Turbulence is ubiquitous in nature yet even for the case of ordinary Newtonian fluids like water our understanding of this phenomenon is limited. Many liquids of practical importance however are more complicated (e.g. blood, polymer melts or paints), they exhibit elastic as well as viscous characteristics and the relation between stress and strain is nonlinear. We here demonstrate for a model system of such complex fluids that at high shear rates turbulence is not simply modified as previously believed but it is suppressed and replaced by a new type of disordered motion, elasto-inertial turbulence (EIT). EIT is found to occur at much lower Reynolds numbers than Newtonian turbulence and the dynamical properties differ significantly. In particular the drag is strongly reduced and the observed friction scaling resolves a longstanding puzzle in non-Newtonian fluid mechanics regarding the nature of the so-called maximum drag reduction asymptote. Theoretical considerations imply that EIT will arise in complex fluids if the extensional viscosity is sufficiently large

Adding a nonadsorbing polymer to passive colloids induces an attraction between the particles via the "depletion" mechanism. High enough polymer concentrations lead to phase separation. We combine experiments, theory, and simulations to demonstrate that using active colloids (such as motile bacteria) dramatically changes the physics of such mixtures. First, significantly stronger interparticle attraction is needed to cause phase separation. Secondly, the finite size aggregates formed at lower interparticle attraction show unidirectional rotation. These micro-rotors demonstrate the self-assembly of functional structures using active particles. The angular speed of the rotating clusters scales approximately as the inverse of their size, which may be understood theoretically by assuming that the torques exerted by the outermost bacteria in a cluster add up randomly. Our simulations suggest that both the suppression of phase separation and the self-assembly of rotors are generic features of aggregating swimmers and should therefore occur in a variety of biological and synthetic active particle systems. M otile bacteria are simple examples of "living active matter." Passive particles with sizes similar to those of most bacteria, viz., 0.2-2 μm, are colloids. Such particles are in thermal equilibrium with the surrounding solvent and undergo Brownian motion. In contrast, self-propelled bacteria are active colloids. Such particles function far from equilibrium. This renders their physics far richer than that of passive colloids, mainly because they are not subject to thermodynamic constraints such as detailed balance or the fluctuation-dissipation theorem. Thus, bacteria are able to harness their activity to power externally added micro gear wheels (1-3), self-concentrate, and cluster to form a variety of patterns due to geometry, steric effects, or biochemical cues (4-6).Currently, no general statistical mechanical theory relates the microscopic properties of individual active particles to the macroscopic behavior of large collections of such particles. Recent experiments on noninteracting suspensions of synthetic swimmers (7) show that, as in a dilute suspension of passive particles, there is an exponential distribution of particles with height, but with an increased sedimentation length. To date, however, there has been no experiment designed specifically to probe the effect of activity on macroscopic properties that arise from interparticle interaction, such as phase transitions, perhaps the quintessential many-body phenomenon. Here, we report a systematic study of the physics of phase separation and self-assembly in a suspension of interacting active colloids in the form of mutually attracting motile bacteria. Our experimental results, supported by theory and simulations, provide a foundation for general treatments of the statistical mechanics of interacting active particles.Interparticle attraction in passive colloids leads to aggregation and phase separation. Such attraction can be induced by nonadsorbing polymer...

