History hydrodynamic torque transitions in oscillatory spinning of stick-slip Janus particles

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.