The Young-Dupré equation is a cornerstone of the equilibrium theory of capillary and wetting phenomena. In the biological world, interfacial phenomena are ubiquitous, from the spreading of bacterial colonies to tissue growth and flocking of birds, but the description of such active systems escapes the realm of equilibrium physics. Here we show how a microscopic, mechanical definition of surface tension allows us to build an Active Young-Dupré equation able to account for the partial wetting observed in simulations of active particles interacting via pairwise forces. Remarkably, the equation shows that the corresponding steady interfaces do not result from a simple balance between the surface tensions at play but instead emerge from a complex feedback mechanism. The interfaces are indeed stabilized by a drag force due to the emergence of steady currents, which are themselves a by-product of the symmetry breaking induced by the interfaces. These currents also lead to new physics by selecting the sizes and shapes of adsorbed droplets, breaking the equilibrium scale-free nature of the problem. Finally, we demonstrate a spectacular consequence of the negative value of the liquid-gas surface tensions in systems undergoing motility-induced phase separation: partially-immersed objects are expelled from the liquid phase, in stark contrast with what is observed in passive systems. All in all, our results lay the foundations for a theory of wetting in active systems.

We analyze the surface tension exerted at the interface between an active fluid and a solid boundary in terms of tangential forces. Focusing on active systems known to possess an equation of state for the pressure, we show that interfacial forces are of a more complex nature. Using a number of macroscopic setups, we show that the surface tension is a combination of an equation-of-state abiding part and of setup-dependent contributions. The latter arise from generic setup-dependent steady currents which "dress" the measurement of the "bare" surface tension. The former shares interesting properties with its equilibrium counterpart, and can be used to generalize the Young-Laplace law to active systems. Finally, we show how a suitably designed probe can directly access this bare surface tension, which can also be computed using a generalized virial formula.

Self-organization is a prerequisite of biological complexity. At the population level, it amounts to spontaneously sorting different individuals through space and time. Here, we reveal a simple mechanism by which different populations of motile cells can self-organize through a reciprocal control of their motilities. We first show how the reciprocal activation of motility between two populations of engineered Escherichia coli makes an initially mixed population of cells segregate, leading to out-of-phase population oscillations without the need of any preexisting positional or orientational cues. By redesigning the interaction, the original segregation between the two populations can be turned into co-localization. We account for this self-organization using a theoretical model that shows the reciprocal control of motility to be a robust and versatile self-organization pathway in multi-component systems. We finally show how our theoretical and experimental results can be generalized to three interacting bacterial populations. The authors engineer Escherichia coli into two distinct strains with tunable motility. The induced control of motility leads to the formation of patterns through a self-organizing mechanism that is specific to multi-component active systems.

The course "Phy Ex" was created by Yves Couder in the Paris VII university to teach experimental physics through projects. In this article, we present this teaching method through a particular project that took place in the autumn semester 2019: the ping-pong ball water cannon. In this experiment, a glass containing water and a floating table tennis ball is dropped from some height to the ground. Following the impact, the ball is ejected vertically upwards at speeds that can be several times the impact speed. We report the student team's initial dimensional and order-of-magnitude analysis, and describe the successive experimental set-ups that showed (1) that free flight is essential for the phenomenon to occur, (2) that the order of magnitude of the ball ejection momentum is correctly predicted by a momentum balance based on integrating the pressure impulse during impact and (3) that making the ball surface more wettable, or stirring the liquid, drastically increases the momentum transfer. The proposed explanation, confirmed by direct high-speed video observations, is that the immersion depth of the ball increases during free fall due to capillary forces or vortex depression-in the absence of buoyancy-and that the enormous excess pressure on the bottom of the ball during impact drives the ball up towards its buoyancy equilibrium. The transfered momentum is sufficient to expel the ball at high velocity, very similar to the formation of liquid jets in collapsing cavities in liquids.

