- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Fluids

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Letter
  • Open Access

Flow field disturbance due to point viscosity variations in a heterogeneous fluid

Debasish Das*

  • Department of Mathematics and Statistics, University of Strathclyde, 26 Richmond Street, Glasgow G1 1XH, Scotland, United Kingdom

  • *debasish.das@strath.ac.uk
PDF

Phys. Rev. Fluids 8, L051301 – Published 8 May, 2023

DOI: https://doi.org/10.1103/PhysRevFluids.8.L051301

Abstract

We derive the flow field disturbance produced by point viscosity variations in a heterogeneous fluid when subject to a background flow while neglecting fluid inertia. The disturbance flow field is found to be identical to that generated by a force dipole called a stresslet. Using a combination of theory and numerical simulations, we show how the hydrodynamics of an active rigid particle is altered due to the presence of point viscosity variations, and how this can be exploited to manipulate and steer them in microfluidic environments.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (41)

  1. S. Chien, Biophysical behavior of red cells in suspensions, in Red Blood Cell, edited by D. M. Surgenor (Academic, New York, 1975), Vol. 2, pp. 1031–1133.
  2. C.-H. Heldin, K. Rubin, K. Pietras, and A. Östman, High interstitial fluid pressure—an obstacle in cancer therapy, Nat. Rev. Cancer 4, 806 (2004).
  3. R. K. Jain and T. Stylianopoulos, Delivering nanomedicine to solid tumors, Nat. Rev. Clin. Oncol. 7, 653 (2010).
  4. C. P. Brangwynne, C. R. Eckmann, D. S. Courson, A. Rybarska, C. Hoege, J. Gharakhani, F. Jülicher, and A. A. Hyman, Germline P granules are liquid droplets that localize by controlled dissolution/condensation, Science 324, 1729 (2009).
  5. C. P. Brangwynne, T. J. Mitchison, and A. A. Hyman, Active liquid-like behavior of nucleoli determines their size and shape in Xenopus laevis oocytes, Proc. Natl. Acad. Sci. USA 108, 4334 (2011).
  6. A. A. Hyman, C. A. Weber, and F. Jülicher, Liquid-liquid phase separation in biology, Annu. Rev. Cell Dev. Biol. 30, 39 (2014).
  7. L. G. Leal, The motion of small particles in non-Newtonian fluids, J. Non-Newtonian Fluid Mech. 5, 33 (1979).
  8. R. B. Bird, R. C. Armstrong, and O. Hassager, Dynamics of Polymeric Liquids, Volume 1: Fluid Mechanics (Wiley, New York, 1987).
  9. J. R. A. Pearson, Variable-viscosity flows in channels with high heat generation, J. Fluid Mech. 83, 191 (1977).
  10. H. Ockendon and J. R. Ockendon, Variable-viscosity flows in heated and cooled channels, J. Fluid Mech. 83, 177 (1977).
  11. H. Ockendon, Channel flow with temperature-dependent viscosity and internal viscous dissipation, J. Fluid Mech. 93, 737 (1979).
  12. A. Hooper, B. R. Duffy, and H. K. Moffatt, Flow of fluid of non-uniform viscosity in converging and diverging channels, J. Fluid Mech. 117, 283 (1982).
  13. S. Morris, The effects of a strongly temperature-dependent viscosity on slow flow past a hot sphere, J. Fluid Mech. 124, 1 (1982).
  14. N. Oppenheimer, S. Navardi, and H. A. Stone, Motion of a hot particle in viscous fluids, Phys. Rev. Fluids 1, 014001 (2016).
  15. M. Mittasch, P. Gross, M. Nestler, A. W. Fritsch, C. Iserman, M. Kar, M. Munder, A. Voigt, S. Alberti, S. W. Grill, and M. Kreysing, Non-invasive perturbations of intracellular flow reveal physical principles of cell organization, Nat. Cell Biol. 20, 344 (2018).
  16. W. Liao, E. Erben, M. Kreysing, and E. Lauga, Theoretical model of confined thermoviscous flows for artificial cytoplasmic streaming, Phys. Rev. Fluids 8, 034202 (2023).
  17. H. Lamb, Hydrodynamics (Cambridge University Press, Cambridge, UK, 1932).
  18. J. Happel and H. Brenner, Low Reynolds Number Hydrodynamics: With Special Applications to Particulate Media (Springer, Berlin, 2012).
