We study a class of cyclic Brownian heat engines in the framework of finite-time thermodynamics. For infinitely long cycle times, the engine works at the Carnot efficiency limit producing, however, zero power. For the efficiency at maximum power, we find a universal expression, different from the endoreversible Curzon-Ahlborn efficiency. Our results are illustrated with a simple one-dimensional engine working in and with a time-dependent harmonic potential.

Efficiency at maximum power: An analytically solvable model for stochastic heat engines

We examine a minimal model for an active colloidal fluid in the form of self-propelled Brownian spheres that interact purely through excluded volume with no aligning interaction. Using simulations and analytic modeling, we quantify the phase diagram and separation kinetics. We show that this nonequilibrium active system undergoes an analog of an equilibrium continuous phase transition, with a binodal curve beneath which the system separates into dense and dilute phases whose concentrations depend only on activity. The dense phase is a unique material that we call an active solid, which exhibits the structural signatures of a crystalline solid near the crystal-hexatic transition point, and anomalous dynamics including superdiffusive motion on intermediate time scales.

http://absimage.aps.org/image/MAR13/MWS_MAR13-2012-003161.pdf

Structure and Dynamics of a Phase-Separating Active Colloidal Fluid

The membranes of red blood cells exhibit a flickering motion that has long been ascribed a thermal origin. Microrheology experiments provide direct evidence that flickering is an active process characterized by non-equilibrium dynamics.

Equilibrium physics breakdown reveals the active nature of red blood cell flickering

We study the statistical properties of active Ornstein-Uhlenbeck particles (AOUPs). In this simplest of models, the Gaussian white noise of overdamped Brownian colloids is replaced by a Gaussian colored noise. This suffices to grant this system the hallmark properties of active matter, while still allowing for analytical progress. We study in detail the steady-state distribution of AOUPs in the small persistence time limit and for spatially varying activity. At the collective level, we show AOUPs to experience motility-induced phase separation both in the presence of pairwise forces or due to quorum-sensing interactions. We characterize both the instability mechanism leading to phase separation and the resulting phase coexistence. We probe how, in the stationary state, AOUPs depart from their thermal equilibrium limit by investigating the emergence of ratchet currents and entropy production. In the small persistence time limit, we show how fluctuation-dissipation relations are recovered. Finally, we discuss how the emerging properties of AOUPs can be characterized from the dynamics of their collective modes.

Statistical mechanics of active Ornstein-Uhlenbeck particles

We study the thermodynamic properties induced by non-reciprocal interactions between stochastic degrees of freedom in time- and space-continuous systems. We show that, under fairly general conditions, non-reciprocal coupling alone implies a steady energy flow through the system, i.e., non- equilibrium. Projecting out the non-reciprocally coupled degrees of freedom renders non-Markovian, one-variable Langevin descriptions with complex types of memory, for which we find a generalized second law involving information flow. We demonstrate that non-reciprocal linear interactions can be used to engineer non-monotonic memory, which is typical for, e.g., time-delayed feedback control, and is automatically accompanied with a nonzero information flow through the system. Furthermore, already a single non-reciprocally coupled degree of freedom can extract energy from a single heat bath (at isothermal conditions), and can thus be viewed as a minimal version of a time-continuous, autonomous "Maxwell demon". We also show that for appropriate parameter settings, the non-reciprocal system has characteristic features of active matter, such as a positive energy input on the level of the fluctuating trajectories without global particle transport.

/pdf/irreversibility-heat-and-information-flows-induced-by-non-4zlqtty9w9.pdf

Irreversibility, heat and information flows induced by non-reciprocal interactions

Asymmetric obstacles in active matter can act as novel type of engine. A new analysis reveals the optimal obstacle shape for such devices and benchmarks for the extraction of useful work from these systems.

/pdf/autonomous-engines-driven-by-active-matter-energetics-and-173c1pexv1.pdf

Autonomous Engines Driven by Active Matter: Energetics and Design Principles

Because of its nonequilibrium character, active matter in a steady state can drive engines that autonomously deliver work against a constant mechanical force or torque. As a generic model for such an engine, we consider systems that contain one or several active components and a single passive one that is asymmetric in its geometrical shape or its interactions. Generally, one expects that such an asymmetry leads to a persistent, directed current in the passive component, which can be used for the extraction of work. We validate this expectation for a minimal model consisting of an active and a passive particle on a one-dimensional lattice. It leads us to identify thermodynamically consistent measures for the efficiency of the conversion of isotropic activity to directed work. For systems with continuous degrees of freedom, work cannot be extracted using a one-dimensional geometry under quite general conditions. In contrast, we put forward two-dimensional shapes of a movable passive obstacle that are best suited for the extraction of work, which we compare with analytical results for an idealised work-extraction mechanism. For a setting with many noninteracting active particles, we use a mean-field approach to calculate the power and the efficiency, which we validate by simulations. Surprisingly, this approach reveals that the interaction with the passive obstacle can mediate cooperativity between otherwise noninteracting active particles, which enhances the extracted power per active particle significantly.

