Advertisement

Creeping motion of a solid particle inside a spherical elastic cavity: II. Asymmetric motion

  • Christian HoellEmail author
  • Hartmut Löwen
  • Andreas M. Menzel
  • Abdallah Daddi-Moussa-Ider
Regular Article

Abstract.

An analytical method is proposed for computing the low-Reynolds-number hydrodynamic mobility function of a small colloidal particle asymmetrically moving inside a large spherical elastic cavity, the membrane of which is endowed with resistance toward shear and bending. In conjunction with the results obtained in the first part (A. Daddi-Moussa-Ider, H. Löwen, S. Gekle, Eur. Phys. J. E 41, 104 (2018)), in which the axisymmetric motion normal to the surface of an elastic cavity is investigated, the general motion for an arbitrary force direction can now be addressed. The elastohydrodynamic problem is formulated and solved using the classic method of images through expressing the hydrodynamic flow fields as a multipole expansion involving higher-order derivatives of the free-space Green’s function. In the quasi-steady limit, we demonstrate that the particle self-mobility function of a particle moving tangent to the surface of the cavity is larger than that predicted inside a rigid stationary cavity of equal size. This difference is justified by the fact that a stationary rigid cavity introduces additional hindrance to the translational motion of the encapsulated particle, resulting in a reduction of its hydrodynamic mobility. Furthermore, the motion of the cavity is investigated, revealing that the translational pair (composite) mobility, which linearly couples the velocity of the elastic cavity to the force exerted on the solid particle, is solely determined by membrane shear properties. Our analytical predictions are favorably compared with fully-resolved computer simulations based on a completed-double-layer boundary integral method.

Graphical abstract

Keywords

Flowing matter: Nonlinear Physics and Mesoscale Modeling 

References

  1. 1.
    H.A. Stone, A.D. Stroock, A. Ajdari, Annu. Rev. Fluid Mech. 36, 381 (2004)ADSGoogle Scholar
  2. 2.
    A.Y. Fu, C. Spence, A. Scherer, F.H. Arnold, S.R. Quake, Nat. Biotechnol. 17, 1109 (1999)Google Scholar
  3. 3.
    H. Lu, S. Gaudet, M.A. Schmidt, K.F. Jensen, Anal. Chem. 76, 5705 (2004)Google Scholar
  4. 4.
    D. Huh, W. Gu, Y. Kamotani, J.B. Grotberg, S. Takayama, Physiol. Meas. 26, R73 (2005)ADSGoogle Scholar
  5. 5.
    L. Schmid, D.A. Weitz, T. Franke, Lab Chip 14, 3710 (2014)Google Scholar
  6. 6.
    S. Darvishmanesh, L. Firoozpour, J. Vanneste, P. Luis, J. Degreve, B. Van der Bruggen, Green Chem. 13, 3476 (2011)Google Scholar
  7. 7.
    A. Adamo, P.L. Heider, N. Weeranoppanant, K.F. Jensen, Ind. Eng. Chem. Res. 52, 10802 (2013)Google Scholar
  8. 8.
    B. Gutmann, D. Cantillo, C.O. Kappe, Angew. Chem. Int. Ed. 54, 6688 (2015)Google Scholar
  9. 9.
    Y.L. Colson, M.W. Grinstaff, Adv. Mater. 24, 3878 (2012)Google Scholar
  10. 10.
    H. Hillaireau, P. Couvreur, Cell. Mol. Life Sci. 66, 2873 (2009)Google Scholar
  11. 11.
    J. Liu, T. Wei, J. Zhao, Y. Huang, H. Deng, A. Kumar, C. Wang, Z. Liang, X. Ma, X.J. Liang, Biomaterials 91, 44 (2016)Google Scholar
  12. 12.
    H. Maeda, H. Nakamura, J. Fang, Adv. Drug Deliv. Rev. 65, 71 (2013)Google Scholar
  13. 13.
    S. Naahidi, M. Jafari, F. Edalat, K. Raymond, A. Khademhosseini, P. Chen, J. Control. Release 166, 182 (2013)Google Scholar
  14. 14.
    J.M. Rosenholm, C. Sahlgren, M. Linden, Nanoscale 2, 1870 (2010)ADSGoogle Scholar
  15. 15.
    R. Singh, J.W. Lillard, Exp. Mol. Pathol. 86, 215 (2009)Google Scholar
  16. 16.
    L.M. Bareford, P.W. Swaan, Adv. Drug Deliv. Rev. 59, 748 (2007)Google Scholar
  17. 17.
    J. Happel, H. Brenner, Low Reynolds Number Hydrodynamics: With Special Applications to Particulate Media, Vol. 1 (Springer Netherlands, Dordrecht, Netherlands, 2012)Google Scholar
  18. 18.
    S. Kim, S.J. Karrila, Microhydrodynamics: Principles and Selected Applications (Dover Publications, Mineola, New York, 2013)Google Scholar
  19. 19.
    L.G. Leal, Annu. Rev. Fluid Mech. 12, 435 (1980)ADSGoogle Scholar
  20. 20.
    J.R. Blake, Math. Proc. Camb. Philos. Soc. 70, 303 (1971)ADSGoogle Scholar
  21. 21.
    C.W. Oseen, Neuere Methoden und Ergebnisse in der Hydrodynamik (Akademische Verlagsgesellschaft, Leipzig, Germany, 1928)Google Scholar
  22. 22.
    S.F.J. Butler, Math. Proc. Cambridge Philos. Soc. 49, 169 (1953)ADSGoogle Scholar
  23. 23.
    W.D. Collins, Mathematika 1, 125 (1954)MathSciNetGoogle Scholar
  24. 24.
    H. Hasimoto, J. Phys. Soc. Jpn. 11, 793 (1956)ADSGoogle Scholar
  25. 25.
    H. Hasimoto, J. Phys. Soc. Jpn. 61, 3027 (1992)ADSGoogle Scholar
  26. 26.
    H. Hasimoto, Phys. Fluids 9, 1838 (1997)ADSMathSciNetGoogle Scholar
  27. 27.
    R. Shail, Quart. J. Mech. Appl. Math. 40, 223 (1987)MathSciNetGoogle Scholar
  28. 28.
    R. Shail, S.H. Onslow, Mathematika 35, 233 (1988)MathSciNetGoogle Scholar
  29. 29.
    A. Sellier, Comput. Model. Eng. Sci. 25, 165 (2008)Google Scholar
  30. 30.
    C. Maul, S. Kim, Phys. Fluids 6, 2221 (1994)ADSGoogle Scholar
  31. 31.
    C. Maul, S. Kim, in The Centenary of a Paper on Slow Viscous Flow by the Physicist H.A. Lorentz (Springer Netherlands, Dordrecht, Netherlands, 1996) pp. 119--130Google Scholar