Self-organization is a hallmark of all living systems [[1][1]]. In particular, coordinated cellular behavior, commonly orchestrated at the population level through reciprocal interactions among different cell species [[2][2]–[4][3]], regulates the spatial arrangement of specialized cell types to generate tissue patterning and form complex body layouts [[5][4], [6][5]]. The overwhelming complexity of living systems, however, makes deciphering the underlying mechanisms difficult and limits our knowledge of basic pattern-forming mechanism in vivo [[7][6], [8][7]]. A successful strategy is then to work with synthetic, engineered systems, in which cellular interactions can be more easily tailored and studied [[9][8]–[13][9]]. Here, we demonstrate a simple mechanism through which different populations of cells can self-organize in periodic patterns. Programmed population interactions are shown to lead to coordinated out-ofphase spatial oscillations of two engineered populations of Escherichia coli . Using a combination of experimental and theoretical approaches, we show how such patterns arise autonomously from reciprocal density-dependent activation of cellular motility between the two species, without the need of any preexisting positional or orientational cues. Moreover, by re-designing the interaction, the original out-of-phase spatial oscillation rhythm of the two populations can be accordingly turned into in-phase oscillations. The robustness and versatility of the underlying pattern-formation process suggest that it could both be generically encountered in nature, for instance in the complex bacterial ecosystems found in biofilms [[14][10]–[16][11]], and used to promote the mixing or demixing of active particles in a controlled way. [1]: #ref-1 [2]: #ref-2 [3]: #ref-4 [4]: #ref-5 [5]: #ref-6 [6]: #ref-7 [7]: #ref-8 [8]: #ref-9 [9]: #ref-13 [10]: #ref-14 [11]: #ref-16

Self-organization is a hallmark of all living systems [1]. In particular, coordinated cellular behavior, commonly orchestrated at the population level through reciprocal interactions among different cell species [2-4], regulates the spatial arrangement of specialized cell types to generate tissue patterning and form complex body layouts [5, 6]. The overwhelming complexity of living systems, however, makes deciphering the underlying mechanisms difficult and limits our knowledge of basic pattern-forming mechanism in vivo [7, 8]. A successful strategy is then to work with synthetic, engineered systems, in which cellular interactions can be more easily tailored and studied [9-13]. Here, we demonstrate a simple mechanism through which different populations of cells can self-organize in periodic patterns. Programmed population interactions are shown to lead to coordinated out-ofphase spatial oscillations of two engineered populations of Escherichia coli. Using a combination of experimental and theoretical approaches, we show how such patterns arise autonomously from reciprocal density-dependent activation of cellular motility between the two species, without the need of any preexisting positional or orientational cues. Moreover, by re-designing the interaction, the original out-of-phase spatial oscillation rhythm of the two populations can be accordingly turned into in-phase oscillations. The robustness and versatility of the underlying pattern-formation process suggest that it could both be generically encountered in nature, for instance in the complex bacterial ecosystems found in biofilms [14-16], and used to promote the mixing or demixing of active particles in a controlled way.

The string shooter experiment uses counter-rotating pulleys to propel a closed string forward. Its steady state exhibits a transition from a gravity-dominated regime at low velocity towards a high-velocity regime where the string takes the form of a self-supporting loop. Here we show that this loop of light string is not suspended in the air due to inertia, but through the hydrodynamic drag exerted by the surrounding fluid, namely air. We investigate this drag experimentally and theoretically for a smooth long cylinder moving along its axis. We then derive the equations describing the shape of the string loop in the limit of vanishing string radius. The solutions present a critical point, analogous to a hydraulic jump, separating a supercritical zone where the wave velocity is smaller than the rope velocity, from a subcritical zone where waves propagate faster than the rope velocity. This property could be leveraged to create a white hole analogue similar to what has been demonstrated using surface waves on a flowing fluid. Loop solutions that are regular at the critical point are derived, discussed and compared to the experiment. In the general case, however, the critical point turns out to be the locus of a sharp turn of the string, which is modelled theoretically as a discontinuity. The hydrodynamic regularisation of this geometrical singularity, which involves non-local and added mass effects, is discussed on the basis of dimensional analysis.

