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Register a new userHydrodynamic correlations and instabilities in stress-balanced pusher-puller mixtures
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Multispecies swarms are found for microorganisms living in microfluidic environments where they can take advantage of collective motions during transport and spreading. Nevertheless, there is a general lack of physical understandings of the origins of the multiscale unstable dynamics. Here we build a computation model to study the binary suspensions of rear- and front-actuated microswimmers, or respectively the so-called pusher and puller particles, that have different populations and swimming speeds. We perform direct particle simulations to reveal that even in the scenarios of stress-balanced mixtures which produce approximately zero net extra stresses, the longtime dynamics can exhibit non-trivial density fluctuations and spatially-correlated motions. We then construct a continuum kinetic model and perform linear stability analysis to reveal the underlying mechanisms of hydrodynamic instabilities. Our theoretical predictions qualitatively agree with numerical results and explain the onsets of the observed collective motions.
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Suspensions of rear- and front-actuated microswimmers immersed in a fluid, known respectively as ``pushers and ``pullers, display qualitatively different collective behaviours: beyond a characteristic density, pusher suspensions exhibit a hydrodynamic instability leading to collective motion known as active turbulence, a phenomenon which is absent for pullers. In this Letter, we describe the collective dynamics of a binary pusher--puller mixture using kinetic theory and large-scale particle-resolved simulations. We derive and verify an instability criterion, showing that the critical density for active turbulence moves to higher values as the fraction $chi$ of pullers is increased and disappears for $chi geq 0.5$. We then show analytically and numerically that the two-point hydrodynamic correlations of the 1:1 mixture are equal to those of a suspension of noninteracting swimmers. Strikingly, our numerical analysis furthermore shows that the full probability distribution of the fluid velocity fluctuations collapses onto the one of a noninteracting system at the same density, where swimmer--swimmer correlations are strictly absent. Our results thus indicate that the fluid velocity fluctuations in 1:1 pusher--puller mixtures are exactly equal to those of the corresponding noninteracting suspension at any density, a surprising cancellation with no counterpart in equilibrium long-range interacting systems.
Eutectic gallium-indium (EGaIn), a room-temperature liquid metal alloy, has the largest tension of any liquid at room temperature, and yet can nonetheless undergo fingering instabilities. This effect arises because, under an applied voltage, oxides deposit on the surface of the metal, which leads to a lowering of the interfacial tension, allowing spreading under gravity. Understanding the spreading dynamics of room temperature liquid metals is important for developing soft electronics and understanding fluid dynamics of liquids with extreme surface tensions. When the applied voltage or the oxidation rate becomes too high, the EGaIn undergoes fingering instabilities, including tip-splitting, which occur due to a Marangoni stress on the interface. Our experiments are performed with EGaIn droplets placed in an electrolyte (sodium hydroxide); by placing the EGaIn on copper electrodes, which EGaIn readily wets, we are able to control the initial width of EGaIn fingers, setting the initial conditions of the spreading. Two transitions are observed: (1) a minimum current density at which all fingers become unstable to narrower fingers; (2) a current density at which the wider fingers undergo a single splitting event into two narrower fingers. We present a phase diagram as a function of current density and initial finger width, and identify the minimum width below which the single tip-splitting does not occur.
Viscoelastic fluids are a common subclass of rheologically complex materials that are encountered in diverse fields from biology to polymer processing. Often the flows of viscoelastic fluids are unstable in situations where ordinary Newtonian fluids are stable, owing to the nonlinear coupling of the elastic and viscous stresses. Perhaps more surprisingly, the instabilities produce flows with the hallmarks of turbulence -- even though the effective Reynolds numbers may be $O(1)$ or smaller. We provide perspectives on viscoelastic flow instabilities by integrating the input from speakers at a recent international workshop: historical remarks, characterization of fluids and flows, discussion of experimental and simulation tools, and modern questions and puzzles that motivate further studies of this fascinating subject. The materials here will be useful for researchers and educators alike, especially as the subject continues to evolve in both fundamental understanding and applications in engineering and the sciences.
Understanding the mechanics of detrimental convective instabilities in drying polymer solutions is crucial in many applications such as the production of film coatings. It is well known that solvent evaporation in polymer solutions can lead to Rayleigh-Benard or Marangoni-type instabilities. Here we reveal another mechanism, namely that evaporation can cause the interface to display Rayleigh-Taylor instabilities due to the build-up of a dense layer at the air-liquid interface. We study experimentally the onset time ($t_p$) of the instability as a function of the macroscopic properties of aqueous polymer solutions, which we tune by varying the polymer concentration ($c_0$), molecular weight and polymer type. In dilute solutions, $t_p$ shows two limiting behaviors depending on the polymer diffusivity. For high diffusivity polymers (low molecular weight), the pluming time scales as $c_0^{-2/3}$. This result agrees with previous studies on gravitational instabilities in miscible systems where diffusion stabilizes the system. On the other hand, in low diffusivity polymers the pluming time scales as $c_0^{-1}$. The stabilizing effect of an effective interfacial tension, similar to those in immiscible systems, explains this strong concentration dependence. Above a critical concentration, $hat{c}$, viscosity delays the growth of the instability, allowing time for diffusion to act as the dominant stabilizing mechanism. This results in $t_p$ scaling as $( u/c_0)^{2/3}$.
Phoretic particles self-propel using self-generated physico-chemical gradients at their surface. Within a suspension, they interact hydrodynamically by setting the fluid around them into motion, and chemically by modifying the chemical background seen by their neighbours. While most phoretic systems evolve in confined environments due to buoyancy effects, most models focus on their interactions in unbounded flows. Here, we propose a first model for the interaction of phoretic particles in Hele-Shaw confinement and show that in this limit, hydrodynamic and phoretic interactions share not only the same scaling but also the same form, albeit in opposite directions. In essence, we show that phoretic interactions effectively reverse the sign of the interactions that would be obtained for swimmers interacting purely hydrodynamically. Yet, hydrodynamic interactions can not be neglected as they significantly impact the magnitude of the interactions. This model is then used to analyse the behaviour of a suspension. The suspension exhibits swirling and clustering collective modes dictated by the orientational interactions between particles, similar to hydrodynamic swimmers, but here governed by the surface properties of the phoretic particle; the reversal in the sign of the interaction tends to slow down the swimming motion of the particles.
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