Nonequilibrium dynamics of a confined colloidal bilayer in a planar shear flow

Nonequilibrium dynamics and entropy production of a trapped colloidal particle in a complex nonreciprocal medium

We discuss the two-dimensional motion of a Brownian particle that is confined to a harmonic trap and driven by a shear flow. The surrounding medium induces memory effects modeled by a linear, typically nonreciprocal coupling of the particle coordinates to an auxiliary (hidden) variable. The system's behavior resulting from the microscopic Langevin equations for the three variables is analyzed by means of exact moment equations derived from the Fokker-Planck representation, and numerical Brownian dynamics simulations. Increasing the shear rate beyond a critical value we observe, for suitable coupling scenarios with nonreciprocal elements, a transition from a stationary to a nonstationary state, corresponding to an escape from the trap. We analyze this behavior, analytically and numerically, in terms of the associated moments of the probability distribution, and from the perspective of nonequilibrium thermodynamics. Intriguingly, the entropy production rate remains finite when crossing the stability threshold.

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 behavior of such systems under pure oscillatory shearing with shear rate γ[over ̇](t)=γ[over ̇]_{0}cos(ωt), as it is a common scenario in rheological experiments. The colloids' depinning behavior 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 γ[over ̇]_{0} and frequencies ω, we observe complete pinning as well as temporary depinning behavior. We discover that temporary depinning occurs for shear rate amplitudes above a frequency-dependent critical amplitude γ[over ̇]_{0}^{crit}(ω), for which we attain an approximate functional expression. For a range of frequencies, approaching γ[over ̇]_{0}^{crit}(ω) is accompanied by a strongly increasing settling time. Above γ[over ̇]_{0}^{crit}(ω), we further observe a variety of dynamical structures, whose stability exhibits an intriguing (γ[over ̇]_{0},ω) dependence. This might enable new perspectives for potential control schemes.

Dynamical modes of sheared confined microscale matter

Based on (overdamped) Stokesian dynamics simulations and video microscopy experiments, we study the non equilibrium dynamics of a sheared colloidal cluster, which is confined to a two-dimensional disk. The experimental system is composed of a mixture of paramagnetic and non magnetic polystyrene particles, which are held in the disk by time shared optical tweezers. The paramagnetic particles are located at the center of the disk and are actuated by an external, rotating magnetic field that induces a magnetic torque. We identify two different steady states by monitoring the mean angular velocities per ring. The first one is characterized by rare slip events, where the inner rings momentarily depin from the outer ring, which is kept static by the set of optical traps. For the second state, we find a bistability of the mean angular velocities, which can be understood from the analysis of the slip events in the particle trajectories. We calculate the particle waiting- and jumping time distributions and estimate a time scale between slips, which is also reflected by a plateau in the mean squared azimuthal displacement. The dynamical transition is further reflected by the components of the stress tensor, revealing a shear-thinning behavior as well as shear stress overshoots. Finally, we briefly discuss the observed transition in the context of stochastic thermodynamics and how it may open future directions in this field.

Shear-induced laning transition in a confined colloidal film

Using Brownian dynamics simulations, we investigate a dense system of charged colloids exposed to shear flow in a confined (slit-pore) geometry. The equilibrium system at zero flow consists of three well-pronounced layers with a squarelike crystalline in-plane structure. We demonstrate that, for sufficiently large shear rates, the middle layer separates into two sublayers where the particles organize into moving lanes with opposite velocities. The formation of this "microlaned" state results in a destruction of the applied shear profile; it also has a strong impact on the structure of the system, and on its rheology as measured by the elements of the stress tensor. At higher shear rates, we observe a disordered state and finally a recrystallization reminiscent of the behavior of bilayer films. We also discuss the system size dependence and the robustness of the microlaned state against variations of the slit-pore width. In fact, for a pore width allowing for four layers, we observe a similar shear-induced state in which the system splits into two domains with opposite velocities.