ABSTRACT Bacteria adopt social behavior to expand into new territory, led by specialized swarmers, before forming a biofilm. Such mass migration of Bacillus subtilis on a synthetic medium produces hyperbranching dendrites that transiently (equivalent to 4 to 5 generations of growth) maintain a cellular monolayer over long distances, greatly facilitating single-cell gene expression analysis. Paradoxically, while cells in the dendrites (nonswarmers) might be expected to grow exponentially, the rate of swarm expansion is constant, suggesting that some cells are not multiplying. Little attention has been paid to which cells in a swarm are actually multiplying and contributing to the overall biomass. Here, we show in situ that DNA replication, protein translation and peptidoglycan synthesis are primarily restricted to the swarmer cells at dendrite tips. Thus, these specialized cells not only lead the population forward but are apparently the source of all cells in the stems of early dendrites. We developed a simple mathematical model that supports this conclusion. IMPORTANCE Swarming motility enables rapid coordinated surface translocation of a microbial community, preceding the formation of a biofilm. This movement occurs in thin films and involves specialized swarmer cells localized to a narrow zone at the extreme swarm edge. In the B. subtilis system, using a synthetic medium, the swarm front remains as a cellular monolayer for up to 1.5 cm. Swarmers display high-velocity whirls and vortexing and are often assumed to drive community expansion at the expense of cell growth. Surprisingly, little attention has been paid to which cells in a swarm are actually growing and contributing to the overall biomass. Here, we show that swarmers not only lead the population forward but continue to multiply as a source of all cells in the community. We present a model that explains how exponential growth of only a few cells is compatible with the linear expansion rate of the swarm.

Kovacs et al. (1) have greatly contributed to the characterization of “sliding” (2⇓–4), a flagella-independent, “passive type of [bacterial] movement, [...] powered by the pushing force of dividing cells and additional factors facilitating the expansion over surfaces” (2). They suggest that bacterial surfing (5) should be described by the same name to “facilitate the understanding between the biophysics and the microbiology communities.”Providing a clear and systematic classification of bacterial modes of motility is indeed a common objective of both communities, but one still has to agree on the best way to proceed. Bacteria possess a surprisingly rich toolbox to … [↵][1]1To whom correspondence should be addressed. Email: adrian.daerr{at}univ-paris-diderot.fr. [1]: #xref-corresp-1-1

We observe that small drops of a Bacillus subtilis suspension deposited on agar strongly increase in volume while similar bacteria-void drops do not. By measuring the bacterial concentration within the drop at different heights, we show that the biomass increase due to the constant bacterial cell-division is too small to explain the drop bloating. Rather, the increased volume is caused by the presence of surfactin - a surfactant produced by the bacteria - which induces a water flow out of the environment by an osmotic capillary effect. The required concentration is very low (< 1 mM), four orders of magnitude smaller than the concentration of, for example, glucose to produce a similar effect. The ability of B. subtilis to extract water from its environment probably contributes to collective migration modes like mass swarming. It also gives rise to a new displacement mode independent of cellular motility: By combining the osmotic and wetting effects of the surfactant, B. subtilis can actively induce the sliding of the bacterial colony on substrates tilted by angles as small as 0.1 degrees.

How systems are endowed with migration capacity is a fascinating question with implications ranging from the design of novel active systems to the control of microbial populations. Bacteria, which can be found in a variety of environments, have developed among the richest set of locomotion mechanisms both at the microscopic and collective levels. Here, we uncover, experimentally, a mode of collective bacterial motility in humid environment through the depinning of bacterial droplets. Although capillary forces are notoriously enormous at the bacterial scale, even capable of pinning water droplets of millimetric size on inclined surfaces, we show that bacteria are able to harness a variety of mechanisms to unpin contact lines, hence inducing a collective slipping of the colony across the surface. Contrary to flagella-dependent migration modes like swarming, we show that this much faster "colony surfing" still occurs in mutant strains of Bacillus subtilis lacking flagella. The active unpinning seen in our experiments relies on a variety of microscopic mechanisms, which could each play an important role in the migration of microorganisms in humid environment.

