Abstract
We theoretically investigate the oscillatory spinning of an axisymmetric stick-slip Janus particle (SSJP) under the creeping flow condition. Solving the unsteady Stokes equation together with a matched asymptotic boundary layer theory, we find that such a particle can display unusual viscous torque responses in the high frequency regime depending on the Stokes boundary layer thickness δ, the slip length λ of the slip face, and the coverage of the stick face. Our analysis reveals that an SSJP will always experience a reduced Basset torque of 1/δ decay due to the presence of the slip face, with amplitude smaller than the no-slip counterpart irrespective of the value of λ. If the coverage of the stick face is sufficiently small, the reduced Basset torque can turn into a constant torque plateau due to prevailing slip effects at larger values of δ, representing a new history torque transition prior to the slip-stick transition at δ ∼ λ. All these features are markedly different from those for no-slip and uniform slip particles, providing not only distinctive fingerprints for Janus particles but also a new means for manipulating these particles.
Highlights
A Janus particle is a compartmentalized colloid of two faces having distinct properties
Purely no-slip and slip particles have completely different characteristics in their torque responses. This raises a question, what if a particle is comprised of both no-slip and slip faces like an stick-slip Janus particle (SSJP)? In our recent study on an oscillatory translating SSJP,16 we found that the force response can be mixed with both no-slip and uniform slip contributions
As for a half cap SSJP, we find that all the curves with different values of λtend to approach the same Basset-like 1/δdecay as δ → 0, but in a reduced amplitude compared to the no-slip case due to drag reduction imparted by the slip face
Summary
A Janus particle is a compartmentalized colloid of two faces having distinct properties. The present work is motivated by magnetically driven microrotors for generating rotational flows or by the use of rotating magnetic beads for biosensing applications.10 In the former, an SSJP could be a more efficient microrotor by having its slip portion faced down to the bottom wall to reduce drag. Since there exists a phase difference between the rotational velocity and the torque, the behavior of such phase difference for an SSJP is expected to vary with the stick-slip partition This might provide a distinct fingerprint for an SSJP to differentiate from no-slip and uniform slip particles hydrodynamically. Prior to extending the uniform sphere situation to SSJP, it is necessary to analyze the leading order flow characteristics of SSJP under the Stokes flow condition This is another reason why we would like to pursue this yet-explored spinning SSJP problem in this work
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