Differently from passive Brownian particles, active particles, also known as self-propelled Brownian particles or microswimmers and nanoswimmers, are capable of taking up energy from their environment and converting it into directed motion. Because of this constant flow of energy, their behavior can be explained and understood only within the framework of nonequilibrium physics. In the biological realm, many cells perform directed motion, for example, as a way to browse for nutrients or to avoid toxins. Inspired by these motile microorganisms, researchers have been developing artificial particles that feature similar swimming behaviors based on different mechanisms. These man-made micromachines and nanomachines hold a great potential as autonomous agents for health care, sustainability, and security applications. With a focus on the basic physical features of the interactions of self-propelled Brownian particles with a crowded and complex environment, this comprehensive review will provide a guided tour through its basic principles, the development of artificial self-propelling microparticles and nanoparticles, and their application to the study of nonequilibrium phenomena, as well as the open challenges that the field is currently facing.

We study experimentally and numerically a (quasi) two dimensional colloidal suspension of selfpropelled spherical particles. The particles are carbon-coated Janus particles, which are propelled due to diffusiophoresis in a near-critical water-lutidine mixture. At low densities, we find that the driving stabilizes small clusters. At higher densities, the suspension undergoes a phase separation into large clusters and a dilute gas phase. The same qualitative behavior is observed in simulations of a minimal model for repulsive self-propelled particles lacking any alignment interactions. The observed behavior is rationalized in terms of a dynamical instability due to the self-trapping of self-propelled particles.PACS numbers: 82.70. Dd,64.60.Cn Following our physical intuition, "agitating" a system by, e.g., increasing the temperature also increases disorder. The most simple and paradigmatic example is the Ising model of interacting spins on a lattice, which, in two or more dimensions, displays a second-order phase transition from an ordered state to a disordered state as we increase the temperature [1]. Non-equilibrium driven systems, however, may defy our intuition and show the opposite behavior: increasing the noise strength leads to the emergence of an ordered state [2,3], for example the "freezing by heating" transition of oppositely driven particles in a narrow channel [4].One class of non-equilibrium systems that currently receives considerable attention are self-propelled, or "active", particles [5][6][7][8][9][10][11][12][13]. These are model systems for "living active matter" ranging from microtubules [14] to dense bacterial solutions [15][16][17] to flocks of birds [18]. A common feature of many of these models is that the particle orientations align, which leads to a multitude of collective phenomena such as swarming [19] and even micro-bacterial turbulence [20]. This alignment interaction can be either explicit (Vicsek-type models [21]) or indirect. For example, in dense granular systems of rods [22] and disks [23], the combination of hardcore repulsion and propulsion implies an effective alignment. Somewhat surprisingly, recently it has been found that also self-propelled suspensions lacking any alignment mechanism are able to show collective behavior. Specifically, simulations of a minimal model for a suspension of repulsive disks below the freezing transition [24] show phase separation into a dense large cluster and a dilute gas phase [25,26]. Phase separation due to a densitydependent mobility has been discussed theoretically in the context of run-and-tumble bacteria [27], and a link has been made recently to self-propelled Brownian particles [28].Experimentally, active clustering of spherical colloidal particles has been observed for sedimenting, platinumcoated gold particles [10] and colloidal particles with an embedded hematite cube [13], where platinum and hematite act as catalysts for the decomposition of water peroxide. In both studies, aggregation is attributed to attractive forces. In thi...

When fluctuating fields are confined between two surfaces, long range forces arise. A famous example is the quantum electrodynamical Casimir force that results from zero point vacuwn fluctuations confuted between two conducting metal plates'. A thermodynamic analogue is the critical Casimir force: it acts between surfaces immersed in a binary liquid mixture dose to its critical point and arises from the confiuement of con centra tion fluctuations within the thin film of fluid separating the sur faces 2 • So far, all ell:peri.mental evidence for the existence of this effect has been indirece 5 • Here we report the direct measurement of critical Casimir force between a single colloidal sphere and a flat silica surface immersed in a mixture of water and 2,6 lutidi.ne near its critical point. We use total internal reflection microscopy to detemti.ue in situ the forces between the sphere and the surface, with femtonewton resolution 6 • Depending on whether the adsorp tion preferences of the sphere and the surface for water and 2,6 lutidi.ne are identical or opposite, we measure attractive and repulsive forces, respectively, that agree quantitatively with theoretical predictions and exhibit exquisite dependence on the temperature of the system. We expect that these features of critical Casimir forces may result in novel uses of colloids as model systems.The simple act of confining a fluid can give rise to new ph en om en a not observed in the bulk. An intriguing example is the critical Casi.urir force predicted to occur in binary fluid mixtures close to their critical point; like other critical phenomena, it is characterized by universal scaling functions that depend only on the internal symmetries of the system rather than on its specific material properties' . Colloidal particles suspended in binary liquids offer a particularly interesting setting for the experintental observations of such forces. At suffi ciently small particle distances, concentration fluctuations of the solvent become confined between neighbouring colloidal surfaces and modify the pair interaction 8 • If tlte Casinlir interaction strengtlt is comparable to the thermal energy, drastic changes in the phase behaviour are expected. Reversible flocculation of silica colloids in water 2,6 lutidi.ue mixtures close to the critical point has in fact been observed 9 , and critical Casinlir forces may be invoked to explain tills phenomenon. However, flocculation was observed even far away from tlte critical point where critical fluctuations are negligible, so it cannot serve as conclusive evidence for the presence of Casi.utir forces 10 " 11 • Our experiments, ainted at directly measuring critical Casi.utir forces, use a single colloidal sphere and a planar surface immersed in a binary liquid mixture of water and 2,6 lutidine. Forces are deter mined using total internal reflection microscopy (TIRM, see Methods) 6 which allows itt situ measurements with femtonewton resolution 12 (Fig. 1). The binary liquid mixture bas a lower critical demixing point at Tc = ...