# Difference between revisions of "Hydrodynamic metamaterials: Microfabricated arrays to steer, refract and focus streams of biomaterials"

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

## Summary

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, $\alpha$, 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 $\alpha$ 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 of the array uniquely define the angle, at which large particles are deflected, and also the critical size of particles, at which particles transition from passing around the posts in the array to being deflected along the rows. The authors define four parameters, the horizontal spacing $\lambda$, the vertical gap between posts, G, the vertical offset between rows, $\delta$, and the obstacle size, D.

Qualitatively, for a given G, the critical particle size decreases as the angle is increased

$\alpha = tan^{-1}\frac{\delta}{\lambda}$

For a fixed particle size and angle, the critical particle size decreases with G. These behave more or less what as we would expect.

The likely cause of the observed results is that the hydraulic object is much larger than the cross-sectional gap between the posts. Objects with large hydraulic diameters are less likely to fit through the space between the post. We would also expect the critical size to change as a function of flow rate. The inertia of particles in the flow is a parameter that we expect to contribute to which mode the particle finds itself in. This dependence is not addressed in the paper.

## Applications

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. This size can be tuned to select for the distinct particles of interest in a system, whether they be surfactant-stabilized droplets, vesicles, cells or beads. As a result, this technique is applicable to many relevant systems of interest.

Although these ideas are applicable, in general, to nearly any system where micro-scale particles should be manipulated based on size, because this is intrinsically a microfluidic technique, many of the most interesting applications are in the field of microfluidics. Because these posts are already within a microfluidic channel and they are compatible with the standard soft lithography methds, 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 mitotic cells based on their size from interphase cells in a label-free manner. This could be combined with methods for optical interrogation and on-chip cell culture techniques to achieve a highly integrated system for studying cells.

Another potential microfluidics application would be in separating a polydisperse suspension of particles into a set of monodisperse flows. These flows could then be split and routed to other parts of the microfluidic device for highly parallel experiments, in which particle size is a parameter of interest.