Deterministic Microfluidic Ratchet

Kevin Loutherback, Jason Puchalla, Robert H. Austin, and James C. Sturm

Phys. Rev. Lett. 102, 045301 – Published 26 January 2009

Abstract

We present a deterministic, nonthermal ratchet where the trajectory of particles in a certain size range is not reversible when the sign of the pressure gradient is reversed at a low Reynolds number. This effect is produced by employing triangular rather than the conventional circular posts in an array that selectively displaces particles transported through the array. The ratchet irreversibly moves particles of a certain size range in a direction orthogonal to an oscillating flow, with no net displacement of the fluid itself. The underlying mechanism of this ratchet is shown to be connected to irreversible particle-post interactions and the asymmetric fluid velocity distribution through the gap between the triangular posts. Diffusion plays no role in this ratchet, and hence the device parameters presented here can be scaled up to high rates of flow, of clear importance in separation technologies.

Received 18 August 2008

DOI:https://doi.org/10.1103/PhysRevLett.102.045301

Authors & Affiliations

Kevin Loutherback^1,2, Jason Puchalla³, Robert H. Austin^1,3, and James C. Sturm^1,2

¹Princeton Institute for Science and Technology of Materials (PRISM), Princeton, New Jersey, USA
²Department of Electrical Engineering, Princeton University, Princeton, New Jersey, USA
³Department of Physics, Princeton University, Princeton, New Jersey, USA

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 102, Iss. 4 — 30 January 2009

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Irreversible particle motion results when a particle runs into an obstacle. (a) A particle moving left to right is displaced to a new streamline when it runs into a post. (b) When the flow is reversed, the particle does not cross a streamline but instead follows its new streamline and returns to a different initial position.Reuse & Permissions
Figure 2
Micrograph of the ratcheting triangular post array used in the experiments presented here. The right isosceles triangles are $6 μ m$ on a side with post-to-post separation of $10 μ m$ and tilt angle of 5.71° (0.1 rad) with respect to the fluid flow. Confining walls on the top and bottom of the device (not shown) force the fluid to flow on average horizontally. The solid line represents the fluid flow direction and the dotted line represents the post array rotation.Reuse & Permissions
Figure 3
Time-lapse image of the trajectories of spherical polystyrene beads in a triangular post array oriented as in Fig. 2 as the direction of fluid flow is cycled back and forth twice. Particle diameters are (a) $1.1 μ m$ , (b) $3.1 μ m$ , and (c) $1.9 μ m$ . Particles in (a) and (b) retrace their paths when the direction of the fluid is reversed, while the trajectory in (c) changes with the direction of the fluid flow. In (c), small arrows indicate the direction of the fluid along the particle path.Reuse & Permissions
Figure 4
Schematic of flow in post arrays with $ϵ$ of $1 / 3$ , showing boundaries between three stream tubes of equal flow between each gap for (a) round posts and (b) triangular posts. Insets indicate the widths of the stream tubes in the gap adjacent to the posts in each cases. Shown in (a) is the path of a “small” and a “large” particle moving left to right and then right to left, both sizes return to the same position with one cycle. Shown in (b) is the path of a ratcheting particle in a triangular post array, where it acts as a large particle traveling right to left but as a small particle when traveling left to right, resulting in a net vertical displacement after 1.5 cycles of pressure.Reuse & Permissions
Figure 5
Normalized velocity profile across gaps with (a) round and (b) triangular posts. Insets shows orientation of cross-sectional line. Shaded areas bound by dotted lines indicate fluid in stream tubes closest to a post on either side of the gap for $ϵ = 1 / 3$ .Reuse & Permissions
Figure 6
Predicted critical diameter as a ratio of gap for flat edge and triangle vertex versus array tilt angle. Central shaded region indicates range of particles that will exhibit ratcheting behavior under oscillatory flow. Experimental results for $ϵ = 1 / 10$ indicated by “ $+$ ” for $3.1 μ m$ ( $0.66 G$ ), $1.9 μ m$ ( $0.41 G$ ), and $1.1 μ m$ ( $0.24 G$ ) beads.Reuse & Permissions

Physical Review Letters