Autonomous engines driven by active matter: Energetics and design principles

The intrinsic permeability is a crucial parameter to characterise and quantify fluid flow through porous media. However, this parameter is typically uncertain, even if the geometry of the pore structure is available. In this paper, we perform a comparative study of experimental, semi-analytical and numerical methods to calculate the permeability of a regular porous structure. In particular, we use the Kozeny–Carman relation, different homogenisation approaches (3D, 2D, very thin porous media and pseudo 2D/3D), pore-scale simulations (lattice Boltzmann method, Smoothed Particle Hydrodynamics and finite-element method) and pore-scale experiments (microfluidics). A conceptual design of a periodic porous structure with regularly positioned solid cylinders is set up as a benchmark problem and treated with all considered methods. The results are discussed with regard to the individual strengths and limitations of the used methods. The applicable homogenisation approaches as well as all considered pore-scale models prove their ability to predict the permeability of the benchmark problem. The underestimation obtained by the microfluidic experiments is analysed in detail using the lattice Boltzmann method, which makes it possible to quantify the influence of experimental setup restrictions.

/pdf/permeability-estimation-of-regular-porous-structures-a-1fnjgbtnik.pdf

Permeability Estimation of Regular Porous Structures: A Benchmark for Comparison of Methods

We study the transport of bacteria in a porous media modeled by a square channel containing one cylindrical obstacle via molecular dynamics simulations coupled to a lattice Boltzmann fluid. Our bacteria model is a rod-shaped rigid body which is propelled by a force-free mechanism. To account for the behavior of living bacteria, the model also incorporates a run-and-tumble process. The model bacteria are capable of hydrodynamically interacting with both of the channel walls and the obstacle. This enables the bacteria to get reoriented when experiencing a shear-flow. We demonstrate that this model is capable of reproducing the bacterial accumulation on the rear side of an obstacle, as has recently been experimentally observed by [G. L. Mino, et al., Adv. Microbiol., 2018, 8, 451] using E. coli bacteria. By systematically varying the external flow strength and the motility of the bacteria, we resolve the interplay between the local flow strength and the swimming characteristics that lead to the accumulation. Moreover, by changing the geometry of the channel, we also reveal the important role of the interactions between the bacteria and the confining walls for the accumulation process.

/pdf/the-influence-of-motility-on-bacterial-accumulation-in-a-3v1usaxp6v.pdf

The influence of motility on bacterial accumulation in a microporous channel.

We study the transport of bacteria in a porous media modeled by a square channel containing one cylindrical obstacle via molecular dynamics simulations coupled to a lattice Boltzmann fluid. Our bacteria model is a rod-shaped rigid body which is propelled by a force-free mechanism. To account for the behavior of living bacteria, the model also incorporates a run-and-tumble process. The model bacteria are capable of hydrodynamically interacting with both of the channel walls and the obstacle. This enables the bacteria to get reoriented when experiencing a shear-flow. We demonstrate that this model is capable of reproducing the bacterial accumulation on the rear side of an obstacle, as has recently been experimentally observed by [G. L. Mino, et al., Advances in Microbiology 8, 451 (2018)] using E.coli bacteria. By systematically varying the external flow strength and the motility of the bacteria, we resolve the interplay between the local flow strength and the swimming characteristics that lead to the accumulation. Moreover, by changing the geometry of the channel, we also reveal the important role of the interactions between the bacteria and the confining walls for the accumulation process.

/pdf/the-influence-of-motility-on-bacterial-accumulation-in-a-fdyc46temm.pdf

Christoph Lohrmann

Papers

Autonomous Engines Driven by Active Matter: Energetics and Design Principles

Autonomous engines driven by active matter: Energetics and design principles

Permeability Estimation of Regular Porous Structures: A Benchmark for Comparison of Methods

The influence of motility on bacterial accumulation in a microporous channel.

The Influence of Motility on Bacterial Accumulation in a Microporous Channel