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Locomotion inside a surfactant-laden drop at low surface Péclet numbers

Published online by Cambridge University Press:  19 July 2018

Vaseem A. Shaik ,
Vishwa Vasani  and
Arezoo M. Ardekani Open the ORCID record for Arezoo M. Ardekani [Opens in a new window]
Vaseem A. Shaik
Affiliation:
School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907, USA
Vishwa Vasani
Affiliation:
School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907, USA
Arezoo M. Ardekani*
Affiliation:
School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907, USA
*
†Email address for correspondence: [email protected]
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Abstract

We investigate the dynamics of a swimming microorganism inside a surfactant-laden drop for axisymmetric configurations under the assumptions of small Reynolds number and small surface Péclet number $(Pe_{s})$. Expanding the variables in $Pe_{s}$, we solve the Stokes equations for the concentric configuration using Lamb’s general solution, while the dynamic equation for the stream function is solved in the bipolar coordinates for the eccentric configurations. For a two-mode squirmer inside a drop, the surfactant redistribution can either increase or decrease the magnitude of swimmer and drop velocities, depending on the value of the eccentricity. This was explained by analysing the influence of surfactant redistribution on the thrust and drag forces acting on the swimmer and the drop. The far-field representation of a surfactant-covered drop enclosing a pusher swimmer at its centre is a puller; the strength of this far field is reduced due to the surfactant redistribution. The advection of surfactant on the drop surface leads to a time-averaged propulsion of the drop and the time-reversible swimmer that it engulfs, thereby causing them to escape from the constraints of the scallop theorem. We quantified the range of parameters for which an eccentrically stable configuration can be achieved for a two-mode squirmer inside a clean drop. The surfactant redistribution shifts this eccentrically stable position towards the top surface of the drop, although this shift is small.

JFM classification

Drops and Bubbles: Drops Biological Fluid Dynamics: Micro-organism dynamics Biological Fluid Dynamics: Swimming/flying
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 851 , 25 September 2018 , pp. 187 - 230
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Copyright
© 2018 Cambridge University Press 

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