- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Fluids

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Weakly nonlinear dynamics of a chemically active particle near the threshold for spontaneous motion. I. Adjoint method

Ory Schnitzer

  • Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom

PDF

Phys. Rev. Fluids 8, 034201 – Published 13 March, 2023

DOI: https://doi.org/10.1103/PhysRevFluids.8.034201

Abstract

In this series, we study the weakly nonlinear dynamics of chemically active particles near the threshold for spontaneous motion. In this part, we focus on steady solutions and develop an “adjoint method” for deriving the nonlinear amplitude equation governing the particle's velocity, first assuming the canonical model in the literature of an isotropic chemically active particle and then considering general perturbations about that model. As in previous works, the amplitude equation is obtained from a solvability condition on the inhomogeneous problem at second order of a particle-scale weakly nonlinear expansion, the formulation of that problem involving asymptotic matching with a leading-order solution in a remote region where advection and diffusion are balanced. We develop a generalized solvability condition based on a Fredholm alternative argument, which entails identifying the adjoint linear operator at the threshold and calculating its kernel. This circumvents the apparent need in earlier theories to solve the second-order inhomogeneous problem, resulting in considerable simplification and adding insight by making it possible to treat a wide range of perturbation scenarios on a common basis. To illustrate our approach, we derive and solve amplitude equations for a number of perturbation scenarios (external force and torque fields, nonuniform surface properties, first-order surface kinetics and bulk absorption), demonstrating that sufficiently near the threshold weak perturbations can appreciably modify and enrich the landscape of steady solutions.

View figure in article

Physics Subject Headings (PhySH)

See Also

Weakly nonlinear dynamics of a chemically active particle near the threshold for spontaneous motion. II. History-dependent motion

Gunnar G. Peng and Ory Schnitzer
Phys. Rev. Fluids 8, 033602 (2023)

Article Text

References (48)

