Research Article

Transition from turbulent to coherent flows in confined three-dimensional active fluids

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Science  24 Mar 2017:
Vol. 355, Issue 6331, eaal1979
DOI: 10.1126/science.aal1979

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Go with the changing flow

The transport of ordinary fluids tends to be driven by pressure differentials, whereas for active or biological matter, transport may be isotropic or governed by the presence of specific chemical gradients. Wu et al. analyzed the emergence of spontaneous directional flows in active fluids containing a suspension of microtubules and clusters of the molecular motor kinesin, confined in a variety of microfluidic geometries (see the Perspective by Morozov). When confined in periodic toroidal channels and cylindrical domains, the flow was organized and persisted in a unidirectional motion, either clockwise or counterclockwise. Oddly, this behavior was independent of scale; as long as the aspect ratio of the geometry was chosen appropriately, flows were observed for a wide range of system dimensions.

Science, this issue p. eaal1979; see also p. 1262

Structured Abstract

INTRODUCTION

Conventional nonequilibrium systems are composed of inanimate components whose dynamics is powered by the external input of energy. For example, in a turbulent fluid, energy cascades down many length scales before being dissipated. In comparison, diverse nonequilibrium processes in living organisms are powered at the microscopic scale by energy-transducing molecular processes. Energy injected at the smallest scales cascades up many levels of structural organization, collectively driving dynamics of subcellular organelles, cells, tissues, and entire organisms. However, the fundamental principles by which animate components self-organize into active materials and machines capable of producing macroscopic work remain unknown. Elucidating these rules would not only provide insight into organization processes that take place in living matter but might lay the foundation for the engineering of self-organized machines composed of energy-consuming animate components that are capable of mimicking the properties of the living matter.

METHODS

We studied isotropic active fluids composed of filamentous microtubules, clusters of kinesin molecular motors, and depleting polymers. The polymer bundles microtubules, whereas the adenosine triphosphate (ATP)–fueled motion of kinesin clusters powers their extension. The extensile bundles consist of oppositely aligned polar microtubules and thus have quadrupolar (nematic) symmetry. They generate local active stresses that collectively drive mesoscale turbulent-like dynamics of bulk active fluids. Upon ATP depletion, the motion of microscopic motors grinds to a halt; the turbulent-like dynamics of active fluids ceases, and one recovers the behavior of conventional gels. We confined such active isotropic fluids into three-dimensional (3D) toroids, disks, and other complex geometries whose dimensions’ range from micrometers to meters and studied their self-organized dynamics. Using particle tracking and image analysis, we simultaneously quantified the flow of the background fluid and the structure of the active microtubule network that drives such fluid flows.

RESULTS

We demonstrate that 3D confinements and boundaries robustly transform turbulent-like dynamics of bulk active fluids into self-organized coherent macroscopic flows that persist on length scales ranging from micrometers to meters and time scales of hours. The transition from turbulent to a coherently circulating state is not determined by an inherent length scale of the active fluid but is rather controlled by a universal criterion that is related to the aspect ratio of the confining channel. Coherent flows robustly form in channels with square-like profiles and disappear as the confining channels become too thin and wide or too tall and narrow. Consequently, this transition to coherent flows is an intrinsically 3D phenomenon that is impossible in systems with reduced dimensionality. For toroids whose channel width is much smaller than the outer radius, the coherent flows assume a Poiseuille-like velocity profile. As the channel width becomes comparable with that of the toroid outer diameter, the time-averaged flow velocity profile becomes increasingly asymmetric. For disk-like confinements, the inner two thirds of the fluid assumes rotation dynamics that is similar to that of a solid body. Analysis of the microtubule network structure reveals that the transition to coherent flows is accompanied by the increase in the thickness of the nematic layer that wets the confining surfaces. The spatial variation of the nematic layer can be correlated to the velocity profiles of the self-organized flows. In mirror-symmetric geometries, the coherent flows can have either handedness. Ratchet-like chiral geometries establish geometrical control over the flow direction.

DISCUSSION

Thousands of nanometer-sized molecular motors collectively generate a gradient in active stress, which powers fluid flow over meter scales. Our findings illustrate the essential role of boundaries in organizing the dynamics of active matter. In contrast to equilibrium systems in which boundaries are a local perturbation, in microtubule-based active fluid the influence of boundaries propagates across the entire system, regardless of its size. Our experiments also demonstrate that active isotropic fluids with apolar symmetry can generate large-scale motion and flows. From a technology perspective, self-pumping active fluids set the stage for the engineering of soft self-organized machines that directly transform chemical energy into mechanical work. From a biology perspective, our results provide insight into collective many-body cellular phenomena such as cytoplasmic streaming, in which molecular motors generate local active stresses that power coherent flows of the entire cytoplasm, enhancing the nutrient transport that is essential for the development and survival of many organisms.

Increasing the height of the annulus induces a transition from locally turbulent to globally coherent flows of a confined active isotropic fluid.

The left and right half-plane of each annulus illustrate the instantaneous and time-averaged flow and vorticity map of the self-organized flows. The transition to coherent flows is an intrinsically 3D phenomenon that is controlled by the aspect ratio of the channel cross section and vanishes for channels that are either too shallow or too thin.

Abstract

Transport of fluid through a pipe is essential for the operation of macroscale machines and microfluidic devices. Conventional fluids only flow in response to external pressure. We demonstrate that an active isotropic fluid, composed of microtubules and molecular motors, autonomously flows through meter-long three-dimensional channels. We establish control over the magnitude, velocity profile, and direction of the self-organized flows and correlate these to the structure of the extensile microtubule bundles. The inherently three-dimensional transition from bulk-turbulent to confined-coherent flows occurs concomitantly with a transition in the bundle orientational order near the surface and is controlled by a scale-invariant criterion related to the channel profile. The nonequilibrium transition of confined isotropic active fluids can be used to engineer self-organized soft machines.

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