Designing a Herringbone Mixer with FLUI'DEVICE: A Microfluidics Tutorial

Microfluidic mixers overcome the diffusion-limited mixing in laminar flows by using engineered surface patterns (such as chevron/herringbone structures) that induce rotational vortices, or acoustic streaming with piezoelectric transducers and air bubbles that create intense mixing within 100 milliseconds; these passive and active techniques enable rapid fluid mixing in microscale devices without requiring external pumps or valves.

Chaotic mixing overcomes slow molecular diffusion by inducing exponential stretching and folding of fluid streamlines. This chaos can arise from fluid inertia (as in serpentine mixers) or from clever channel geometry that induces stretching and folding even in the absence of inertia (as in herringbone mixers). These designs dramatically enhance mixing efficiency compared to purely diffusive processes.

Staggered herringbone mixers use alternating herringbone-shaped grooves on the channel bottom that cause rifling of streamlines. The alternating orientation creates a baker's transform effect, progressively layering initially large chunks of different solutions into progressively smaller layers within the same channel height. Once layers are sufficiently close, diffusion rapidly mixes them. This mixer works efficiently across a wide range of flow rates and Reynolds numbers, including down to Reynolds number 1, making it suitable for low-flow applications.

Chaotic advection uses geometric features (such as herringbone patterns) to create controlled vortex structures that stretch and fold fluid elements, effectively reducing the diffusion length scale. This approach achieves mixing times of approximately 1-2 milliseconds for typical microfluidic geometries, significantly faster than pure diffusive mixing while avoiding full turbulence.

The second major strategy for microsystem mixing involves inducing artificial chaos to simulate turbulent mixing effects. Herringbone groove patterns machined into channel bottoms create alternating circulation cells that reverse direction periodically along the channel length. As fluid flows, angled grooves push boundary layers outward, generating eddies that alternate between channel sides. This time-dependent, reversible flow pattern creates chaotic advection that enhances mixing efficiency. Experimental comparisons show that herringbone designs achieve substantially better mixing over the same channel length compared to static groove patterns, demonstrating how engineered chaos can overcome laminar flow limitations in microfluidic systems.

This comprehensive phase covers the complete digital workflow for microfluidic chip prototyping. It begins with defining chip architecture using two equal-sized sketches—one for channel geometry and another for inlets/outlets and boundaries. Designs are created in CAD software like Fusion 360 or COMSOL and exported as DXF files. The preparation continues in Cricut Design Space where images are uploaded, dimensions are set (typically 0.5 inch width), and layers are attached to ensure overlapping cuts. Critical positioning parameters include coordinates relative to the backing mat (e.g., 8 inches X, 1 inch Y). Material selection specifies vinyl for scoring operations, with the goal of thin scoring rather than complete cutting through the double-sided adhesive tape. This digital foundation enables precise physical fabrication of complex microfluidic structures.

Converting 3D model designs to 2D cutting files through a specific workflow: creating sketches in Fusion 360, exporting as DXF files, importing into vector design software (Affinity Designer or Inkscape), and saving as SVG files for laser cutting. This workflow enables precise cutting of foam panels for custom applications.

FLUI'DEVICE is an online platform that enables users to design microfluidic chips through a systematic workflow: creating projects and sketches, adding and manipulating geometric blocks with snapping and alignment tools, validating designs through computational simulations to calculate hydrodynamic properties like flow rates and Reynolds numbers, and exporting final designs as 2D/3D files for microfabrication.

This comprehensive tutorial covers the complete workflow for designing laboratory equipment using Tinkercad. The instructor demonstrates navigation techniques including right-clicking to move the stage, zooming, and using shift+right-click for additional movement. Two main boolean operations are explained: union (combining objects) and subtraction (removing one object from another). The tutorial covers creating flow cells with outer shells and inner chambers, designing air bubble traps for experimental reliability, and creating microfluidic masters with circular channels. The instructor explains that 3D printing allows rapid design iteration compared to traditional soft lithography methods. STL files are the standard format for 3D printing, and the instructor demonstrates exporting designs as STL files. The tutorial also covers importing existing designs from online sources and understanding Creative Commons licensing for proper attribution.

Microfluidic chips control fluid flow through micrometer-scale channels for rapid sample analysis. 3D printing offers advantages over traditional photolithography: reduced time and cost, high design freedom for complex channel geometries (straight, curved, spiral, wave-shaped), and rapid prototyping. The design workflow involves defining variables (dimensions, channel count, positions), creating base plates, defining point positions using algorithms, generating channel networks via lattice structures, applying wave functions for mixing enhancement, and using Boolean operations for final geometry. Mesh generation converts designs to printable format with appropriate resolution for accurate feature reproduction.

Key dimensionless parameters characterize transport phenomena: (1) Péclet number (Pe) = L/uD, representing the ratio of convective to diffusive transport timescales; (2) Absorption number (α) = kL/D, representing the ratio of absorption timescale to transport timescale. These parameters determine whether convection or diffusion dominates transport and whether absorption significantly depletes the transported substance before reaching downstream regions.

The Peclet number (Pe) is a dimensionless parameter defined as the ratio of advective transport to dispersive/diffusive transport, calculated as Pe = (L × V) / D, where L is characteristic length, V is characteristic velocity, and D is the dispersion coefficient; when Pe >> 1, advection dominates transport processes, while when Pe << 1, diffusion/dispersion dominates, and this number is crucial for predicting contaminant plume behavior, determining numerical stability in transport models, and identifying rate-limiting processes in environmental transport problems.

The Peclet number (Pe) is the ratio of advective flux to diffusive flux, analogous to Reynolds number in fluid mechanics. It is defined as Pe = VA * L / DL, where VA is advective velocity, L is characteristic length, and DL is dispersion coefficient. A high Peclet number indicates advection dominates, while a low Peclet number indicates diffusion dominates. This dimensionless number helps determine which transport mechanisms are important in a given system.

Transport problems require defining four dimensional properties: length, advective velocity, time, and dispersion magnitude. These convert to dimensionless groups for universal analysis. The Peclet number (Pe = vL/D) compares advective to diffusive fluxes. When Pe >> 1, advection dominates (gravel/sand); when Pe << 1, diffusion dominates (clay). The breakthrough curve can be expressed dimensionlessly using Pe, pore volumes, and relative concentration, enabling comparison across different systems and revealing universal transport behavior patterns.

This section develops the mathematical tools for analyzing contaminant transport through dimensional analysis. Using Buckingham Pi theorem, the number of independent dimensionless parameters is determined by subtracting the number of fundamental dimensions from the total variables. For the advection-dispersion equation, this yields two critical dimensionless numbers: the Péclet number (Pe = vL/D) representing the ratio of advective to dispersive flux, and the Courant number (C₀ = vL/t) representing pore volumes filled per unit time. The Péclet number characterizes transport regime: values greater than 10 indicate advection-dominated plug flow with sharp fronts, while values less than 1 indicate diffusion-dominated behavior with broadened concentration profiles. The Courant number determines numerical stability in computational models. Together, these dimensionless parameters fully characterize transport behavior, enabling prediction of breakthrough curves without solving the full partial differential equation for each specific case.