Skip to main content

Advertisement

SpringerLink
Go to cart
  1. Home
  2. The European Physical Journal E
  3. Article
Towards an analytical description of active microswimmers in clean and in surfactant-covered drops
Download PDF
Your article has downloaded

Similar articles being viewed by others

Slider with three articles shown per slide. Use the Previous and Next buttons to navigate the slides or the slide controller buttons at the end to navigate through each slide.

Deformation of clean and surfactant-laden droplets in shear flow

13 May 2019

Giovanni Soligo, Alessio Roccon & Alfredo Soldati

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

16 July 2019

Christian Hoell, Hartmut Löwen, … Abdallah Daddi-Moussa-Ider

Effect of insoluble surfactants on the motion of Reiner–Rivlin fluid sphere in a spherical container with Newtonian fluid

11 August 2021

Shweta Raturi & B. V. Rathish Kumar

Surfing of particles and droplets on the free surface of a liquid: a review

09 December 2022

Prashant Narayan Panday, Aditya Bandopadhyay & Prasanta Kumar Das

Active spheres induce Marangoni flows that drive collective dynamics

01 February 2021

Martin Wittmann, Mihail N. Popescu, … Juliane Simmchen

Stochastic dynamics of dissolving active particles

16 July 2019

Alexander Chamolly & Eric Lauga

Effective squirmer models for self-phoretic chemically active spherical colloids

12 December 2018

M. N. Popescu, W. E. Uspal, … S. Dietrich

From hydrodynamic lubrication to many-body interactions in dense suspensions of active swimmers

14 June 2018

Natsuhiko Yoshinaga & Tanniemola B. Liverpool

Oscillation dynamics of colloidal particles caused by surfactant in an evaporating droplet

03 February 2020

Hae Won Seo, Narian Jung & Chun Sang Yoo

Download PDF

Associated Content

Part of a collection:

Motile Active Matter

  • Regular Article
  • Open Access
  • Published: 11 September 2020

Towards an analytical description of active microswimmers in clean and in surfactant-covered drops

  • Alexander R. Sprenger1,
  • Vaseem A. Shaik2,
  • Arezoo M. Ardekani2,
  • Maciej Lisicki3,
  • Arnold J. T. M. Mathijssen4,5,
  • Francisca Guzmán-Lastra6,
  • Hartmut Löwen1,
  • Andreas M. Menzel7 &
  • …
  • Abdallah Daddi-Moussa-Ider1 

The European Physical Journal E volume 43, Article number: 58 (2020) Cite this article

  • 993 Accesses

  • 12 Citations

  • 62 Altmetric

  • Metrics details

Abstract.

Geometric confinements are frequently encountered in the biological world and strongly affect the stability, topology, and transport properties of active suspensions in viscous flow. Based on a far-field analytical model, the low-Reynolds-number locomotion of a self-propelled microswimmer moving inside a clean viscous drop or a drop covered with a homogeneously distributed surfactant, is theoretically examined. The interfacial viscous stresses induced by the surfactant are described by the well-established Boussinesq-Scriven constitutive rheological model. Moreover, the active agent is represented by a force dipole and the resulting fluid-mediated hydrodynamic couplings between the swimmer and the confining drop are investigated. We find that the presence of the surfactant significantly alters the dynamics of the encapsulated swimmer by enhancing its reorientation. Exact solutions for the velocity images for the Stokeslet and dipolar flow singularities inside the drop are introduced and expressed in terms of infinite series of harmonic components. Our results offer useful insights into guiding principles for the control of confined active matter systems and support the objective of utilizing synthetic microswimmers to drive drops for targeted drug delivery applications.

Graphical abstract

Download to read the full article text

Working on a manuscript?

Avoid the common mistakes

References

  1. G. Gompper, R.G. Winkler, T. Speck, A. Solon, C. Nardini, F. Peruani, H. Löwen, R. Golestanian, U.B. Kaupp, L. Alvarez et al., J. Phys.: Condens. Matter 32, 193001 (2020)

    ADS  Google Scholar 

  2. J. Palacci, S. Sacanna, A.P. Steinberg, D.J. Pine, P.M. Chaikin, Science 339, 936 (2013)

    ADS  Google Scholar 

  3. S. Sacanna, M. Korpics, K. Rodriguez, L. Colón-Meléndez, S.H. Kim, D.J. Pine, G.R. Yi, Nat. Commun. 4, 1688 (2013)

    ADS  Google Scholar 

  4. N. Chronis, L.P. Lee, J. Microelectromech. Syst. 14, 857 (2005)

    Google Scholar 

  5. M. Junkin, S. Ling Leung, S. Whitman, C.C. Gregorio, P.K. Wong, J. Cell Sci. 124, 4213 (2011)

    Google Scholar 

  6. E. Diller, M. Sitti, Adv. Funct. Mater. 24, 4397 (2014)

    Google Scholar 

  7. D. Ahmed, M. Lu, A. Nourhani, P.E. Lammert, Z. Stratton, H.S. Muddana, V.H. Crespi, T.J. Huang, Sci. Rep. 5, 9744 (2015)

    ADS  Google Scholar 

  8. F. Schmidt, B. Liebchen, H. Löwen, G. Volpe, J. Chem. Phys. 150, 094905 (2019)

    ADS  Google Scholar 

  9. D. Kagan, M.J. Benchimol, J.C. Claussen, E. Chuluun-Erdene, S. Esener, J. Wang, Angew. Chem. Int. Ed. 51, 7519 (2012)

    Google Scholar 

  10. D. Walker, B.T. Käsdorf, H.H. Jeong, O. Lieleg, P. Fischer, Sci. Adv. 1, e1500501 (2015)

    ADS  Google Scholar 

  11. B.J. Nelson, I.K. Kaliakatsos, J.J. Abbott, Annu. Rev. Biomed. Eng. 12, 55 (2010)

    Google Scholar 

  12. F. Qiu, S. Fujita, R. Mhanna, L. Zhang, B.R. Simona, B.J. Nelson, Adv. Funct. Mater. 25, 1666 (2015)

    Google Scholar 

  13. B.W. Park, J. Zhuang, O. Yasa, M. Sitti, ACS Nano 11, 8910 (2017)

    Google Scholar 

  14. B. Mostaghaci, O. Yasa, J. Zhuang, M. Sitti, Adv. Sci. 4, 1700058 (2017)

    Google Scholar 

  15. D. Gourevich, O. Dogadkin, A. Volovick, L. Wang, J. Gnaim, S. Cochran, A. Melzer, J. Control. Release 170, 316 (2013)

    Google Scholar 

  16. U. Kei Cheang, K. Lee, A.A. Julius, M.J. Kim, Appl. Phys. Lett. 105, 083705 (2014)

    ADS  Google Scholar 

  17. J. Wang, M.S. Lin, Anal. Chem. 60, 1545 (1988)

    Google Scholar 

  18. E. Lauga, T.R. Powers, Rep. Prog. Phys. 72, 096601 (2009)

    ADS  Google Scholar 

  19. M.C. Marchetti, J.F. Joanny, S. Ramaswamy, T.B. Liverpool, J. Prost, M. Rao, R.A. Simha, Rev. Mod. Phys. 85, 1143 (2013)

    ADS  Google Scholar 

  20. J. Elgeti, R.G. Winkler, G. Gompper, Rep. Prog. Phys. 78, 056601 (2015)

    ADS  Google Scholar 

  21. A.M. Menzel, Phys. Rep. 554, 1 (2015)

    ADS  MathSciNet  Google Scholar 

  22. C. Bechinger, R. Di Leonardo, H. Löwen, C. Reichhardt, G. Volpe, G. Volpe, Rev. Mod. Phys. 88, 045006 (2016)

    ADS  Google Scholar 

  23. A. Zöttl, H. Stark, J. Phys.: Condens. Matter 28, 253001 (2016)

    ADS  Google Scholar 

  24. E. Lauga, Annu. Rev. Fluid Mech. 48, 105 (2016)

    ADS  Google Scholar 

  25. P. Illien, R. Golestanian, A. Sen, Chem. Soc. Rev. 46, 5508 (2017)

    Google Scholar 

  26. N. Desai, A.M. Ardekani, Soft Matter 13, 6033 (2017)

    ADS  Google Scholar 

  27. K.K. Dey, Angew. Chem. Int. Ed. 58, 2208 (2019)

    Google Scholar 

  28. M.R. Shaebani, A. Wysocki, R.G. Winkler, G. Gompper, H. Rieger, Nat. Rev. Phys. 2, 181 (2020)

    Google Scholar 

  29. G. Grégoire, H. Chaté, Phys. Rev. Lett. 92, 025702 (2004)

    ADS  Google Scholar 

  30. S. Mishra, A. Baskaran, M.C. Marchetti, Phys. Rev. E 81, 061916 (2010)

    ADS  Google Scholar 

  31. A.M. Menzel, Phys. Rev. E 85, 021912 (2012)

    ADS  Google Scholar 

  32. H.H. Wensink, H. Löwen, J. Phys.: Condens. Matter 24, 464130 (2012)

    ADS  Google Scholar 

  33. H.H. Wensink, J. Dunkel, S. Heidenreich, K. Drescher, R.E. Goldstein, H. Löwen, J.M. Yeomans, Proc. Natl. Acad. Sci. U.S.A. 109, 14308 (2012)

