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Thermophoresis of Janus particles at large Knudsen numbers

Tobias Baier1,*, Sudarshan Tiwari2,†, Samir Shrestha3,‡, Axel Klar2,§, and Steffen Hardt1,∥

  • 1Institute for Nano- and Microfluidics, Technische Universität Darmstadt, 64287 Darmstadt, Germany
  • 2Department of Mathematics, University of Kaiserslautern, 67653 Kaiserslautern, Germany
  • 3Department of Natural Sciences, Kathmandu University, Dhulikhel 45200, Nepal

  • *baier@nmf.tu-darmstadt.de
  • †tiwari@mathematik.uni-kl.de
  • ‡samirstha@ku.edu.np
  • §klar@mathematik.uni-kl.de
  • ∥hardt@nmf.tu-darmstadt.de
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Phys. Rev. Fluids 3, 094202 – Published 12 September, 2018

DOI: https://doi.org/10.1103/PhysRevFluids.3.094202

Abstract

The force and torque on a Janus sphere moving in a rarefied gas with a thermal gradient are calculated. The regime of large Knudsen number is considered, with the momenta of impinging gas molecules either obtained from a Chapman-Enskog distribution or from a binary Maxwellian distribution between two opposing parallel plates at different temperature. The reflection properties at the surface of the Janus particle are characterized by accommodation coefficients having constant but dissimilar values on each hemisphere. It is shown that the Janus particle preferentially orients such that the hemisphere with a larger accommodation coefficient points toward the lower temperature. The thermophoretic velocity of the particle is computed, and the influence of the thermophoretic motion on the magnitude of the torque responsible for the particle orientation is studied. The analytical calculations are supported by direct simulation Monte Carlo results, extending the scope of the study toward smaller Knudsen numbers. The results shed light on the efficiency of oriented deposition of nanoparticles from the gas phase onto a cold surface.

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References (44)