  19. S. Kim and S. J. Karrila, Microhydrodynamics: Principles and Selected Applications (Courier Corporation, North Chelmsford, MA, 2013).
  20. M. J. Lighthill, An Introduction to Fourier Analysis and Generalised Functions (Cambridge University Press, Cambridge, UK, 1958).
  21. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevFluids.8.L051301 for the detailed derivation of Eqs. (3), (4), (6), (10), and (11) and an illustrative example of how to capture the hydrodynamic interaction between point viscosities, which includes Ref. [22].
  22. M. Lisicki, Four approaches to hydrodynamic Green's functions—the Oseen tensors, arXiv:1312.6231.
  23. G. I. Taylor, The viscosity of a fluid containing small drops of another fluid, Proc. R. Soc. London, Ser. A 138, 41 (1932).
  24. M. G. Petrino and R. N. Doetsch, ‘Viscotaxis’, a new behavioural response of Leptospira interrogans (biflexa) strain B16, J. Gen. Microbiol. 109, 113 (1978).
  25. M. J. Lighthill, On the squirming motion of nearly spherical deformable bodies through liquids at very small Reynolds numbers, Commun. Pure Appl. Math. 5, 109 (1952).
  26. J. R. Blake, A spherical envelope approach to ciliary propulsion, J. Fluid Mech. 46, 199 (1971).
  27. J. R. Howse, R. A. L. Jones, A. J. Ryan, T. Gough, R. Vafabakhsh, and R. Golestanian, Self-Motile Colloidal Particles: From Directed Propulsion to Random Walk, Phys. Rev. Lett. 99, 048102 (2007).
  28. C. Pozrikidis, Boundary Integral and Singularity Methods for Linearized Viscous Flow (Cambridge University Press, Cambridge, UK, 1992).
  29. C. Pozrikidis, A Practical Guide to Boundary Element Methods with the Software Library BEMLIB (Chapman & Hall/CRC, Boca Raton, FL, 2002).
  30. C. Pozrikidis, Reciprocal identities and integral formulations for diffusive scalar transport and Stokes flow with position-dependent diffusivity or viscosity, J. Eng. Math. 96, 95 (2016).
  31. E. Lauga and T. R. Powers, The hydrodynamics of swimming microorganisms, Rep. Prog. Phys. 72, 096601 (2009).
  32. N. Pellicciotta, D. Das, J. Kotar, M. Faucourt, N. Spassky, E. Lauga, and P. Cicuta, Cilia density and flow velocity affect alignment of motile cilia from brain cells, J. Expt. Biol. 223, jeb229310 (2020).
  33. J. P. Celli, B. S. Turner, N. H. Afdhal, S. Keates, I. Ghiran, C. P. Kelly, R. H. Ewoldt, G. H. McKinley, P. So, S. Erramilli, and R. Bansil, Helicobacter pylori moves through mucus by reducing mucin viscoelasticity, Proc. Natl. Acad. Sci. USA 106, 14321 (2009).
  34. Y. Man and E. Lauga, Phase-separation models for swimming enhancement in complex fluids, Phys. Rev. E 92, 023004 (2015).
  35. S. A. Mirbagheri and H. C. Fu, Helicobacter pylori Couples Motility and Diffusion to Actively Create a Heterogeneous Complex Medium in Gastric Mucus, Phys. Rev. Lett. 116, 198101 (2016).
  36. D. Das and E. Lauga, Computing the motor torque of Escherichia coli, Soft Matter 14, 5955 (2018).
  37. D. Das and E. Lauga, Transition to bound states for bacteria swimming near surfaces, Phys. Rev. E 100, 043117 (2019).
  38. M. R. Stehnach, N. Waisbord, D. M. Walkama, and J. S. Guasto, Viscophobic turning dictates microalgae transport in viscosity gradients, Nat. Phys. 17, 926 (2021).
  39. S. Coppola and V. Kantsler, Green algae scatter off sharp viscosity gradients, Sci. Rep. 11, 399 (2021).
  40. B. Liebchen, P. Monderkamp, B. ten Hagen, and H. Löwen, Viscotaxis: Microswimmer Navigation in Viscosity Gradients, Phys. Rev. Lett. 120, 208002 (2018).
  41. C. Datt and G. J. Elfring, Active Particles in Viscosity Gradients, Phys. Rev. Lett. 123, 158006 (2019).

Outline

Information

Phys. Rev. Fluids 8, L051301– Published 8 May, 2023
  • Received 24 March 2022
  • Accepted 12 April 2023
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation