Towards an analytical description of active microswimmers in clean and in surfactant-covered drops
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THE EUROPEAN PHYSICAL JOURNAL E
Regular Article
Towards an analytical description of active microswimmers in clean and in surfactant-covered drops Alexander R. Sprenger1,a , Vaseem A. Shaik2 , Arezoo M. Ardekani2 , Maciej Lisicki3 , Arnold J.T.M. Mathijssen4,5 , owen1 , Andreas M. Menzel7 , and Abdallah Daddi-Moussa-Ider1,b Francisca Guzm´an-Lastra6 , Hartmut L¨ 1
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Institut f¨ ur Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universit¨ at D¨ usseldorf, Universit¨ atsstraße 1, D-40225 D¨ usseldorf, Germany School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907, USA Institute of Theoretical Physics, Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland Department of Bioengineering, Stanford University, 443 Via Ortega, Stanford, CA 94305, USA Department of Physics and Astronomy, University of Pennsylvania, 209 South 33rd Street, Philadelphia, PA 19104, USA Centro de Investigaci´ on DAiTA Lab, Facultad de Estudios Interdisciplinarios, Universidad Mayor, Av. Manuel Montt 367, Providencia, Santiago de Chile, Chile Institut f¨ ur Physik, Otto-von-Guericke-Universit¨ at Magdeburg, Universit¨ atsplatz 2, 39106 Magdeburg, Germany Received 29 May 2020 / Received in final form 3 August 2020 / Accepted 10 August 2020 Published online: 11 September 2020 c The Author(s) 2020. This article is published with open access at Springerlink.com 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 farfield 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.
1 Introduction Controlled locomotion of nano- and micro-scale objects in viscous media is of considerable importance in many areas of engineering and science [1]. Synthetic nano- and micro-motors hold significant promise for future biotechnological and medical applications such as precise assembly of materials [2–8], non-invasive microsurgery [9–11], targeted dru
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