The pendent drop method for surface tension measurement consists in analysing the shape of an axisymmetric drop hanging from a capillary tube. This software is an add-on for the public domain image processing software ImageJ which matches a theoretical profile to the contour of a pendent drop, either interactively or by automatically minimising the mismatch. It provides an estimate of the surface tension, drop volume and surface area from the best matching parameters. It can be used in a headless setup. It is hosted on http://fiji.sc/List_of_update_sites with the source code on https://github.com/adaerr/pendent-drop

Microorganisms often form complex multicellular assemblies such as biofilms and colonies. Understanding the interplay between assembly expansion, metabolic yield, and nutrient diffusion within a freely growing colony remains a challenge. Most available data on microorganisms are from planktonic cultures, due to the lack of experimental tools to control the growth of multicellular assemblies. Here, we propose a method to constrain the growth of yeast colonies into simple geometric shapes such as cylinders. To this end, we designed a simple, versatile culture system to control the location of nutrient delivery below a growing colony. Under such culture conditions, yeast colonies grow vertically and only at the locations where nutrients are delivered. Colonies increase in height at a steady growth rate that is inversely proportional to the cylinder radius. We show that the vertical growth rate of cylindrical colonies is not defined by the single-cell division rate, but rather by the colony metabolic yield. This contrasts with cells in liquid culture, in which the single-cell division rate is the only parameter that defines the population growth rate. This method also provides a direct, simple method to estimate the metabolic yield of a colony. Our study further demonstrates the importance of the shape of colonies on setting their expansion. We anticipate that our approach will be a starting point for elaborate studies of the population dynamics, evolution, and ecology of microbial colonies in complex landscapes.

We studied the dynamics of a liquid contact line receding on a hydrophobic soft gel (SBS–paraffin). In order to realize a well-defined geometry with an accurate control of velocity, a dip-coating setup was implemented. Provided that the elastic modulus is small enough, a significant deformation takes place near the contact line, which in turn drastically influences the wetting behaviour. Depending on the translation velocity of the substrate, the contact line exhibits different regimes of motions. Continuous motions are observed at high and low velocities, meanwhile two types of stick–slip motion – periodic and erratic – appear at intermediate velocities. We suggest that the observed transitions could be explained in terms of the competition between different frequencies, i.e., the frequency of the strain field variation induced by the contact line motion and the crossover frequency of the gel related to the material relaxation. Our results provide systematic views on how the wetting of liquid is modified by the rheological properties of a complex soft substrate.

In a recent paper, we investigated the stability of a rivulet of water flowing down a vertical glass pane. This system exhibits various flow regimes for increasing flow rate, as described by Nakagawa [1] for water on PMMA: at very low flow rate water runs down in distinct drops. As the flow rate is increased, one observes first stationary, pinned rivulets (straight or meandering), then nonstationary streams meandering and breaking up, and at higher flow rates “restable” (Nakagawa) straight streams. Our aim was to determine why straight rivulets become unstable and start meandering. In total wetting conditions, where there are no pinning forces, we had already shown [2] that anisotropic friction due to the contact lines leads to an inertial instability. In partial wetting the pinning of the contact lines suppresses the linear instability. The instability still exists, however, because a flow rate increase will eventually increase the contact angle beyond its maximum static value, at which point the contact line recovers its mobility. The main result of our paper is to show experimentally that the critical flow rate at which this happens can be predicted by analysing the initial rivulet shape, specifically its width and roughness. In their Comment, Fathi et al. describe experiments that, they claim, disagree with our findings. Although their system behaves differently in some respects (maybe due to different wetting characteristics), we do not feel that the details provided contradict our observations on the destabilisation of a straight rivulet. Indeed Fathi et al. agree that a “Q [flow rate] variation can [. . . ] destabilize a rivulet”, and explaining the required variation is precisely the question addressed in our paper. The central difference of the experimental systems seems to lie in the evolution after meandering has started: we notice that meanders eventually become stationary, whereas Fathi et al. observe that meandering resulting from a flow rate change is only transient. While it is quite interesting that there exist systems differing in their long-term dynamics, this has little to do with the point we make in our paper, viz. that straight rivulets become unstable as the flow rate is increased to a critical value entirely determined by the spacing and roughness of the rivulet’s contact lines. Fathi et al. see a potential for misreading the notations in our paper, notably in fig. 4 depicting a transverse cut through the rivulet, not a top view of the rivulet path. The revisited fig. 1 hopefully dissipates any ambiguity. Fathi et al. criticise two points in our simple model for the transverse rivulet profile: that we assume that the cross-sectional area remains constant when the rivulet deforms, and that a cubic can be a reasonable approximation. For typical heights (∼ 1mm) and velocities (several 10 cm/s) of the stream, the viscous boundary layer develops over a distance of several 10 cm. The fluid velocity will hardly change when passing through a perturbation which