    ADS  Google Scholar 

  34. J. Dunkel, S. Heidenreich, K. Drescher, H.H. Wensink, M. Bär, R.E. Goldstein, Phys. Rev. Lett. 110, 228102 (2013)

    ADS  Google Scholar 

  35. R. Großmann, P. Romanczuk, M. Bär, L. Schimansky-Geier, Phys. Rev. Lett. 113, 258104 (2014)

    ADS  Google Scholar 

  36. A. Kaiser, A. Peshkov, A. Sokolov, B. ten Hagen, H. Löwen, I.S. Aranson, Phys. Rev. Lett. 112, 158101 (2014)

    ADS  Google Scholar 

  37. S. Heidenreich, S.H.L. Klapp, M. Bär, J. Phys.: Conf. Ser. 490, 012126 (2014)

    Google Scholar 

  38. S. Heidenreich, J. Dunkel, S.H.L. Klapp, M. Bär, Phys. Rev. E 94, 020601 (2016)

    ADS  Google Scholar 

  39. A. Doostmohammadi, T.N. Shendruk, K. Thijssen, J.M. Yeomans, Nat. Commun. 8, 15326 (2017)

    ADS  Google Scholar 

  40. M.E. Cates, J. Tailleur, Annu. Rev. Condens. Matter Phys. 6, 219 (2015)

    ADS  Google Scholar 

  41. M.E. Cates, J. Tailleur, EPL 101, 20010 (2013)

    ADS  Google Scholar 

  42. J. Tailleur, M.E. Cates, Phys. Rev. Lett. 100, 218103 (2008)

    ADS  Google Scholar 

  43. I. Buttinoni, J. Bialké, F. Kümmel, H. Löwen, C. Bechinger, T. Speck, Phys. Rev. Lett. 110, 238301 (2013)

    ADS  Google Scholar 

  44. T. Speck, J. Bialké, A.M. Menzel, H. Löwen, Phys. Rev. Lett. 112, 218304 (2014)

    ADS  Google Scholar 

  45. T. Speck, A.M. Menzel, J. Bialké, H. Löwen, J. Chem. Phys. 142, 224109 (2015)

    ADS  Google Scholar 

  46. P. Digregorio, D. Levis, A. Suma, L.F. Cugliandolo, G. Gonnella, I. Pagonabarraga, Phys. Rev. Lett. 121, 098003 (2018)

    ADS  Google Scholar 

  47. S. Mandal, B. Liebchen, H. Löwen, Phys. Rev. Lett. 123, 228001 (2019)

    ADS  Google Scholar 

  48. L. Caprini, U.M.B. Marconi, A. Puglisi, Phys. Rev. Lett. 124, 078001 (2020)

    ADS  Google Scholar 

  49. A. Menzel, J. Phys.: Condens. Matter 25, 505103 (2013)

    Google Scholar 

  50. F. Kogler, S.H.L. Klapp, EPL 110, 10004 (2015)

    ADS  Google Scholar 

  51. P. Romanczuk, H. Chaté, L. Chen, S. Ngo, J. Toner, New J. Phys. 18, 063015 (2016)

    ADS  Google Scholar 

  52. A.M. Menzel, New J. Phys. 18, 071001 (2016)

    ADS  Google Scholar 

  53. C. Reichhardt, C.J.O. Reichhardt, Soft Matter 14, 490 (2018)

    ADS  Google Scholar 

  54. C.W. Wächtler, F. Kogler, S.H.L. Klapp, Phys. Rev. E 94, 052603 (2016)

    ADS  Google Scholar 

  55. S.H.L. Klapp, Curr. Opin. Colloid Interface Sci. 21, 76 (2016)

    Google Scholar 

  56. A.M. Earl, R. Losick, R. Kolter, Trends Microbiol. 16, 269 (2008)

    Google Scholar 

  57. M. Pantastico-Caldas, K.E. Duncan, C.A. Istock, J.A. Bell, Ecology 73, 1888 (1992)

    Google Scholar 

  58. H.W. Moon, R.E. Isaacson, J. Pohlenz, Am. J. Clin. Nutr. 32, 119 (1979)

    Google Scholar 

  59. C. Palmela, C. Chevarin, Z. Xu, J. Torres, G. Sevrin, R. Hirten, N. Barnich, S.C. Ng, J.F. Colombel, Gut 67, 574 (2018)

    Google Scholar 

  60. T.J. Moriarty, M.U. Norman, P. Colarusso, T. Bankhead, P. Kubes, G. Chaconas, PLoS Pathog. 4, e1000090 (2008)

    Google Scholar 

  61. S.S. Suarez, A.A. Pacey, Hum. Reprod. Update 12, 23 (2006)

    Google Scholar 

  62. V. Kantsler, J. Dunkel, M. Blayney, R.E. Goldstein, eLife 3, e02403 (2014)

    Google Scholar 

  63. R. Nosrati, A. Driouchi, C.M. Yip, D. Sinton, Nat. Commun. 6, 8703 (2015)

    ADS  Google Scholar 

  64. A.J. Reynolds, J. Fluid Mech. 23, 241 (1965)

    ADS  Google Scholar 

  65. D.F. Katz, J. Fluid Mech. 64, 33 (1974)

    ADS  Google Scholar 

  66. A.P. Berke, L. Turner, H.C. Berg, E. Lauga, Phys. Rev. Lett. 101, 038102 (2008)

    ADS  Google Scholar 

  67. J. Elgeti, G. Gompper, EPL 85, 38002 (2009)

    ADS  Google Scholar 

  68. G. Li, J.X. Tang, Phys. Rev. Lett. 103, 078101 (2009)

    ADS  Google Scholar 

  69. I. Llopis, I. Pagonabarraga, J. Non-Newton. Fluid Mech. 165, 946 (2010)

    Google Scholar 

  70. S.E. Spagnolie, E. Lauga, J. Fluid Mech. 700, 105 (2012)

    ADS  MathSciNet  Google Scholar 

  71. K. Ishimoto, E.A. Gaffney, Phys. Rev. E 88, 062702 (2013)

    ADS  Google Scholar 

  72. K. Ishimoto, E.A. Gaffney, J. Theor. Biol. 360, 187 (2014)

    Google Scholar 

  73. G.J. Li, A.M. Ardekani, Phys. Rev. E 90, 013010 (2014)

    ADS  Google Scholar 

  74. D. Lopez, E. Lauga, Phys. Fluids 26, 071902 (2014)

    ADS  Google Scholar 

  75. W.E. Uspal, M.N. Popescu, S. Dietrich, M. Tasinkevych, Soft Matter 11, 434 (2015)

    ADS  Google Scholar 

  76. Y. Ibrahim, T.B. Liverpool, EPL 111, 48008 (2015)

    ADS  Google Scholar 

  77. K. Schaar, A. Zöttl, H. Stark, Phys. Rev. Lett. 115, 038101 (2015)

    ADS  Google Scholar 

  78. S. Das, A. Garg, A.I. Campbell, J. Howse, A. Sen, D. Velegol, R. Golestanian, S.J. Ebbens, Nat. Commun. 6, 8999 (2015)

    ADS  Google Scholar 

  79. J. Elgeti, G. Gompper, Eur. Phys. J. ST 225, 2333 (2016)

    Google Scholar 

  80. A. Mozaffari, N. Sharifi-Mood, J. Koplik, C. Maldarelli, Phys. Fluids 28, 053107 (2016)

    ADS  Google Scholar 

  81. J. Simmchen, J. Katuri, W.E. Uspal, M.N. Popescu, M. Tasinkevych, S. Sánchez, Nat. Commun. 7, 10598 (2016)

    ADS  Google Scholar 

  82. J.S. Lintuvuori, A.T. Brown, K. Stratford, D. Marenduzzo, Soft Matter 12, 7959 (2016)

    ADS  Google Scholar 

  83. E. Lushi, V. Kantsler, R.E. Goldstein, Phys. Rev. E 96, 023102 (2017)

    ADS  Google Scholar 

  84. K. Ishimoto, Phys. Rev. E 96, 043103 (2017)

    ADS  Google Scholar 

  85. S. Yazdi, A. Borhan, Phys. Fluids 29, 093104 (2017)

    ADS  Google Scholar 

  86. F. Rühle, J. Blaschke, J.-T. Kuhr, H. Stark, New J. Phys. 20, 025003 (2018)

    ADS  Google Scholar 

  87. A. Mozaffari, N. Sharifi-Mood, J. Koplik, C. Maldarelli, Phys. Rev. Fluids 3, 014104 (2018)

    ADS  Google Scholar 

  88. Z. Shen, A. Würger, J.S. Lintuvuori, Eur. Phys. J. E 41, 39 (2018)

    Google Scholar 

  89. M. Mirzakhanloo, M.R. Alam, Phys. Rev. E 98, 012603 (2018)

    ADS  Google Scholar 

  90. A. Ahmadzadegan, S. Wang, P.P. Vlachos, A.M. Ardekani, Phys. Rev. E 100, 062605 (2019)

    ADS  Google Scholar 

  91. E. Lauga, W.R. DiLuzio, G.M. Whitesides, H.A. Stone, Biophys. J. 90, 400 (2006)

    ADS  Google Scholar 

  92. R. Di Leonardo, D. Dell'Arciprete, L. Angelani, V. Iebba, Phys. Rev. Lett. 106, 038101 (2011)

    ADS  Google Scholar 

  93. J. Hu, A. Wysocki, R.G. Winkler, G. Gompper, Sci. Rep. 5, 9586 (2015)

    ADS  Google Scholar 

  94. A. Daddi-Moussa-Ider, M. Lisicki, C. Hoell, H. Löwen, J. Chem. Phys. 148, 134904 (2018)

    ADS  Google Scholar 

  95. A. Daddi-Moussa-Ider, M. Lisicki, S. Gekle, A.M. Menzel, H. Löwen, J. Chem. Phys. 149, 014901 (2018)

    ADS  Google Scholar 

  96. S.M. Mousavi, G. Gompper, R.G. Winkler, Soft Matter 16, 4866 (2020)

    ADS  Google Scholar 

  97. A. Bilbao, E. Wajnryb, S.A. Vanapalli, J. Bławzdziewicz, Phys. Fluids 25, 081902 (2013)

    ADS  Google Scholar 

  98. H. Wu, M. Thiébaud, W.-F. Hu, A. Farutin, S. Rafai, M.C. Lai, P. Peyla, C. Misbah, Phys. Rev. E 92, 050701 (2015)

    ADS  Google Scholar 

  99. H. Wu, A. Farutin, W.F. Hu, M. Thiébaud, S. Rafaï, P. Peyla, M.C. Lai, C. Misbah, Soft Matter 12, 7470 (2016)

    ADS  Google Scholar 

  100. A. Daddi-Moussa-Ider, M. Lisicki, A.J.T.M. Mathijssen, C. Hoell, S. Goh, Bławzdziewicz, A.M. Menzel, H. Löwen, J. Phys.: Condens. Matter 30, 254004 (2018)

    ADS  Google Scholar 

  101. S. Dalal, A. Farutin, C. Misbah, Soft Matter 16, 1599 (2020)

    ADS  Google Scholar 

  102. T. Brotto, J.-B. Caussin, E. Lauga, D. Bartolo, Phys. Rev. Lett. 110, 038101 (2013)

    ADS  Google Scholar 

  103. A.J.T.M. Mathijssen, A. Doostmohammadi, J.M. Yeomans, T.N. Shendruk, J. Fluid Mech. 806, 35 (2016)

    ADS  MathSciNet  Google Scholar 

  104. N. Desai, A.M. Ardekani, Soft Matter 16, 1731 (2020)

    ADS  Google Scholar 

  105. S. Das, A. Cacciuto, J. Chem. Phys. 151, 244904 (2019)

    ADS  Google Scholar 

  106. P. Malgaretti, G. Oshanin, J. Talbot, J. Phys.: Condens. Matter 31, 270201 (2019)

    Google Scholar 

  107. H. Wioland, F.G. Woodhouse, J. Dunkel, J.O. Kessler, R.E. Goldstein, Phys. Rev. Lett. 110, 268102 (2013)

    ADS  Google Scholar 

  108. M. Theillard, R. Alonso-Matilla, D. Saintillan, Soft Matter 13, 363 (2017)

    ADS  Google Scholar 

  109. T. Gao, M.D. Betterton, A.-S. Jhang, M.J. Shelley, Phys. Rev. Fluids 2, 093302 (2017)

    ADS  Google Scholar 

  110. E. Lushi, H. Wioland, R.E. Goldstein, Proc. Natl. Acad. Sci. U.S.A. 111, 9733 (2014)

    ADS  Google Scholar 

  111. D.P. Singh, A. Domínguez, U. Choudhury, S.N. Kottapalli, M.N. Popescu, S. Dietrich, P. Fischer, Nat. Commun. 11, 2210 (2020)

    ADS  Google Scholar 

  112. B. Vincenti, G. Ramos, M.L. Cordero, C. Douarche, R. Soto, E. Clement, Nat. Commun. 10, 5082 (2019)

    ADS  Google Scholar 

  113. G. Ramos, M.L. Cordero, R. Soto, Soft Matter 16, 1359 (2020)

    ADS  Google Scholar 

  114. T. Mirkovic, N.S. Zacharia, G.D. Scholes, G.A. Ozin, ACS Nano 4, 1782 (2010)

    Google Scholar 

  115. Y. Ding, F. Qiu, X. Casadevall i Solvas, F.W.Y. Chiu, B.J. Nelson, A. DeMello, Micromachines 7, 25 (2016)

    Google Scholar 

  116. L. Zhu, F. Gallaire, Phys. Rev. Lett. 119, 064502 (2017)

    ADS  Google Scholar 

  117. D. Takagi, J. Palacci, A.B. Braunschweig, M.J. Shelley, J. Zhang, Soft Matter 10, 1784 (2014)

    ADS  Google Scholar 

  118. S.E. Spagnolie, G.R. Moreno-Flores, D. Bartolo, E. Lauga, Soft Matter 11, 3396 (2015)

    ADS  Google Scholar 

  119. H. Jashnsaz, M. Al Juboori, C. Weistuch, N. Miller, T. Nguyen, V. Meyerhoff, B. McCoy, S. Perkins, R. Wallgren, B.D. Ray, K. Tsekouras, G.G. Anderson, S. Presse, Biophys. J. 112, 1282 (2017)

    ADS  Google Scholar 

  120. N. Desai, V.A. Shaik, A.M. Ardekani, Soft Matter 14, 264 (2018)

    ADS  Google Scholar 

  121. N. Desai, A.M. Ardekani, Phys. Rev. E 98, 012419 (2018)

    ADS  Google Scholar 

  122. N. Desai, V.A. Shaik, A.M. Ardekani, Front. Microbiol. 10, 289 (2019)

    Google Scholar 

  123. V.A. Shaik, V. Vasani, A.M. Ardekani, J. Fluid Mech. 851, 187 (2018)

    ADS  MathSciNet  Google Scholar 

  124. V.A. Shaik, A.M. Ardekani, Phys. Rev. E 99, 033101 (2019)

    ADS  Google Scholar 

  125. G.I. Taylor, Proc. R. Soc. Lond. A 209, 447 (1951)

    ADS  Google Scholar 

  126. G.J. Elfring, E. Lauga, Phys. Rev. Lett. 103, 088101 (2009)

    ADS  Google Scholar 

  127. M. Sauzade, G.J. Elfring, E. Lauga, Physica D 240, 1567 (2011)

    ADS  Google Scholar 

  128. M. Dasgupta, B. Liu, H.C. Fu, M. Berhanu, K.S. Breuer, T.R. Powers, A. Kudrolli, Phys. Rev. E 87, 013015 (2013)

    ADS  Google Scholar 

  129. T.D. Montenegro-Johnson, E. Lauga, Phys. Rev. E 89, 060701 (2014)

    ADS  Google Scholar 

  130. M.J. Lighthill, Commun. Pure Appl. Math. 5, 109 (1952)

    Google Scholar 

  131. J.R. Blake, J. Fluid Mech. 46, 199 (1971)

    ADS  Google Scholar 

  132. O.S. Pak, E. Lauga, J. Eng. Math. 88, 1 (2014)

    Google Scholar 

  133. I.O. Götze, G. Gompper, Phys. Rev. E 82, 041921 (2010)

    ADS  Google Scholar 

  134. S. Thutupalli, R. Seemann, S. Herminghaus, New J. Phys. 13, 073021 (2011)

    ADS  Google Scholar 

  135. L. Zhu, E. Lauga, L. Brandt, Phys. Fluids 24, 051902 (2012)

    ADS  Google Scholar 

  136. L. Zhu, E. Lauga, L. Brandt, J. Fluid Mech. 726, 285 (2013)

    ADS  MathSciNet  Google Scholar 

  137. A. Zöttl, H. Stark, Phys. Rev. Lett. 112, 118101 (2014)

    ADS  Google Scholar 

  138. J.S. Lintuvuori, A. Würger, K. Stratford, Phys. Rev. Lett. 119, 068001 (2017)

    ADS  Google Scholar 

  139. J.-T. Kuhr, J. Blaschke, F. Rühle, H. Stark, Soft Matter 13, 7548 (2017)

    ADS  Google Scholar 

  140. A. Zöttl, H. Stark, Eur. Phys. J. E 41, 61 (2018)

    Google Scholar 

  141. M. Kuron, P. Stärk, C. Burkard, J. De Graaf, C. Holm, J. Chem. Phys. 150, 144110 (2019)

    ADS  Google Scholar 

  142. J.-T. Kuhr, F. Rühle, H. Stark, Soft Matter 15, 5685 (2019)

    ADS  Google Scholar 

  143. A. Zöttl, Chinese Phys. B (2020)

  144. A. Najafi, R. Golestanian, Phys. Rev. E 69, 062901 (2004)

    ADS  Google Scholar 

  145. R. Golestanian, A. Ajdari, Phys. Rev. E 77, 036308 (2008)

    ADS  Google Scholar 

  146. R. Golestanian, Eur. Phys. J. E 25, 1 (2008)

    Google Scholar 

  147. B. Liebchen, P. Monderkamp, B. ten Hagen, H. Löwen, Phys. Rev. Lett. 120, 208002 (2018)

    ADS  Google Scholar 

  148. G.P. Alexander, C.M. Pooley, J.M. Yeomans, J. Phys.: Condens. Matter 21, 204108 (2009)

    ADS  Google Scholar 

  149. S. Ziegler, M. Hubert, N. Vandewalle, J. Harting, A.-S. Smith, New J. Phys. 21, 113017 (2019)

    ADS  Google Scholar 

  150. A. Sukhov, S. Ziegler, Q. Xie, O. Trosman, J. Pande, G. Grosjean, M. Hubert, N. Vandewalle, A.-S. Smith, J. Harting, J. Chem. Phys. 151, 124707 (2019)

    ADS  Google Scholar 

  151. B. Nasouri, A. Vilfan, R. Golestanian, Phys. Rev. Fluids 4, 073101 (2019)

    ADS  Google Scholar 

  152. A.M. Menzel, A. Saha, C. Hoell, H. Löwen, J. Chem. Phys. 144, 024115 (2016)

    ADS  Google Scholar 

  153. C. Hoell, H. Löwen, A.M. Menzel, New J. Phys. 19, 125004 (2017)

    ADS  Google Scholar 

  154. T.C. Adhyapak, S. Jabbari-Farouji, Phys. Rev. E 96, 052608 (2017)

    ADS  Google Scholar 

  155. T.C. Adhyapak, S. Jabbari-Farouji, J. Chem. Phys. 149, 144110 (2018)

    ADS  Google Scholar 

  156. C. Hoell, H. Löwen, A.M. Menzel, J. Chem. Phys. 149, 144902 (2018)

    ADS  Google Scholar 

  157. A. Daddi-Moussa-Ider, A.M. Menzel, Phys. Rev. Fluids 3, 094102 (2018)

    ADS  Google Scholar 

  158. A. Daddi-Moussa-Ider, M. Lisicki, H. Löwen, A.M. Menzel, Phys. Fluids 32, 021902 (2020)

    ADS  Google Scholar 

  159. C. Hoell, H. Löwen, A.M. Menzel, J. Chem. Phys. 151, 064902 (2019)

    ADS  Google Scholar 

  160. V.A. Shaik, A.M. Ardekani, J. Fluid Mech. 824, 42 (2017)

    ADS  MathSciNet  Google Scholar 

  161. S.Y. Reigh, L. Zhu, F. Gallaire, E. Lauga, Soft Matter 13, 3161 (2017)

    ADS  Google Scholar 

  162. S.Y. Reigh, E. Lauga, Phys. Rev. Fluids 2, 093101 (2017)

    ADS  Google Scholar 

  163. C. Pozrikidis, Boundary Integral and Singularity Methods for Linearized Viscous Flow (Cambridge University Press, Cambridge, UK, 1992)

  164. C. K.V.S., S. Thampi, J. Phys. D: Appl. Phys. 53, 314001 (2020)

    Google Scholar 

  165. L. Rückert, A. Zippelius, R. Kree, Trajectories of a droplet driven by an internal active device (2019) arXiv:1902.01159

  166. R. Kree, L. Rückert, A. Zippelius, Dynamics of a droplet driven by an internal active device arXiv:2004.10045 (2020)

  167. J.R. Blake, Math. Proc. Camb. Philos. Soc. 70, 303 (1971)

    ADS  Google Scholar 

  168. J.W. Swan, J.F. Brady, Phys. Fluids 19, 113306 (2007)

    ADS  Google Scholar 

  169. R. Usha, S.D. Nigam, Fluid Dyn. Res. 11, 75 (1993)

    ADS  Google Scholar 

  170. C. Maul, S. Kim, Phys. Fluids 6, 2221 (1994)

    ADS  Google Scholar 

  171. C. Maul, S. Kim, J. Eng. Math. 30, 119 (1996)

    Google Scholar 

  172. H. Hasimoto, Phys. Fluids 9, 1838 (1997)

    ADS  MathSciNet  Google Scholar 

  173. A. Sellier, Comput. Model. Eng. Sci. 25, 165 (2008)

    Google Scholar 

  174. B.U. Felderhof, A. Sellier, J. Chem. Phys. 136, 054703 (2012)

    ADS  Google Scholar 

  175. C. Aponte-Rivera, R.N. Zia, Phys. Rev. Fluids 1, 023301 (2016)

    ADS  Google Scholar 

  176. C.A. Aponte Rivera, Spherically confined colloidal suspensions of hydrodynamically interacting particles: A model for intracellular transport PhD Thesis, Cornell University, USA (2017)

  177. D.A. Edwards, H. Brenner, D.T. Wasan, Interfacial Transport Processes and Rheology (Elsevier Butterworth-Heinemann, Oxford, UK, 1991)

  178. Y.O. Fuentes, S. Kim, D.J. Jeffrey, Phys. Fluids 31, 2445 (1988)

    ADS  Google Scholar 

  179. Y.O. Fuentes, S. Kim, D.J. Jeffrey, Phys. Fluids A 1, 61 (1989)

    ADS  Google Scholar 

  180. A. Daddi-Moussa-Ider, S. Gekle, Phys. Rev. E 95, 013108 (2017)

    ADS  Google Scholar 

  181. A. Daddi-Moussa-Ider, M. Lisicki, S. Gekle, Phys. Rev. E 95, 053117 (2017)

    ADS  Google Scholar 

  182. A. Daddi-Moussa-Ider, H. Löwen, S. Gekle, Eur. Phys. J. E 41, 104 (2018)

    Google Scholar 

  183. C. Hoell, H. Löwen, A.M. Menzel, A. Daddi-Moussa-Ider, Eur. Phys. J. E 42, 89 (2019)

    Google Scholar 

  184. V.A. Shaik, A.M. Ardekani, Phys. Rev. Fluids 2, 113606 (2017)

    ADS  Google Scholar 

  185. S. Kim, S.J. Karrila, Microhydrodynamics: Principles and Selected Applications (Courier Corporation, New York, USA, 2013)

  186. K.C. Neuman, S.M. Block, Rev. Sci. Instrum. 75, 2787 (2004)

    ADS  Google Scholar 

  187. B.U. Felderhof, R.B. Jones, Physicochem. Hydrodyn. 11, 507 (1989)

    Google Scholar 

  188. H.A. Stone, Phys. Fluids A: Fluid Dyn. 2, 111 (1990)

    ADS  Google Scholar 

  189. L.C. Andrews, Special Functions of Mathematics for Engineers, Vol. 49 (SPIE Press, Bellingham, Washington, USA, 1998)

  190. H. Lamb, Hydrodynamics (Cambridge University Press, Cambridge, UK, 1932)

  191. R.G. Cox, J. Fluid Mech. 37, 601 (1969)

    ADS  Google Scholar 

  192. J. Happel, H. Brenner, Low Reynolds Number Hydrodynamics: With Special Applications to Particulate Media (Springer Netherlands, Martinus Nijhoff Publishers, The Hague, 2012)

  193. M. Abramowitz, I.A. Stegun, Handbook of Mathematical Functions, Vol. 5 (Dover, New York, 1972)

  194. C. Misbah, Phys. Rev. Lett. 96, 028104 (2006)

    ADS  Google Scholar 

  195. J. Bławzdziewicz, V. Cristini, M. Loewenberg, Phys. Fluids 11, 251 (1999)

    ADS  Google Scholar 

  196. L.G. Leal, Advanced Transport Phenomena: Fluid Mechanics and Convective Transport Processes, Vol. 7 (Cambridge University Press, Cambridge, UK, 2007)

  197. P.C.-H. Chan, L.G. Leal, J. Fluid Mech. 82, 549 (1977)

    ADS  Google Scholar 

  198. H.K. Moffatt, J. Fluid Mech. 18, 1 (1964)

    ADS  Google Scholar 

  199. S.E. Spagnolie, E. Lauga, J. Fluid Mech. 700, 105 (2012)

    ADS  MathSciNet  Google Scholar 

  200. D. Lopez, E. Lauga, Phys. Fluids 26, 400 (2014)

    Google Scholar 

  201. S.D. Ryan, L. Berlyand, B.M. Haines, D.A. Karpeev, Multiscale Model. Simul. 11, 1176 (2013)

    MathSciNet  Google Scholar 

  202. S.E. Spagnolie, G.R. Moreno-Flores, D. Bartolo, E. Lauga, Soft Matter 11, 3396 (2015)

    ADS  Google Scholar 

  203. A. Daddi-Moussa-Ider, C. Kurzthaler, C. Hoell, A. Zöttl, M. Mirzakhanloo, M.-R. Alam, A.M. Menzel, H. Löwen, S. Gekle, Phys. Rev. E 100, 032610 (2019)

    ADS  MathSciNet  Google Scholar 

  204. H.C. Berg, R.A. Anderson, Nature 245, 380 (1973)

    ADS  Google Scholar 

  205. H.C. Berg, E. coli in Motion (Springer-Verlag New York, Inc., NY, USA, 2008)

  206. J. Schwarz-Linek, J. Arlt, A. Jepson, A. Dawson, T. Vissers, D. Miroli, T. Pilizota, V.A. Martinez, W.C.K. Poon, Colloid Surf. B 137, 2 (2016)

    Google Scholar 

  207. S. Chattopadhyay, R. Moldovan, C. Yeung, X.L. Wu, Proc. Natl. Acad. Sci. U.S.A. 103, 13712 (2006)

    ADS  Google Scholar 

  208. N.C. Darnton, L. Turner, S. Rojevsky, H.C. Berg, J. Bacteriol. 189, 1756 (2007)

    Google Scholar 

  209. A.P. Berke, L. Turner, H.C. Berg, E. Lauga, Phys. Rev. Lett. 101, 038102 (2008)

    ADS  Google Scholar 

  210. G.B. Folland, Real Analysis: Modern Techniques and Their Applications, Vol. 40 (John Wiley & Sons, New York, USA, 1999)

Download references

Acknowledgments

Open Access funding provided by Projekt DEAL.

Author information

Authors and Affiliations

  1. Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, D-40225, Düsseldorf, Germany

    Alexander R. Sprenger, Hartmut Löwen & Abdallah Daddi-Moussa-Ider

  2. School of Mechanical Engineering, Purdue University, 47907, West Lafayette, IN, USA

    Vaseem A. Shaik & Arezoo M. Ardekani

  3. Institute of Theoretical Physics, Faculty of Physics, University of Warsaw, Pasteura 5, 02-093, Warsaw, Poland

    Maciej Lisicki

  4. Department of Bioengineering, Stanford University, 443 Via Ortega, 94305, Stanford, CA, USA

    Arnold J. T. M. Mathijssen

  5. Department of Physics and Astronomy, University of Pennsylvania, 209 South 33rd Street, 19104, Philadelphia, PA, USA

    Arnold J. T. M. Mathijssen

  6. Centro de Investigación DAiTA Lab, Facultad de Estudios Interdisciplinarios, Universidad Mayor, Av. Manuel Montt 367, Providencia, Santiago de Chile, Chile

    Francisca Guzmán-Lastra

  7. Institut für Physik, Otto-von-Guericke-Universität Magdeburg, Universitätsplatz 2, 39106, Magdeburg, Germany

    Andreas M. Menzel

Authors
  1. Alexander R. Sprenger
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Vaseem A. Shaik
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Arezoo M. Ardekani
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Maciej Lisicki
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Arnold J. T. M. Mathijssen
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Francisca Guzmán-Lastra
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Hartmut Löwen
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Andreas M. Menzel
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. Abdallah Daddi-Moussa-Ider
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alexander R. Sprenger.

Additional information

Publisher's Note

The EPJ Publishers remain neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Contribution to the Topical Issue “Motile Active Matter” edited by Gerhard Gompper, Clemens Bechinger, Roland G. Winkler, Holger Stark.

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sprenger, A.R., Shaik, V.A., Ardekani, A.M. et al. Towards an analytical description of active microswimmers in clean and in surfactant-covered drops. Eur. Phys. J. E 43, 58 (2020). https://doi.org/10.1140/epje/i2020-11980-9

Download citation

  • Received: 29 May 2020

  • Accepted: 10 August 2020

  • Published: 11 September 2020

  • DOI: https://doi.org/10.1140/epje/i2020-11980-9

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Keywords

  • Topical issue: Motile Active Matter
Download PDF

Working on a manuscript?

Avoid the common mistakes

Associated Content

Part of a collection:

Motile Active Matter

Advertisement

Over 10 million scientific documents at your fingertips

Switch Edition
  • Academic Edition
  • Corporate Edition
  • Home
  • Impressum
  • Legal information
  • Privacy statement
  • Your US state privacy rights
  • How we use cookies
  • Your privacy choices/Manage cookies
  • Accessibility
  • FAQ
  • Contact us
  • Affiliate program

Not affiliated

Springer Nature

© 2023 Springer Nature Switzerland AG. Part of Springer Nature.