, 056601-1–

-50.

Evans, A. A., & Lauga, E. (2010). Propulsion by passive filaments and active flagella near

boundaries. Physical Review E, 82, 041915-1–041915-12.

Gagnon, D., & Arratia, P. (2016). The cost of swimming in generalized Newtonian fluids:

Experiments with C. elegans. Journal of Fluid Mechanics, 800, 753–765.

Gagnon, D. A., Keim, N. C., & Arratia, P. E. (2014). Undulatory swimming in shear-thinning

fluids: Experiments with Caenorhabditis elegans. Journal of Fluid Mechanics, 758, R3-1–

R3-11.

Giesekus, H. (1982). A simple constitutive equation for polymer fluids based on the concept

of deformation-dependent tensorial mobility. Journal of Non-Newtonian Fluid Mechanics,

, 69–109.

Glowinski, R., Pan, T., Hesla, T., Joseph, D.,&Periaux, J. (2001).Afictitious domain approach

to the direct numerical simulation of incompressible viscous flow pastmoving rigid bodies:

Application to particulate flow. Journal of Computational Physics, 169, 363–426.

Guénette, R., & Fortin, M. (1995). A new mixed finite element method for computing

viscoelastic flows. Journal of Non-Newtonian Fluid Mechanics, 60, 27–52.

Guy, R. D., & Thomases, B. (2015). Computational challenges for simulating strongly elastic

flows in biology. In S.E. Spagnolie (Ed.), Complex fluids in biological systems (pp. 359–397).

New York, NY: Springer.

Hall-Stoodley, L., Costerton, J.W., & Stoodley, P. (2004). Bacterial biofilms: From the natural

environment to infectious diseases. Nature Reviews Microbiology, 2, 95–108.

Harman, M. W., Dunham-Ems, S. M., Caimano, M. J., Belperron, A. A., Bockenstedt, L. K.,

Fu, H. C., et al. (2012). The heterogeneous motility of the lyme disease spirochete in gelatin

mimics dissemination through tissue. Proceedings of the National Academy of Sciences of

the United States of America, 109, 3059–3064.

Hwang, S., Litt, M., & Forsman,W. (1969). Rheological properties ofmucus. Rheologica Acta,

, 438–448.

Ishimoto, K., & Gaffney, E. A. (2014). A study of spermatozoan swimming stability near a

surface. Journal of Theoretical Biology, 360, 187–199.

Kantsler, V., Dunkel, J., Polin, M., & Goldstein, R. E. (2013). Ciliary contact interactions

dominate surface scattering of swimming eukaryotes. Proceedings of the National Academy

of Sciences of the United States of America, 110, 1187–1192.

Katz, D. F. (1974). On the propulsion of micro-organisms near solid boundaries. Journal of

Fluid Mechanics, 64, 33–49.

Lauga, E. (2007). Propulsion in a viscoelastic fluid. Physics of Fluids, 19, 083104-1–083104-13.

Lauga, E., DiLuzio, W. R., Whitesides, G. M., & Stone, H. A. (2006). Swimming in circles:

Motion of bacteria near solid boundaries. Biophysical Journal, 90, 400–412.

Lauga, E., & Powers, T. R. (2009). The hydrodynamics of swimming microorganisms. Reports

on Progress in Physics, 72, 096601-1–096601-36.

Li, G., & Ardekani, A. M. (2014). Hydrodynamic interaction of microswimmers near a wall.

Physical Review E, 90, 013010-1–013010-12.

Li,G., & Ardekani, A. M. (2015). Undulatory swimming in non-Newtonian fluids. Journal of

Fluid Mechanics, 784, R4-1–R4-13.

Li,G., Karimi,A.,&Ardekani,A.M. (2014). Effect of solid boundaries on swimming dynamics

of microorganisms in a viscoelastic fluid. Rheologica Acta, 53, 911–926.

Li, G.,McKinley, G. H., & Ardekani, A.M. (2015). Dynamics of particlemigration in channel

flow of viscoelastic fluids. Journal of Fluid Mechanics, 785, 486–505.

Li, G., & Tang, J. X. (2009). Accumulation of microswimmers near a surface mediated

by collision and rotational brownian motion. Physical Review Letters, 103, 078101-1–

-4.

Martinez, V. A., Schwarz-Linek, J., Reufer,M., Wilson, L. G., Morozov, A. N., & Poon,W. C.

