Abstract
We have analyzed the dynamics of a spherical, uniaxial squirmer which is located inside a spherical liquid drop at general position varvec{r}_s. The squirmer is subject to an external force and torque in addition to the slip velocity on its surface. We have derived exact analytical expressions for the linear and rotational velocity of the squirmer as well as the linear velocity of the drop for general, non-axisymmetric configurations. The mobilities of both, squirmer and drop, are in general anisotropic, depending on the orientation of varvec{r}_s, relative to squirmer axis, external force or torque. We discuss their dependence on the size of the squirmer, its distance from the center of the drop and the viscosities. Our results provide a framework for the discussion of the trajectories of the composite system of drop and enclosed squirmer.Graphical
Highlights
Controlled locomotion on micro- or nanometer scales is of great interest for both, cell biology and microrobotics [1,2,3,4,5,6]
We have analyzed the dynamics of a spherical, uniaxial squirmer which is located inside a spherical liquid drop at general position rs
A linear velocity of the drop is generated by all three driving mechanisms: slip velocity of the squirmer, external force and external torque vcm = μhU 0 + μ F F ext + μDa × Dext
Summary
Controlled locomotion on micro- or nanometer scales is of great interest for both, cell biology and microrobotics [1,2,3,4,5,6]. The analytical solution is constructed in a special geometry, for which the displacement of the squirmer is perpendicular to the squirmer axis or the direction of external force We superimpose this solution with that of reference I and use frame independence to obtain our results for general displacements and orientations. The results of the analytical calculation are the mobilities of the squirmer and the drop as functions of the sizes of particle and drop, the displacement vector and the viscosities The active device is either a squirmer with a tangential slip velocity on its surface (1) or a passive particle, subject to an external force F ext and/or torque Dext (2), or a combination of both.
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