Fluids That Flow Themselves

Original paper: Transition from turbulent to coherent flows in confined three-dimensional active fluids  (Non-paywall version here.)

Disclosure: The first author of the paper discussed in this post, Kun-Ta Wu, did his Ph.D. at New York University, in the same research group as the present writer (CPK). At NYU, both Wu and CPK worked on topics unrelated to the research discussed here.

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When we think about fluid flow, we generally think of motion in response to some external force: rivers run downhill because of gravity, while soda moves through a straw because of the pressure difference created by sucking on one end. Recently, however, scientists have become interested in a class of fluids that have the capacity to move all by themselves — the so-called “active fluids.” Active materials — of which active fluids are a subset — are distinct from regular materials because energy is injected into the system at the level of individual molecules. In today’s paper, Kun-Ta Wu and his co-workers explore how such a material can turn its stored chemical energy into useful work: cargo transport.

Why are active materials so interesting? For one thing, many biological systems are active — for example the actin filaments that drive muscle contraction or bacterial swarms. Although active systems are both common and important in our everyday lives, the physical laws that govern their behavior are not well understood [1]. Studying artificial active systems, which are much simpler than living ones, might give us insight into this difficult problem.

As well as helping us to understand basic physics and biology, Wu and his co-workers hope that their research will move us closer to producing artificial materials that transport cargo without adding energy from an external source — a self–powered fluidic conveyer belt [2]. Such a material would be totally different from those that we currently use, and would greatly expand the possibilities available to engineers in fields such as microfluidics and soft robotics.

Wu’s research focuses on a system made up of protein molecules that assemble into cylindrical rods called microtubules. While microtubules are very important in biology [3], Wu uses these tiny rods, suspended in water, to make an artificial active fluid. As well as microtubules, Wu adds two other critical ingredients: kinesin molecular motors, and ATP (adenosine triphosphate), a chemical that many biological systems use as an energy source [4].

fig1
A sliding force is generated between microtubules by the action of molecular motors. (Adapted from Figure 1 of the original paper.)

A single kinesin molecule attaches to two parallel microtubules and creates a lateral force that slides or “walks” them along each other. A single “step” of this walk involves a chemical reaction that converts one ATP molecule into ADP (adenosine diphosphate), a lower-energy state, thereby converting chemical potential energy into motion. A collection of millions or billions of microtubules (and a similar number of kinesin and ATP molecules) forms a material that writhes and squirms without any forces acting upon it. In the following video, Wu records the motion of both the microtubules themselves (they’re tagged with a fluorescent red dye), and micrometer-sized green particles, which he uses to trace the flow.

Video 1 Using fluorescence microscopy, Wu and colleagues can observe the motion of microtubules (red), as well as test cargo — colloidal particles (green) that are carried along in the flow generated by the motion of microtubules. (Movie 1 of the original paper.)

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But converting energy into useful work doesn’t just require motion; it requires motion that is controlled, directed, and uniform over time — coherent motion. This brings us to the main finding of Wu and coworkers: in the microtubules-motors-ATP system, coherent motion can be produced by controlling the shape of the container. Placed in a large rectangular box, the flow in the middle of the box (“in the bulk”) is turbulent but directionless (see panel A of the below figure). However, when placed in a ring with appropriate dimensions, the flow spontaneously organizes into large-scale circular patterns that are capable of transporting cargo — like fluorescent colloidal particles — over lengths of centimeters or even longer (panel B below).

fig2
Panel A shows the pattern of flow of a bulk sample of active fluid. The arrows represent the velocity field, and colors represent the normalized vorticity of the flow: the extent to which it is rotating clockwise or anticlockwise in a local frame of reference. The left half of the panel shows a snapshot of the flow at a single instant in time, while the right half shows the time average. (This convention is also used in the other flow visualizations shown in this post.) In the time-averaged plot, both velocity and vorticity are almost zero: the flow is turbulent but directionless. Panel B-i shows the ring geometry of one of the sample chambers Wu uses to create coherent flow, and B-ii shows the flow pattern in that chamber. Unlike in the bulk sample, a long-lived circular pattern is generated that pushes the cargo around the ring. (Adapted from Figure 1 of the original paper.)

Interestingly, whether or not this happens is controlled only by the aspect ratio of the container: the channel width divided by its height [5]. Coherent flow is observed when the aspect ratio is between ⅓ and 3; in other words, it disappears if the ring is too flat or too tall. Additionally, Wu shows that the direction of the flow– whether it goes clockwise or counterclockwise —  can be controlled by decorating the outside of the container with appropriately shaped notches, which Wu calls ratchets.

Finally, the researchers show that the appearance of directed flow coincides with the onset of nematic order: in circulating samples, the rod-like microtubules tend to align with their neighbors, while in the turbulent samples, they are oriented randomly. According to Wu, this alignment allows the fluid to collectively push itself off the walls of the container, thus generating global circulation.

fig3
Wu and co-workers use ratchets — small asymmetrical notches on the outside of the ring — to control whether the flow is clockwise (CW) or counterclockwise (CCW). The scale bar shows that flow is coherent over lengths of centimeters. (Adapted from Figure 3 of the original paper.)

Of course, this paper only scratches the surface of the technological potential of active materials. Research on this, and similar ideas, continues both at Brandeis University, where this research was done, and in Worcester Polytechnical Institute, where Wu has recently been appointed professor. Here, according to his website, Wu aims to “advance our understanding of self-organization of active matter as well as to create unprecedented bio-inspired materials.”

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[1] Physical systems at thermodynamic equilibrium obey the Boltzmann distribution — a formula that (in principle) allows us to calculate macroscopic properties of many-body systems, if we know the interactions between the constituent particles. We don’t know of a similar theory that describes the behavior of out-of-equilibrium systems, and active systems are by definition out of equilibrium.  

[2] Of course, the energy ultimately has to come from somewhere. In the case of the material studied by Wu et al, the conveyer belt would have to be “charged” with fresh ATP before use.

[3] In particular, microtubules are the most important structural component of the mitotic spindle – the sub-cellular structure that pulls chromosomes copies apart during cell division.

[4] Wu also adds a chemical known as a depletant, which makes the microtubules bundle together, allowing the kinesin to slide them along each other.

[5] Wu also studies cylinders and shows that a similar geometrical parameter controls the appearance of coherent flow.

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