Hydrodynamic metamaterials: Microfabricated arrays to steer, refract and focus streams of biomaterials

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Original entry: Warren Lloyd Ung, APPHY 225, Fall 2009

"Hydrodynamic metamaterials: Microfabricated arrays to steer, refractt, and focus streams of biomaterials"
Keith J. Morton, Kevin Loutherback, David W. Inglis, Ophelia K. Tsui, James C. Sturm, Stephen Y. Chou, and Robert H. Austin.
Proceedings of the National Academy of Science.

Soft Matter Keywords

Hydrodynamic metamaterials, microfluidics, biomaterials, separation

Figure 1: Hydrodynamic metamaterial: an asymmetric array of posts (A) schematic and (B) fluoresecne image of a particle larger than the critical size (red) and smaller than the critical size (green).
Figure 2: Focusing of flowing particles: (A) The analogous case for light is an axicon lens, which focuses light to a line, (B) Schematic of the different regions of distinct metamaterials, (C) Micrograph of the distinct metamaterial regions, (D) fluorescence image showing particle focusing by this geometry of posts.
Figure 3: Steering of cells through a microfluidic channel


Hydrodynamic metamaterials are microfabricated structures that have can be used to manipulate particles to flow along particular paths. In many ways, they are analogous to traditional optical materials, except rather than modifying the propagation of electromagnetic light waves, these metamaterials modify the propagation of particles through a microfluidic channel.

The hydrodynamic metamaterial discussed in here is an asymmetric array of posts. The asymmetry arises, because each subsequent column of posts is vertically offset from the previous column by a small distance. As a result, the rows of posts are at an angle, <math>\alpha</math>, relative to the direction of flow (Figure 1). Small particles and molecules follow the streamlines of fluid through the channel, and as such, they simply follow the direction of bulk fluid flow through the channel, while moving around any posts in their way. On the other hand, particles larger than some critical size cannot do the same, they cannot fully move around the posts, so each time they encounter a new post, they are deflected it. The large particles, thus, follow the asymmetry of the channel, and propagate at the angle <math>\alpha</math> relative to the flow direction. This ability to segregate particles according to their sizes can be compared with the ability of birefringent crystals to separate different polarizations of light in space.

These metamaterials offer exquisite control over the flow direction of particles in solution. By putting metamaterials with different parameters next to one another, it is possible to create devices to control the direction, along which particles of different sizes move. It is also possible to place several different arrays within a single channel to achieve complex devices. The authors showcase a range of possible applications for these simple microstructures, each time demonstrating its analogy in optics.

Soft Matter Discussion

The parameters, which uniquely define an array of posts determine the angle, at which large particles are deflected, and also the critical size of particles, which are deflected. The authors define four parameters, the horizontal spacing <math>\lambda</math>, the vertical gap between posts, G, the vertical offset between rows, <math>\delta</math>, and the obstacle size, D. Qualitatively, for a given G, the critical particle size decreases as the angle is increased <math>\alpha = tan^{-1}\frac{\delta}{\lambda}</math> For a fixed particle size, the critical particle size decreases with G.


Using these asymmetric arrays of posts as building blocks, it is possible to create devices which refract, focus or disperse particles selectively based on size.

Because these posts are already within a microfluidic channel, this is a powerful tool, which can already be integrated directly with many of the other complex microfluidic systems. For instance, one can imagine a system for studying mitotic cells, in which we separate cells based on their size, interrogate them with optical methods such as fluorescence, and then culture them to examine the resulting daughter cells all integrated in a single device.

This can also be used to create parallel monodisperse flows of particles.