Herringbone micromixers for particle filtration

Abstract

Herringbone micromixers are a powerful tool for introducing advection into microfluidic systems. While these mixers are typically used for mixing fluids faster than the rate of diffusion, there has been recent interest in using the device to enhance interactions between suspended particles and channel walls. We show how the common approximations applied to herringbone micromixer theory can have a significant impact on results. We show that the inclusion of gravity can greatly alter the interaction probability between suspended particles and channel walls. We also investigate the proposed impedance matching condition and the inclusion of imperfect binding using numerical methods, and investigate transient behaviors using an experimental system. These results indicate that while traditional methods, such as simple streamline analysis, remain powerful tools, it should not be considered predictive in the general case.

FIG. 1.

(a) Geometry of the design, showing $\gamma =2.5$. The outer boundary indicates the boundaries for fluid simulation. The streamlines indicate fluid flow from the inlet (left) to the outlet (right). (b) A close up of the inlet geometry and initial particle positions in a strict grid pattern. The color of the particles represents their initial velocity, with the yellow particles in the center of the channel beginning with peak velocity, and the blue particles in the corners beginning with minimum velocity. The transparent outer boundary indicates the boundary for fluid simulations as before, while the red inner boundary represents the boundary for particle simulations as addressed in the text. (c) The experimental device consists of two layers of PDMS, the top layer contains the geometry for the main fluid channel, while the bottom layer contains the geometry of the grooves. A glass slide is affixed to the top, and PTFE tubing is attached underneath to act as inlet and outlet, leading from a syringe pump. (d) and (e) Example photomask designs used in these experiments. Black represents emulsion to block UV-light, and white represents clear acetate which allows through UV-light to expose the relevant region. (d) shows the geometry of the channels. (e) shows the herringbone grooves.

FIG. 2.

Simulating the probability of a particle interacting with the wall of the micromixer as a function of $\gamma$. Streamline simulations of varying particle diameter, $d_p$ are represented by lines. Particle simulations of varying $d_p$ and particle density, ${\rho }_p$ (normalized against the density of the fluid) are represented as discrete points.

FIG. 3.

Simulating the interaction probabilities by surface for particles with diameter of 18  $\mu$m. Each plot represents a different normalized particle density, ${\rho }_p$ (normalized against the density of the fluid). For the neutrally buoyant case, ${\rho }_p=1.000$, the favored interaction surfaces lie at the interface between the grooves and the channel. Denser particles increase the interaction probability at the bottom of the channel and the bottom of the grooves due to the increased sedimentation velocity. Less dense particles see a reduction in interaction probability at the channel bottom in favor of an increased interaction probability with the channel top.

FIG. 4.

Simulating the interaction probabilities with a finite binding probability between particle and wall of 0.5%. Each curve represents a different normalized particle density, ${\rho }_p$ (normalized against the density of the fluid), as a function of $\gamma$.

FIG. 5.

Experimental investigation of particle capture. (a)–(d), respectively represent as a function of $\gamma$ the maximum capture capacity, decay constant (bead ^$-1$), half-life and ab initio capture rate. The inset shows an example of the curve fitting to experimental data, measuring the number of beads sedimenting within the device over time; the example case is given for a measurement at a $\gamma =2$. (d) includes both experiment and simulation results. The simulations used for comparison show 15  $\mu$m diameter beads, a ${\rho }_p$ of 1, being neutrally buoyant with fluid and particle density of 1.05 g cm ^$-3$, and only account for the particles captured by the first half cycle of the herringbone, corresponding to the field of view provided by our experimental system.