It is presently believed that flows of viscoelastic polymer solutions in geometries such as a straight pipe or channel are linearly stable. Here we present experimental evidence that such flows can be nonlinearly unstable and can exhibit a subcritical bifurcation. Velocimetry measurements are performed in a long, straight micro-channel; flow disturbances are introduced at the entrance of the channel system by placing a variable number of obstacles. Above a critical flow rate and a critical size of the perturbation, a sudden onset of large velocity fluctuations indicates presence of a nonlinear subcritical instability. Together with the previous observations of hydrodynamic instabilities in curved geometries, our results suggest that any flow of polymer solutions becomes unstable at sufficiently high flow rates.PACS numbers: 47.20.Gv, 61.25.he Solutions containing polymer molecules do not flow like water. Even when flowing slowly, these fluids can exhibit hydrodynamic instabilities [1][2][3][4][5][6][7][8] and a new type of turbulence -the so-called purely elastic turbulence [9,10] even at low Reynolds numbers (Re). These phenomena, driven by the anisotropic elasticity of the fluid, were experimentally observed only in geometries with sufficient curvature, like rotational flows between two cylinders [1,11,12] and plates [13], in curved channels [10,14], and around obstacles [15]. Most of the nonlinear flow behavior observed in these studies arises from the extra elastic stresses due to the presence of polymer molecules in the fluid. These elastic stresses are history dependent and evolve on the time-scale λ that in dilute solutions is proportional to the time needed for a polymer molecule to relax to its equilibrium state [16].A common feature of the above-mentioned geometries is the presence of curved streamlines in the base flow with a sufficient velocity gradient across the streamlines. It has been argued that this is a necessary condition for infinitesimal perturbations to be amplified by the normal stress imbalances in viscoelastic flows [1,8,13]. This condition can be written as (λ U N 1 )/(R Σ) ≥ M [8, 13,17], where M is a constant that only depends on the type of flow geometry, U is a typical velocity along the streamlines, R is the radius of streamline curvature, and N 1 and Σ are the first normal stress difference and the shear stress, correspondingly. According to this condition, purely elastic linear instabilities are not possible when the curvature of the flow geometry is zero, and infinitesimal perturbations decay at a rate proportional to 1/λ [8,18,19].Nevertheless, the absence of a linear instability does not imply absolute stability. Indeed, recent theoretical [17,[20][21][22][23] and indirect experimental [24,25] evidence points towards a finite-amplitude transition in viscoelastic flows with parallel streamlines even at low Reynolds number, where viscous and elastic forces dominate over inertial forces. An earlier study of the flow of a polymeric melt extruded out of a thin cylindrical capi...

It is widely believed that the swimming speed, v, of many flagellated bacteria is a nonmonotonic function of the concentration, c, of high-molecular-weight linear polymers in aqueous solution, showing peaked v(c) curves. Pores in the polymer solution were suggested as the explanation. Quantifying this picture led to a theory that predicted peaked v(c) curves. Using high-throughput methods for characterizing motility, we measured v and the angular frequency of cell body rotation, Ω, of motile Escherichia coli as a function of polymer concentration in polyvinylpyrrolidone (PVP) and Ficoll solutions of different molecular weights. We find that nonmonotonic v(c) curves are typically due to low-molecular-weight impurities. After purification by dialysis, the measured v(c) and Ω(c) relations for all but the highest-molecular-weight PVP can be described in detail by Newtonian hydrodynamics. There is clear evidence for non-Newtonian effects in the highest-molecular-weight PVP solution. Calculations suggest that this is due to the fast-rotating flagella seeing a lower viscosity than the cell body, so that flagella can be seen as nano-rheometers for probing the non-Newtonian behavior of high polymer solutions on a molecular scale. T he motility of microorganisms in polymer solutions is a topic of vital biomedical interest. For example, mucus covers the respiratory (1), gastrointestinal (2), and reproductive (3) tracks of all metazoans. Penetration of this solution of biomacromolecules by motile bacterial pathogens is implicated in a range of diseases, e.g., stomach ulcers caused by Helicobacter pylori (4). Oviduct mucus in hens provides a barrier against Salmonella infection of eggs (5). Penetration of the exopolysaccharide matrix of biofilms by swimming bacteria (6) can stabilize or destabilize them in vivo (e.g., the bladder) and in vitro (e.g., catheters). In reproductive medicine (human and veterinary), the motion of sperms in seminal plasma and vaginal mucus, both non-Newtonian polymer solutions, is a strong determinant of fertility (3), and polymeric media are often used to deliver spermicidal and other vaginal drugs (7).Microorganismic propulsion in non-Newtonian media such as high-polymer solutions is also a hot topic in biophysics, soft matter physics, and fluid dynamics (8). Building on knowledge of propulsion modes at low Reynolds number in Newtonian fluids (8), current work seeks to understand how these are modified to enable efficient non-Newtonian swimming. In particular, there is significant interest in a flapping sheet (9, 10) or an undulating filament (11) (modeling the sperm tail) and in a rotating rigid helix (modeling the flagella of, e.g., Escherichia coli) (12, 13) in non-Newtonian fluids.An influential set of experiments in this field was performed 40 years ago by Schneider and Doetsch (SD) (14), who measured the average speed, v, of seven flagellated bacterial species (including E. coli) in solutions of polyvinylpyrrolidone (PVP, molecular weight given as M = 360 kDa) and in methyl cellulose (MC, M...