Depinning dynamics of confined colloidal dispersions under oscillatory shear

Strongly confined colloidal dispersions under shear can exhibit a variety of dynamical phenomena, including depinning transitions and complex structural changes. Here, we investigate the behaviour of such systems under pure oscillatory shearing with shear rate $\dot{\gamma}(t) = \dot{\gamma}_0 \cos(\omega t)$, as it is a common scenario in rheological experiments. The colloids' depinning behaviour is assessed from a particle level based on trajectories, obtained from overdamped Brownian Dynamics simulations. The numerical approach is complemented by an analytic one based on an effective single-particle model in the limits of weak and strong driving. Investigating a broad spectrum of shear rate amplitudes $\dot{\gamma}_0$ and frequencies $\omega$, we observe complete pinning as well as temporary depinning behaviour. We discover that temporary depinning occurs for shear rate amplitudes above a frequency-dependent critical amplitude $\dot{\gamma}_0^\mathrm{crit}(\omega)$, for which we attain an approximate functional expression. For a range of frequencies, approaching $\dot{\gamma}_0^\mathrm{crit}(\omega)$ is accompanied by a strongly increasing settling time. Above $\dot{\gamma}_0^\mathrm{crit}(\omega)$, we further observe a variety of dynamical structures, whose stability exhibits an intriguing ($\dot{\gamma}_0, \omega$) dependence. This might enable new perspectives for potential control schemes.