  1. J. Aitken, On the formation of small clear spaces in dusty air, Earth Environ. Sci. Trans. Roy. Soc. Edinburgh 32, 239 (1884).
  2. P.-G. De Gennes, Soft matter, Rev. Mod. Phys. 64, 645 (1992).
  3. A. Einstein, Zur Theorie der Radiometerkräfte, Z. Phys. 27, 1 (1924).
  4. L. Waldmann, Über die Kraft eines inhomogenen Gases auf kleine suspendierte Kugeln, Zeitschrift Naturforschung Teil A 14, 589 (1959).
  5. S. Bakanov and B. Derjaguin, The motion of a small particle in a nonuniform gas mixture, Discuss. Faraday Soc. 30, 130 (1960).
  6. K. I. Borg and L. H. Söderholm, Thermophoresis of axially symmetric bodies, AIP Conf. Proc. 585, 867 (2001).
  7. K. I. Borg, L. H. Söderholm, and H. Essén, Force on a spinning sphere moving in a rarefied gas, Phys. Fluids 15, 736 (2003).
  8. E. J. Davis and G. Schweiger, The Airborne Microparticle: Its Physics, Chemistry, Optics, and Transport Phenomena (Springer, Berlin, 2002).
  9. F. Zheng, Thermophoresis of spherical and nonspherical particles: A review of theories and experiments, Adv. Colloid Interface Sci. 97, 255 (2002).
  10. Y. Sone, Molecular Gas Dynamics: Theory, Techniques, and Applications (Birkhäuser, Switzerland, 2007).
  11. J. B. Young, Thermophoresis of a spherical particle: Reassessment, clarification, and new analysis, Aerosol Sci. Technol. 45, 927 (2011).
  12. S. C. Glotzer and M. J. Solomon, Anisotropy of building blocks and their assembly into complex structures, Nat. Mater. 6, 557 (2007).
  13. A. Lorke, M. Winterer, R. Schmechel, and C. Schulz, Nanoparticles from the Gasphase (Springer, Berlin, 2012).
  14. J. Hu, S. Zhou, Y. Sun, X. Fang, and L. Wu, Fabrication, properties and applications of Janus particles, Chem. Soc. Rev. 41, 4356 (2012).
  15. A. Walther and A. H. Müller, Janus particles: Synthesis, self-assembly, physical properties, and applications, Chem. Rev. 113, 5194 (2013).
  16. J. Zhang, B. A. Grzybowski, and S. Granick, Janus particle synthesis, assembly, and application, Langmuir 33, 6964 (2017).
  17. A. Agrawal and S. Prabhu, Survey on measurement of tangential momentum accommodation coefficient, J. Vac. Sci. Technol. A 26, 634 (2008).
  18. B.-Y. Cao, J. Sun, M. Chen, and Z.-Y. Guo, Molecular momentum transport at fluid-solid interfaces in MEMS/NEMS: A review, Int. J. Mol. Sci. 10, 4638 (2009).
  19. D. Seo and W. A. Ducker, In Situ Control of Gas Flow by Modification of Gas-Solid Interactions, Phys. Rev. Lett. 111, 174502 (2013).
  20. D. Seo and W. A. Ducker, Effect of gas species on gas-monolayer interactions: Tangential momentum accommodation, J. Phys. Chem. C 118, 20275 (2014).
  21. H.-R. Jiang, N. Yoshinaga, and M. Sano, Active Motion of a Janus Particle by Self-Thermophoresis in a Defocused Laser Beam, Phys. Rev. Lett. 105, 268302 (2010).
  22. T. Bickel, A. Majee, and A. Würger, Flow pattern in the vicinity of self-propelling hot Janus particles, Phys. Rev. E 88, 012301 (2013).
  23. H. Rohatschek, The role of gravitophotophoresis for stratospheric and mesospheric particulates, J. Atmos. Chem. 1, 377 (1984).
  24. S. Beresnev, M. Vasiljeva, and D. Suetin, Predictions and detection of the “accommodation” forces on Janus particles subjected to directed radiation in a rarefied gas, Vacuum 86, 1663 (2012).
  25. L. D. Landau and E. Lifschitz, Physikalische Kinetik (Akademie-Verlag, Berlin, 1983).
  26. G. Bird, Molecular Gas Dynamics and the Direct Simulation of Gas Flows (Clarendon Press, Oxford, UK, 1994).
  27. C.-T. Wang, Free molecular flow over a rotating sphere, AIAA J. 10, 713 (1972).
  28. S. Ivanov and A. Yanshin, Forces and moments acting on bodies rotating about a symmetry axis in a free molecular flow, Fluid Dyn. 15, 449 (1980).
  29. P. D. Weidman and A. Herczynski, On the inverse Magnus effect in free molecular flow, Phys. Fluids 16, L9 (2004).
  30. S. Loyalka, Motion of a sphere in a gas: Numerical solution of the linearized Boltzmann equation, Phys. Fluids A 4, 1049 (1992).
  31. J. R. McConnell, Rotational Brownian Motion and Dielectric Theory (Academic Press, San Diego, 1980).
  32. W. T. Coffey and Y. P. Kalmykov, The Langevin Equation: With Applications to Stochastic Problems in Physics, Chemistry and Electrical Engineering (World Scientific, Singapore, 2012), Vol. 27.
  33. K. Jacobs, Stochastic Processes for Physicists: Understanding Noisy Systems (Cambridge University Press, Cambridge, 2010).
  34. C. Gardiner, Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences, 3rd ed. (Springer-Verlag, Berlin/Heidelberg, 2004).
  35. N. G. Van Kampen, Stochastic Processes in Physics and Chemistry, 3rd ed. (Elsevier, New York, 2007).
  36. W. F. Phillips, Thermal force on spherical particles in a rarefied gas, Phys. Fluids 15, 999 (1972).
  37. M. Gallis, J. Torczynski, and D. Rader, An approach for simulating the transport of spherical particles in a rarefied gas flow via the direct simulation Monte Carlo method, Phys. Fluids 13, 3482 (2001).
  38. M. Abramowitz and I. Stegun, Handbook of Mathematical Functions (Dover Publishing Inc., New York, 1970).
  39. H. Babovsky and R. Illner, A convergence proof for Nanbu's simulation method for the full Boltzmann equation, SIAM J. Numer. Anal. 26, 45 (1989).
  40. H. Neunzert and J. Struckmeier, Particle methods for the Boltzmann equation, Acta Numerica 4, 417 (1995).
  41. S. Shrestha, S. Tiwari, A. Klar, and S. Hardt, Numerical simulation of a moving rigid body in a rarefied gas, J. Comput. Phys. 292, 239 (2015).
  42. N. G. Hadjiconstantinou, A. L. Garcia, M. Z. Bazant, and G. He, Statistical error in particle simulations of hydrodynamic phenomena, J. Comput. Phys. 187, 274 (2003).
  43. K. Jousten, Handbook of Vacuum Technology (Wiley-VCH Verlag, Weinheim, 2008).
  44. F. Sharipov, L. M. G. Cumin, and D. Kalempa, Heat flux between parallel plates through a binary gaseous mixture over the whole range of the Knudsen number, Physica A (Amsterdam) 378, 183 (2007).

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Phys. Rev. Fluids 3, 094202– Published 12 September, 2018
  • Received 12 April 2018
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