(2014). Flagellated bacterial motility in polymer solutions. Proceedings of the National

Academy of Sciences of the United States of America, 111, 17771–17776.

Montecucco, C., & Rappuoli, R. (2001). Living dangerously: How helicobacter pylori survives

in the human stomach. Nature Reviews Molecular Cell Biology, 2, 457–466.

Montenegro-Johnson, T. D., Smith, A. A., Smith, D. J., Loghin, D., & Blake, J. R. (2012).

Modelling the fluid mechanics of cilia and flagella in reproduction and development.

European Physical Journal E, 35, 1–17.

Montenegro-Johnson, T. D., Smith, D. J., & Loghin, D. (2013). Physics of rheologically

enhanced propulsion: Different strokes in generalized Stokes. Physics of Fluids, 25, 081903-

–081903-26.

Qin, B., Gopinath, A., Yang, J., Gollub, J. P., & Arratia, P. E. (2015). Flagellar kinematics

and swimming of algal cells in viscoelastic fluids. Scientific Reports, 5, 9190-1–9190-7. DOI:

1038/srep09190.

Shen, X., & Arratia, P. E. (2011). Undulatory swimming in viscoelastic fluids. Physical Review

Letters, 106, 208101-1–208101-4.

Rothschild, L. (1963). Non-random distribution of bull spermatozoa in a drop of sperm

suspension. Nature, 198, 1221–1222.

Simons, J., Olson, S., Cortez, R., & Fauci, L. (2014). The dynamics of sperm detachment

from epithelium in a coupled fluid-biochemical model of hyperactivated motility. Journal

of Theoretical Biology, 354, 81–94.

Smith, D., Gaffney, E., Blake, J., & Kirkman-Brown, J. (2009). Human sperm accumulation

near surfaces: A simulation study. Journal of Fluid Mechanics, 621, 289–320.

Spagnolie, S. E., & Lauga, E. (2012). Hydrodynamics of self-propulsion near a boundary:

Predictions and accuracy of far-field approximations. Journal of Fluid Mechanics, 700, 105–

Suarez, S., & Pacey, A. (2006). Sperm transport in the female reproductive tract. Human

Reproduction Update, 12, 23–37.

Taylor, G. (1951). Analysis of the swimming of microscopic organisms. Proceedings of the

Royal Society A, 209, 447–461.

Teran, J., Fauci, L., & Shelley, M. (2010). Viscoelastic fluid response can increase the speed

and efficiency of a free swimmer. Physical Review Letters, 104, 038101-1–038101-4.

Thomases, B., & Guy, R. D. (2014). Mechanisms of elastic enhancement and hindrance

for finite-length undulatory swimmers in viscoelastic fluids. Physical Review Letters, 113,

-1–098102-5.

Vélez-Cordero, J. R., & Lauga, E. (2013). Waving transport and propulsion in a generalized

Newtonian fluid. Journal of Non-Newtonian Fluid Mechanics, 199, 37–50.

Wolf, D. P., Blasco, L., Khan, M. A., & Litt, M. (1977). Human cervical mucus. I. rheologic

characteristics. Fertility and Sterility, 28, 41–46.

Woolley, D. (2003). Motility of spermatozoa at surfaces. Reproduction, 126, 259–270.

Yazdi, S.,Ardekani, A. M.,&Borhan, A. (2014). Locomotion of microorganisms near a no-slip

boundary in a viscoelastic fluid. Physical Review E, 90, 043002-1–043002-11.

Yazdi, S., Ardekani, A. M., & Borhan, A. (2015). Swimming dynamics near a wall in a weakly

elastic fluid. Journal of Nonlinear Science, 25, 1153–1167.

Yuan, J., Raizen, D. M., & Bau, H. H. (2015). Propensity of undulatory swimmers, such as

worms, to go against the flow. Proceedings of the National Academy of Sciences of the United

States of America, 112, 3606–3611.

Downloads

Published

2019-01-14

How to Cite

Li, G., & Ardekani, A. M. (2019). Near wall motion of undulatory swimmers in non-Newtonian fluids. European Journal of Computational Mechanics, 26(1-2), 44–60. Retrieved from https://journals.riverpublishers.com/index.php/EJCM/article/view/298

Issue

Section

Original Article