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Register a new userStability of liquid films covered by a carpet of self-propelled surfactant particles
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We consider a carpet of self-propelled particles at the liquid-gas interface of a liquid film on a solid substrate. The particles excert an excess pressure on the interface and also move along the interface while the swimming direction performs rotational diffusion. We study the intricate influence of these self-propelled insoluble surfactants on the stability of the film surface and show that depending on the strength of in-surface rotational diffusion and the absolute value of the in-surface swimming velocity several characteristic instability modes can occur. In particular, rotational diffusion can either stabilize the film or induce instabilities of different character.
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We consider a colony of point-like self-propelled surfactant particles (swimmers) without direct interactions that cover a thin liquid layer on a solid support. Although the particles predominantly swim normal to the free film surface, their motion also has a component parallel to the film surface. The coupled dynamics of the swimmer density and film height profile is captured in a long-wave model allowing for diffusive and convective transport of the swimmers (including rotational diffusion). The dynamics of the film height profile is determined by three physical effects: the upward pushing force of the swimmers onto the liquid-gas interface that always destabilizes the flat film, the solutal Marangoni force due to gradients in the swimmer concentration that always acts stabilising, and finally the rotational diffusion of the swimmers together with the in-plance active motion that acts either stabilising or destabilising. After reviewing and extending the analysis of the linear stability of the flat film with uniform swimmer density, we analyse the full nonlinear dynamic equations and show that point-like swimmers, which only interact via long-wave deformations of the liquid film, self-organise in highly regular (standing, travelling and modulated waves) and various irregular patterns for swimmer density and film height.
A number of novel experimental and theoretical results have recently been obtained on active soft matter, demonstrating the various interesting universal and anomalous features of this kind of driven systems. Here we consider a fundamental but still unexplored aspect of the patterns arising in the system of actively moving units, i.e., their segregation taking place when two kinds of them with different adhesive properties are present. The process of segregation is studied by a model made of self-propelled particles such that the particles have a tendency to adhere only to those which are of the same kind. The calculations corresponding to the related differential equations can be made in parallel, thus a powerful GPU card allows large scale simulations. We find that the segregation kinetics is very different from the non-driven counterparts and is described by the new scaling exponents $zsimeq 1$ and $zsimeq 0.8$ for the 1:1 and the non-equal ratio of the two constituents, respectively. Our results are in agreement with a recent observation of segregating tissue cells emph{in vitro}.
Active particles with their characteristic feature of self-propulsion are regarded as the simplest models for motility in living systems. The accumulation of active particles in low activity regions has led to the general belief that chemotaxis requires additional features and at least a minimal ability to process information and to control motion. We show that self-propelled particles display chemotaxis and move into regions of higher activity, if the particles perform work on passive objects, or cargo, to which they are bound. The origin of this cooperative chemotaxis is the exploration of the activity gradient by the active particle when bound to a load, resulting in an average excess force on the load in the direction of higher activity. Using a minimalistic theoretical model, we capture the most relevant features of these active-passive dimers and in particular we predict the crossover between anti-chemotactic and chemotactic behaviour. Moreover we show that merely connecting active particles to chains is sufficient to obtain the crossover from anti-chemotaxis to chemotaxis with increasing chain length. Such an active complex is capable of moving up a gradient of activity such as provided by a gradient of fuel and to accumulate where the fuel concentration is at its maximum. The observed transition is of significance to proto-forms of life enabling them to locate a source of nutrients even in the absence of any supporting sensomotoric apparatus.
Catching fish with a fishing net is typically done either by dragging a fishing net through quiescent water or by placing a stationary basket trap into a stream. We transfer these general concepts to micron-sized self-motile particles moving in a solvent at low Reynolds number and study their collective trapping behaviour by means of computer simulations of a two-dimensional system of self-propelled rods. A chevron-shaped obstacle is dragged through the active suspension with a constant speed $v$ and acts as a trapping net. Three trapping states can be identified corresponding to no trapping, partial trapping and complete trapping and their relative stability is studied as a function of the apex angle of the wedge, the swimmer density and the drag speed $v$. When the net is dragged along the inner wedge, complete trapping is facilitated and a partially trapped state changes into a complete trapping state if the drag speed exceeds a certain value. Reversing the drag direction leads to a reentrant transition from no trapping, complete trapping, back to no trapping upon increasing the drag speed along the outer wedge contour. The transition to complete trapping is marked by a templated self-assembly of rods forming polar smectic structures anchored onto the inner contour of the wedge. Our predictions can be verified in experiments of artificial or microbial swimmers confined in microfluidic trapping devices.
We develop a statistical theory for the dynamics of non-aligning, non-interacting self-propelled particles confined in a convex box in two dimensions. We find that when the size of the box is small compared to the persistence length of a particles trajectory (strong confinement), the steady-state density is zero in the bulk and proportional to the local curvature on the boundary. Conversely, the theory may be used to construct the box shape that yields any desired density distribution on the boundary. When the curvature variations are small, we also predict the distribution of orientations at the boundary and the exponential decay of pressure as a function of box size recently observed in 3D simulations in a spherical box.
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