  32. 32.
    B.U. Felderhof, A. Sellier, J. Chem. Phys. 136, 054703 (2012)ADSGoogle Scholar
  33. 33.
    D. Tsemakh, O.M. Lavrenteva, A. Nir, Int. J. Multiph. Flow 30, 1337 (2004)Google Scholar
  34. 34.
    O.M. Lavrenteva, D. Tsemakh, A. Nir, Fluid Dyn. Mater. Process. 1, 131 (2005)Google Scholar
  35. 35.
    S.Y. Reigh, L. Zhu, F. Gallaire, E. Lauga, Soft Matter 13, 3161 (2017)ADSGoogle Scholar
  36. 36.
    L. Zhu, F. Gallaire, Phys. Rev. Lett. 119, 064502 (2017)ADSGoogle Scholar
  37. 37.
    S.Y. Reigh, E. Lauga, Phys. Rev. Fluids 2, 093101 (2017)ADSGoogle Scholar
  38. 38.
    V.A. Shaik, V. Vasani, A.M. Ardekani, J. Fluid Mech. 851, 187 (2018)ADSMathSciNetGoogle Scholar
  39. 39.
    A. Daddi-Moussa-Ider, A. Guckenberger, S. Gekle, Phys. Rev. E 93, 012612 (2016)ADSGoogle Scholar
  40. 40.
    A. Daddi-Moussa-Ider, S. Gekle, Eur. Phys. J. E 41, 19 (2018)Google Scholar
  41. 41.
    A. Daddi-Moussa-Ider, S. Gekle, Phys. Rev. E 95, 013108 (2017)ADSGoogle Scholar
  42. 42.
    A. Daddi-Moussa-Ider, M. Lisicki, S. Gekle, Phys. Rev. E 95, 053117 (2017)ADSGoogle Scholar
  43. 43.
    A. Daddi-Moussa-Ider, M. Lisicki, S. Gekle, Phys. Fluids 29, 111901 (2017)ADSGoogle Scholar
  44. 44.
    A. Daddi-Moussa-Ider, M. Lisicki, S. Gekle, Acta Mech. 229, 149 (2018)MathSciNetGoogle Scholar
  45. 45.
    A. Daddi-Moussa-Ider, H. Löwen, S. Gekle, Eur. Phys. J. E 41, 104 (2018)Google Scholar
  46. 46.
    Y.O. Fuentes, S. Kim, D.J. Jeffrey, Phys. Fluids 31, 2445 (1988)ADSGoogle Scholar
  47. 47.
    Y.O. Fuentes, S. Kim, D.J. Jeffrey, Phys. Fluids 1, 61 (1989)ADSGoogle Scholar
  48. 48.
    K. Sekimoto, L. Leibler, Europhys. Lett. 23, 113 (1993)ADSGoogle Scholar
  49. 49.
    S.J. Weekley, S.L. Waters, O.E. Jensen, Q. J. Mech. Appl. Math. 59, 277 (2006)Google Scholar
  50. 50.
    T. Salez, L. Mahadevan, J. Fluid Mech. 779, 181 (2015)ADSMathSciNetGoogle Scholar
  51. 51.
    B. Saintyves, T. Jules, T. Salez, L. Mahadevan, Proc. Natl. Acad. Sci. U.S.A. 113, 5847 (2016)ADSGoogle Scholar
  52. 52.
    B. Rallabandi, B. Saintyves, T. Jules, T. Salez, C. Schönecker, L. Mahadevan, H.A. Stone, Phys. Rev. Fluids 2, 074102 (2017)ADSGoogle Scholar
  53. 53.
    A. Daddi-Moussa-Ider, B. Rallabandi, S. Gekle, H.A. Stone, Phys. Rev. Fluids 3, 084101 (2018)ADSGoogle Scholar
  54. 54.
    B. Rallabandi, N. Oppenheimer, M.Y.B. Zion, H.A. Stone, Nat. Phys. 14, 1211 (2018)Google Scholar
  55. 55.
    R. Skalak, A. Tozeren, R.P. Zarda, S. Chien, Biophys. J. 13, 245 (1973)ADSGoogle Scholar
  56. 56.
    J.B. Freund, Annu. Rev. Fluid Mech. 46, 67 (2014)ADSGoogle Scholar
  57. 57.
    T. Krüger, Computer Simulation Study of Collective Phenomena in Dense Suspensions of Red Blood Cells under Shear (Vieweg+Teubner Verlag, Wiesbaden, Germany, 2012)Google Scholar
  58. 58.
    T. Krüger, F. Varnik, D. Raabe, Comput. Math. Appl. 61, 3485 (2011)MathSciNetGoogle Scholar
  59. 59.
    A.E. Green, J.C. Adkins, Large Elastic Deformations and Non-linear Continuum Mechanics (Oxford University Press, Oxford, UK, 1960)Google Scholar
  60. 60.
    L. Zhu, PhD Thesis (2014)Google Scholar
  61. 61.
    E. Lac, D. Barthes-Biesel, N.A. Pelekasis, J. Tsamopoulos, J. Fluid Mech. 516, 303 (2004)ADSMathSciNetGoogle Scholar
  62. 62.
    W. Helfrich, Z. Naturforsch. C 28, 693 (1973)Google Scholar