Depinning and heterogeneous dynamics of colloidal crystal layers under shear flow

Using Brownian dynamics (BD) simulations and an analytical approach we investigate the shear-induced, nonequilibrium dynamics of dense colloidal suspensions confined to a narrow slit-pore. Focusing on situations where the colloids arrange in well-defined layers with solidlike in-plane structure, the confined films display complex, nonlinear behavior such as collective depinning and local transport via density excitations. These phenomena are reminiscent of colloidal monolayers driven over a periodic substrate potential. In order to deepen this connection, we present an effective model that maps the dynamics of the shear-driven colloidal layers to the motion of a single particle driven over an effective substrate potential. This model allows us to estimate the critical shear rate of the depinning transition based on the equilibrium configuration, revealing the impact of important parameters, such as the slit-pore width and the interaction strength. We then turn to heterogeneous systems where a layer of small colloids is sheared with respect to bottom layers of large particles. For these incommensurate systems we find that the particle transport is dominated by density excitations resembling the so-called "kink" solutions of the Frenkel-Kontorova (FK) model. In contrast to the FK model, however, the corresponding "antikinks" do not move.

Understanding the approximations of mode-coupling theory for sheared steady states of colloids

The lack of clarity of various mode-coupling theory (MCT) approximations, even in equilibrium, makes it hard to understand the relation between various MCT approaches for sheared steady states as well as their regime of validity. Here we try to understand these approximations indirectly by deriving the MCT equations through two different approaches for a colloidal system under shear, first through a microscopic approach, as suggested by Zaccarelli et al., and second through fluctuating hydrodynamics, where the approximations used in the derivation are quite clear. The qualitative similarity of our theory with a number of existing theories show that linear response theory might play a role in various approximations employed in deriving those theories and one needs to be careful while applying them for systems arbitrarily far away from equilibrium, such as a granular system or when shear is very strong. As a by-product of our calculation, we obtain the extension of the Yvon-Born-Green (YBG) equation for a sheared system and under the assumption of random-phase approximation, the YBG equation yields the distorted structure factor that was earlier obtained through different approaches.

Segregation of oppositely driven colloidal particles in hard-walled channels: A finite-size study

We investigate segregation phenomena of particles driven in opposite directions with Brownian dynamics simulations. The particles interact via a repulsive potential and are confined in three-dimensional hard-walled pipes with quadratic cross sections. In a systematic finite-size study, the pipe length is varied. Ordering on finite length scales can be observed, but global segregation seems to vanish for infinite channel length, as it was recently found for lane formation in two dimensions. As an additional effect of the finite hard-walled boundary conditions, interface vibrations and longitudinal demixing are found.

Transport and diffusion properties of interacting colloidal particles in two-dimensional microchannels with a periodic potential

We report a Brownian dynamics simulation study of a two-dimensional system of repulsive colloidal particles in a channel geometry with a sinusoidal substrate potential under influence of a constant driving. The effect of this driving on the structure, mobility, and diffusion is discussed as well as the appearance of kink and antikink solitons. The competing order principles of the hexagonal crystal structure, the period of the substrate, and the layering due to the confining walls can be either commensurable or incommensurable. The combination of those three leads to new effects. The simultaneous occurrence of kinks and antikinks can be observed, due to the energy difference between boundary- and midlanes, and similarities to the electron-hole conductivity in a semiconductor can be found.

Manipulating shear-induced non-equilibrium transitions in colloidal films by feedback control

Using Brownian Dynamics (BD) simulations we investigate non-equilibrium transitions of sheared colloidal films under controlled shear stress σxz. In our approach the shear rate [small gamma, Greek, dot above] is a dynamical variable, which relaxes on a time scale τc such that the instantaneous, configuration-dependent stress σxz(t) approaches a pre-imposed value. Investigating the dynamics under this "feedback-control" scheme we find unique behavior in regions where the flow curve σxz([small gamma, Greek, dot above]) of the uncontrolled system is monotonic. However, in non-monotonic regions our method allows to select between dynamical states characterized by different in-plane structure and viscosities. Indeed, the final state strongly depends on τc relative to an intrinsic relaxation time of the uncontrolled system. The critical values of τc are estimated on the basis of a simple model.