  1. J. L. Anderson, Colloid transport by interfacial forces, Annu. Rev. Fluid Mech. 30, 139 (1998).
  2. R. Golestanian, T. B. Liverpool, and A. Ajdari, Propulsion of a Molecular Machine by Asymmetric Distribution of Reaction Products, Phys. Rev. Lett. 94, 220801 (2005).
  3. R. Golestanian, T. B. Liverpool, and A. Ajdari, Designing phoretic micro- and nano-swimmers, New J. Phys. 9, 126 (2007).
  4. S. Ebbens, D. A. Gregory, G. Dunderdale, J. R. Howse, Y. Ibrahim, T. B. Liverpool, and R. Golestanian, Electrokinetic effects in catalytic platinum-insulator janus swimmers, Europhys. Lett. 106, 58003 (2014).
  5. S. Michelin and E. Lauga, Autophoretic locomotion from geometric asymmetry, Eur. Phys. J. E 38, 1 (2015).
  6. M. N. Popescu, W. E. Uspal, and S. Dietrich, Self-diffusiophoresis of chemically active colloids, Eur. Phys. J.: Spec. Top. 225, 2189 (2016).
  7. J. L. Moran and J. D. Posner, Phoretic self-propulsion, Annu. Rev. Fluid Mech. 49, 511 (2017).
  8. S. Michelin and E. Lauga, Geometric tuning of self-propulsion for Janus catalytic particles, Sci. Rep. 7, 42264 (2017).
  9. S. M. Rubinstein, G. Manukyan, A. Staicu, I. Rubinstein, B. Zaltzman, R. G. H. Lammertink, F. Mugele, and M. Wessling, Direct Observation of a Nonequilibrium Electro-Osmotic Instability, Phys. Rev. Lett. 101, 236101 (2008).
  10. S. E. Game, E. E. Keaveny, D. T. Papageorgiou, and M. Hodes, Physical mechanisms relevant to flow resistance in textured microchannels, Phys. Rev. Fluids 2, 094102 (2017).
  11. Y. Chen, K. L. Chong, L. Liu, R. Verzicco, and D. Lohse, Instabilities driven by diffusiophoretic flow on catalytic surfaces, J. Fluid Mech. 919, A10 (2021).
  12. S. Michelin, E. Lauga, and D. Bartolo, Spontaneous autophoretic motion of isotropic particles, Phys. Fluids 25, 061701 (2013).
  13. S. Michelin and E. Lauga, Phoretic self-propulsion at finite Péclet numbers, J. Fluid Mech. 747, 572 (2014).
  14. M. Morozov and S. Michelin, Nonlinear dynamics of a chemically-active drop: From steady to chaotic self-propulsion, J. Chem. Phys. 150, 044110 (2019).
  15. R. Kailasham and A. S. Khair, Dynamics of forced and unforced autophoretic particles, J. Fluid Mech. 938, A41 (2022).
  16. A. Y. Rednikov, Y. S. Ryazantsev, and M. G. Velarde, Drop motion with surfactant transfer in a homogeneous surrounding, Phys. Fluids 6, 451 (1994).
  17. M. Schmitt and H. Stark, Swimming active droplet: A theoretical analysis, Europhys. Lett. 101, 44008 (2013).
  18. Z. Izri, M. N. van der Linden, S. Michelin, and O. Dauchot, Self-Propulsion of Pure Water Droplets by Spontaneous Marangoni-Stress-Driven Motion, Phys. Rev. Lett. 113, 248302 (2014).
  19. S. Suda, T. Suda, T. Ohmura, and M. Ichikawa, Straight-to-Curvilinear Motion transition of a Swimming Droplet Caused by the Susceptibility to Fluctuations, Phys. Rev. Lett. 127, 088005 (2021).
  20. B. V. Hokmabad, R. Dey, M. Jalaal, D. Mohanty, M. Almukambetova, K. A. Baldwin, D. Lohse, and C. C. Maass, Emergence of Bimodal Motility in Active Droplets, Phys. Rev. X 11, 011043 (2021).
  21. Gaojin Li, Swimming dynamics of a self-propelled droplet, J. Fluid Mech. 934, A20 (2022).
  22. B. V. Hokmabad, A. Nishide, P. Ramesh, and C. C. Maass, Spontaneously rotating clusters of active droplets, Soft Matter 18, 2731 (2022).
  23. S. Michelin, Self-propulsion of chemically active droplets, Ann. Rev. Fluid Mech. 55, 77 (2023).
  24. A. Farutin and C. Misbah, Singular bifurcations: A regularization theory, arXiv:2112.12094.
  25. S. Saha and E. Yariv, Phoretic self-propulsion of a slightly inhomogeneous disc, J. Fluid Mech. 940, A24 (2022).
  26. F. Picella and S. Michelin, Confined self-propulsion of an isotropic active colloid, J. Fluid Mech. 933, A27 (2022).
  27. E. Yariv and U. Kaynan, Phoretic drag reduction of chemically active homogeneous spheres under force fields and shear flows, Phys. Rev. Fluids 2, 012201(R) (2017).
  28. S. Saha, E. Yariv, and O. Schnitzer, Isotropically active colloids under uniform force fields: From forced to spontaneous motion, J. Fluid Mech. 916, A47 (2021).
  29. I. S. Riazantsev and A. E. Rednikov, Self-sustained motion of a drop in homogeneous surroundings, in Proceedings of the International Astronautical Federation Congress (Washington, DC, 1992).
  30. M. Morozov and S. Michelin, Self-propulsion near the onset of marangoni instability of deformable active droplets, J. Fluid Mech. 860, 711 (2019).
  31. A. Y. Rednikov, V. N. Kurdyumov, Y. S. Ryazantsev, and M. G. Velarde, The role of time-varying gravity on the motion of a drop induced by Marangoni instability, Phys. Fluids 7, 2670 (1995).
  32. K. Lippera, M. Morozov, M. Benzaquen, and S. Michelin, Collisions and rebounds of chemically active droplets, J. Fluid Mech. 886, A17 (2020).
  33. K. Lippera, M. Benzaquen, and S. Michelin, Bouncing, chasing, or pausing: Asymmetric collisions of active droplets, Phys. Rev. Fluids 5, 032201(R) (2020).
  34. N. Desai and S. Michelin, Instability and self-propulsion of active droplets along a wall, Phys. Rev. Fluids 6, 114103 (2021).
  35. W. F. Hu, T. S. Lin, S. Rafai, and C. Misbah, Chaotic Swimming of Phoretic Particles, Phys. Rev. Lett. 123, 238004 (2019).
  36. A. Farutin, M. S. Rizvi, W. F. Hu, T. S. Lin, S. Rafaï, and C. Misbah, A reduced model for a phoretic swimmer, J. Fluid Mech. 952, A6 (2022).
  37. W. F. Hu, T. S. Lin, S. Rafai, and C. Misbah, Spontaneous locomotion of phoretic particles in three dimensions, Phys. Rev. Fluids 7, 034003 (2022).
  38. D. Boniface, C. Cottin-Bizonne, R. Kervil, C. Ybert, and F. Detcheverry, Self-propulsion of symmetric chemically active particles: Point-source model and experiments on camphor disks, Phys. Rev. E 99, 062605 (2019).
  39. K. Lippera, M. Benzaquen, and S. Michelin, Alignment and scattering of colliding active droplets, Soft Matter 17, 365 (2021).
  40. A. R. Ye, Y. S. Ryazantsev and M. G. Velarde, Drop motion and the Maragoni effect. Interaction of modes, Phys. Scr. 1994, 115 (1994).
  41. A. Acrivos and T. D. Taylor, Heat and mass transfer from single spheres in Stokes flow, Phys. Fluids 5, 387 (1962).
  42. E. J. Hinch, Perturbation Methods (Cambridge University Press, Cambridge, UK, 1991).
  43. J. P. Keener, Principles of Applied Mathematics: Transformation and Approximation (CRC Press, Boca Raton, FL, 2000).
  44. G. G. Peng and O. Schnitzer, Weakly nonlinear dynamics of a chemically active particle near the threshold for spontaneous motion. II. History-dependent motion, Phys. Rev. Fluids 8, 033602 (2023).
  45. J. Happel and H. Brenner, Low Reynolds Number Hydrodynamics (Prentice-Hall, Englewood Cliffs, NJ, 1965).
  46. H. A. Stone and A. D. T. Samuel, Propulsion of Microorganisms by Surface Distortions, Phys. Rev. Lett. 77, 4102 (1996).
  47. P. de Buyl, A. S. Mikhailov, and R. Kapral, Self-propulsion through symmetry breaking, Europhys. Lett. 103, 60009 (2013).
  48. J. G. Van Bladel, Electromagnetic Fields (John Wiley & Sons, New York, NY, 2007), Vol. 19.

Outline

Information

Phys. Rev. Fluids 8, 034201– Published 13 March, 2023
  • Received 13 May 2022
  • Accepted 18 July 2022
Crossmark - Check for updates button

©2023 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation