Micropillar sequence designs for fundamental inertial flow transformations

Abstract

The ability to control the shape of a flow in a passive microfluidic device enables potential applications in chemical reaction control, particle separation, and complex material fabrication. Recent work has demonstrated the concept of sculpting fluid streams in a microchannel using a set of pillars or other structures that individually deform a flow in a predictable pre-computed manner. These individual pillars are then placed in a defined sequence within the channel to yield the composition of the individual flow deformations -and ultimately complex user-defined flow shapes. In this way, an elegant mathematical operation can yield the final flow shape for a sequence without an experiment or additional numerical simulation. Although these approaches allow for programming complex flow shapes without understanding the detailed fluid mechanics, the design of an arbitrary flow shape of interest remains difficult, requiring significant design iteration. The development of intuitive basic operations (i.e. higher-level functions that consist of combinations of obstacles) that act on the flow field to create a basis for more complex transformations would be useful in systematically achieving a desired flow shape. Here, we show eight transformations that could serve as a partial basis for more complex transformations. We initially used inhouse, freely available custom software (uFlow), which allowed us to arrive at these transformations that include making a fluid stream concave and convex, tilting, stretching, splitting, adding a vertex, shifting, and encapsulating another flow stream. The pillar sequences corresponding to these transformations were subsequently fabricated and optically analyzed using confocal imaging -yielding close agreement with uFlowpredicted shapes. We performed topological analysis on each transformation, characterizing potential sequences leading to these outputs and trends associated with changing diameter and placement of the pillars. We classify operations into four sets of sequence-building concatenations: stacking, recursion, mirroring, and shaping. The developed basis should help in the design of microfluidic systems that have a phenomenal variety of applications, such as optofluidic lensing, enhanced heat transfer, or new polymer fiber design.

Optimization of micropillar sequences for fluid flow sculpting

“…in-house finite element Computational Fluid Dynamics (CFD) framework. 11,12,18 We then translate the displacement information from the maps into transition matrices, which are an effective method for fast and accurate pillar program simulation.…”

“…[4][5][6][7][8][9][10] More recently, fluid sculpting via inertial flow has been demonstrated through so-called "pillar programming." 11,12 See Fig. 1 for a general schematic of pillar programming.…”

“…17 Such manual exploration of flow deformations will quickly run up against the combinatorial phase space of possible pillar combinations. 12 For example, consider creating pillar sequences where each pillar is chosen from a set of 32 possible pillars of varying sizes and transverse locations 18 FIG. 2.…”

“…Set of previously used micropillar configurations. 11,12,18 Each pillar spans the height of the microchannel. Note the periodic boundary condition, for which a pillar being placed so close to the microchannel wall, will have the merged volume protrude from the opposite wall.…”

“…A user-friendly graphics processing unit (GPU)-based software platform "uFlow" was developed in tandem with this work and made freely available, enabling any researcher with modest computing power to manually test various micropillar sequence designs for their own purposes. uFlow is built on top of computationally expensive solutions to the Navier-Stokes equations, 12 but as a standalone product, it uses lightweight, pre-computed advection maps, relieving the end-user of time consuming calculations. Using this framework, manual pillar programming has been successfully employed for shaping polymer precursors for streams 13 and particles, 14,15 reducing inertial flow focusing positions, 16 and solution transfer around particles.…”