  63. 63.
    K. Berndl, J. Käs, R. Lipowsky, E. Sackmann, U. Seifert, Europhys. Lett. 13, 659 (1990)ADSGoogle Scholar
  64. 64.
    U. Seifert, Adv. Phys. 46, 13 (1997)ADSGoogle Scholar
  65. 65.
    A. Guckenberger, S. Gekle, J. Phys.: Condens. Matter 29, 203001 (2017)ADSGoogle Scholar
  66. 66.
    S. Kobayashi, K. Nomizu, Foundations of Differential Geometry, Vol. 1 (Interscience Publishers, New York, 1963)Google Scholar
  67. 67.
    M. Deserno, Chem. Phys. Lipids 185, 11 (2015)Google Scholar
  68. 68.
    J.R. Blake, A.T. Chwang, J. Eng. Math. 8, 23 (1974)Google Scholar
  69. 69.
    D. Zill, W.S. Wright, M.R. Cullen, Advanced Engineering Mathematics (Jones & Bartlett Learning, Burlington, Massachusetts, 2011)Google Scholar
  70. 70.
    H. Lamb, Hydrodynamics (Cambridge University Press, Cambridge, UK, 1932)Google Scholar
  71. 71.
    M. Abramowitz, I.A. Stegun, Handbook of Mathematical Functions, Vol. 1 (Dover Publications, Mineola, New York, 1972)Google Scholar
  72. 72.
    A.R. Edmonds, Angular Momentum in Quantum Mechanics, Vol. 4 (Princeton University Press, Princeton, New Jersey, 1996)Google Scholar
  73. 73.
    Y. Rui, S. Wang, P.S. Low, D.H. Thompson, J. Am. Chem. Soc. 120, 11213 (1998)Google Scholar
  74. 74.
    V.P. Torchilin, Nat. Rev. Drug Discov. 4, 145 (2005)Google Scholar
  75. 75.
    C. Zylberberg, S. Matosevic, Drug Deliv. 23, 3319 (2016)Google Scholar
  76. 76.
    T. Bickel, Eur. Phys. J. E 20, 379 (2006)Google Scholar
  77. 77.
    T. Bickel, Phys. Rev. E 75, 041403 (2007)ADSGoogle Scholar
  78. 78.
    J.W. Swan, J.F. Brady, Phys. Fluids 19, 113306 (2007)ADSGoogle Scholar
  79. 79.
    J.W. Swan, J.F. Brady, Phys. Fluids 22, 103301 (2010)ADSGoogle Scholar
  80. 80.
    C. Aponte-Rivera, R.N. Zia, Phys. Rev. Fluids 1, 023301 (2016)ADSGoogle Scholar
  81. 81.
    C. Aponte-Rivera, Y. Su, R.N. Zia, J. Fluid Mech. 836, 413 (2018)ADSMathSciNetGoogle Scholar
  82. 82.
    C. Aponte-Rivera, PhD Thesis, Cornell University, USA (2017)Google Scholar
  83. 83.
    N.L. Carothers, Real Analysis (Cambridge University Press, Cambridge, UK, 2000)Google Scholar
  84. 84.
    P. Billingsley, Convergence of Probability Measures (John Wiley & Sons, Hoboken, New Jersey, 2013)Google Scholar
  85. 85.
    S.H. Lee, R.S. Chadwick, L.G. Leal, J. Fluid Mech. 93, 705 (1979)ADSGoogle Scholar
  86. 86.
    C. Pozrikidis, J. Comput. Phys. 169, 250 (2001)ADSGoogle Scholar
  87. 87.
    A. Daddi-Moussa-Ider, A. Guckenberger, S. Gekle, Phys. Fluids 28, 071903 (2016)ADSGoogle Scholar
  88. 88.
    A. Guckenberger, M.P. Schraml, P.G. Chen, M. Leonetti, S. Gekle, Comput. Phys. Commun. 207, 1 (2016)ADSGoogle Scholar
  89. 89.
    B.U. Felderhof, Phys. Rev. E 89, 033001 (2014)ADSGoogle Scholar
  90. 90.
    R. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1999)Google Scholar
  91. 91.
    G. Cipparrone, I. Ricardez-Vargas, P. Pagliusi, C. Provenzano, Opt. Express 18, 6008 (2010)ADSGoogle Scholar

Copyright information

© EDP Sciences, Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Christian Hoell
    • 1
    Email author
  • Hartmut Löwen
    • 1
  • Andreas M. Menzel
    • 1
  • Abdallah Daddi-Moussa-Ider
    • 1
  1. 1.Institut für Theoretische Physik II: Weiche MaterieHeinrich-Heine-Universität DüsseldorfDüsseldorfGermany

Personalised recommendations