Andrey Pototsky

Morphology changes in the evolution of liquid two-layer films

We consider a thin film consisting of two layers of immiscible liquids on a solid horizontal (heated) substrate. Both the free liquid-liquid and the liquid-gas interface of such a bilayer liquid film may be unstable due to effective molecular interactions relevant for ultrathin layers below 100-nm thickness, or due to temperature-gradient-caused Marangoni flows in the heated case. Using a long-wave approximation, we derive coupled evolution equations for the interface profiles for the general nonisothermal situation allowing for slip at the substrate. Linear and nonlinear analyses of the short- and long-time film evolution are performed for isothermal ultrathin layers, taking into account destabilizing long-range and stabilizing short-range molecular interactions. It is shown that the initial instability can be of a varicose, zigzag, or mixed type. However, in the nonlinear stage of the evolution the mode type, and therefore the pattern morphology, can change via switching between two different branches of stationary solutions or via coarsening along a single branch.

Alternative pathways of dewetting for a thin liquid two-layer film

We consider two stacked ultrathin layers of different liquids on a solid substrate. Using long-wave theory, we derive coupled evolution equations for the free liquid-liquid and liquid-gas interfaces. Depending on the long-range van der Waals forces and the ratio of the layer thicknesses, the system follows different pathways of dewetting. The instability may be driven by varicose or zigzag modes and leads to film rupture either at the liquid-gas interface or at the substrate. We predict that the faster layer drives the evolution and may accelerate the rupture of the slower layer by orders of magnitude, thereby promoting the rupture of rather thick films.

Long-wave theory of bounded two-layer films with a free liquid-liquid interface: Short- and long-time evolution

We consider two layers of immiscible liquids confined between an upper and a lower rigid plate. The dynamics of the free liquid–liquid interface is described for arbitrary amplitudes by an evolution equation derived from the basic hydrodynamic equations using long-wave approximation. After giving the evolution equation in a general way, we focus on interface instabilities driven by gravity, thermocapillary and electrostatic fields. First, we study the linear stability discussing especially the conditions for destabilizing the system by heating from above or below. Second, we use a variational formulation of the evolution equation based on an energy functional to predict metastable states and the long-time pattern morphology (holes, drops or maze structures). Finally, fully nonlinear three-dimensional numerical integrations are performed to study the short- and long-time evolution of the evolving patterns. Different coarsening modes are discussed and long-time scaling exponents are extracted.

Rectification of self-propelled particles by symmetric barriers.

The motion of self-propelled particles can be rectified by asymmetric or ratchetlike periodic patterns in space. Here we show that a nonzero average drift can already be induced in a periodic potential with symmetric barriers when the self-propulsion velocity is also symmetric and periodically modulated but phase-shifted against the potential. In the adiabatic limit of slow rotational diffusion we determine the mean drift analytically and discuss the influence of temperature. In the presence of asymmetric barriers, modulating the self-propulsion can largely enhance the mean drift or even reverse it.

Active Brownian particles in two-dimensional traps

We consider a population of self-propelled Brownian particles in 2D traps. For non- interacting particles the stationary distribution for position and orientation is found analytically for small and large rotational diffusivities. These results are used to map the system of interacting active particles onto a system of passive particles in a modified trapping potential which we then formulate as a dynamic density functional theory. Our approach is supported by Brownian dynamics simulations of the original and the effective model. Copyright c EPLA, 2012

Relativistic Brownian motion on a graphene chip

Relativistic Brownian motion can be inexpensively demonstrated on a graphene chip. The interplay of stochastic and relativistic dynamics, governing the transport of charge carrier in graphene, induces noise-controlled effects such as (i) a stochastic effective mass, detectable as a suppression of the particle mobility with increasing the temperature; (ii) transverse harmonic mixing, whereby electron transport can be controlled by two orthogonal, commensurate ac drives; (iii) a transverse ratchet effect, measurable as a net current orthogonal to an ac drive on an asymmetric substrate, and (iv) chaotic stochastic resonance. Such properties can be of practical applications in the emerging graphene technology.

Ratcheting of driven attracting colloidal particles: Temporal density oscillations and current multiplicity

We consider the unidirectional particle transport in a suspension of colloidal particles which interact with each other via a pair potential having a hard-core repulsion plus an attractive tail. The colloids are confined within a long narrow channel and are driven along by a dc or an ac external potential. In addition, the walls of the channel interact with the particles via a ratchetlike periodic potential. We use dynamical density functional theory to compute the average particle current. In the case of dc drive, we show that as the attraction strength between the colloids is increased beyond a critical value, the stationary density distribution of the particles loses its stability leading to depinning and a time-dependent density profile. Attraction induced symmetry breaking gives rise to the coexistence of stable stationary density profiles with different spatial periods and time-periodic density profiles, each characterized by different values for the particle current.

Coarsening modes of clusters of aggregating particles

There are two modes by which clusters of aggregating particles can coalesce: The clusters can merge either (i) by the Ostwald ripening process, in which particles diffuse from one cluster to the other while the cluster centers remain stationary, or (ii) by means of a cluster translation mode, in which the clusters move toward each other and join. To understand in detail the interplay between these different modes, we study a model system of hard particles with an additional attraction between them. The particles diffuse along narrow channels with smooth or periodically corrugated walls, so that the system may be treated as one-dimensional. When the attraction between the particles is strong enough, they aggregate to form clusters. The channel potential influences whether clusters can move easily or not through the system and can prevent cluster motion. We use dynamical density functional theory to study the dynamics of the aggregation process, focusing in particular on the coalescence of two equal-sized clusters. As long as the particle hard-core diameter is nonzero, we find that the coalescence process can be halted by a sufficiently strong corrugation potential. The period of the potential determines the size of the final stable clusters. For the case of smooth channel walls, we demonstrate that there is a crossover in the dominance of the two different coarsening modes, which depends on the strength of the attraction between particles, the cluster sizes, and the separation distance between clusters.

Collective shuttling of attracting particles in asymmetric narrow channels

The rectification of a single file of attracting particles subjected to a low frequency ac drive is proposed as a working mechanism for particle shuttling in an asymmetric narrow channel. Increasing the particle attraction results in the file condensing, as signaled by the dramatic enhancement of the net particle current. The magnitude and direction of the current become extremely sensitive to the actual size of the condensate, which can then be made to shuttle between two docking stations, transporting particles in one direction, with an efficiency much larger than conventional diffusive models predict.

Dipole rectification in an oscillating electric field

Directed transport of a neutral dimer driven by an ac electric field on a one-dimensional asymmetric substrate is demonstrated. We specialize on the case of a short elastic dimer formed by two bound equal masses carrying opposite charges, i.e., a dipole. The combination of ac drive and binding potential induces a net dipole current (strictly zero for a rigid dimer), which can be optimized by tuning the temperature and the driving frequency with distinct activation energies. Under appropriate operating conditions, a dimer can get rectified more efficiently than its constituents set free, thus implying that particle pairing can actually enhance the ratchet effect.