Serpentines, herringbones, and making laminar streams meet
The geometries used to fold one liquid into another without turbulence.
Serpentine and herringbone channels mix two laminar streams by repeatedly folding and stretching the boundary between them, shortening the distance any single molecule has to diffuse before it finds itself surrounded by the other liquid, which gets the job done without the turbulence a small channel cannot produce.
Folding egg whites into batter
Folding whisked egg whites into a cake batter uses a broad, repeated turning motion, because vigorous stirring would beat the air back out of the whites and ruin the structure the recipe is trying to preserve. The folding still combines the two mixtures completely, turning the batter over on itself again and again until every part has passed close to every other part, and at no point does anything violent happen to it. A serpentine or herringbone channel is precision engineering's version of the same trick. It achieves genuine mixing through many gentle, repeated folds of the flow, because turbulence in these channels is as unavailable as vigorous stirring is unwelcome in the egg whites.
The previous article in this set established that a straight channel forces diffusion to cover the full width between two streams, and that this can take more channel length than a real device has room for. Diffusion's own speed is fixed by the liquid and its temperature, so a folded channel works on the other half of the problem, the distance. Bend a channel sharply back and forth and the two streams inside are repeatedly forced to swap sides, stretching and thinning the layers between them with every bend, so the greatest distance any molecule has left to diffuse keeps shrinking even though the two liquids never tumble together the way a turbulent flow would.
Why each fold is worth four times the last
Because diffusion time grows with the square of distance, halving the thickness of the layers each liquid forms cuts the time diffusion needs to finish by a factor of four. An idealised fold that stacks the two streams into layers half as thick as before therefore makes the remaining diffusion four times quicker, and the gain compounds. Five such folds make the layers thirty-two times thinner and the diffusion time about a thousand times shorter. Real channels fold less cleanly than this idealised picture, but the compounding is why a folded or ridged channel can finish in millimetres what a straight channel would need centimetres to achieve, and block space inside a manifold is one of the scarcest things a designer has to spend.
The flat zigzag
A serpentine channel is the more direct application of folding: a single flat path bent into a tight zigzag, so the fluid inside is forced to turn sharply over and over, and each turn stretches the interface between the two streams a little further. It is straightforward to cut into a flat block and needs no variation in depth, which makes it the cheaper and more forgiving of the two geometries to manufacture. Its limitation is that the folding happens only in the flat plane of the channel. It stretches the boundary sideways and never lifts material from the channel floor to turn it over into the flow above.
A serpentine folded too tightly, with turns too sharp for the channel's width, starts trapping fluid in the corner of each bend instead of cleanly stretching the interface. Those small stagnant pockets mix poorly and can become the seed of the dead-volume and cleaning problems this set turns to later, so the tightness of the bends has a lower limit set by the channel's own width.
Ridges on the floor
A herringbone mixer cuts a pattern of angled ridges into the floor of an otherwise straight channel. Fluid dragging across the ridges is steered sideways and downward, setting up a slow, persistent rotation as it travels forward, an effect that survives perfectly well within laminar flow because it comes from the ridges' shape. The rotation lifts fluid from the bottom of the channel and carries it up and across into the stream above, folding the two liquids over each other vertically as well as horizontally, and it does so continuously along the whole channel instead of only at discrete turns. The pattern of ridges is usually switched partway along, with the point of the chevron moved to the other side, so that the rotation is repeatedly broken up and restarted. Each switch acts like another fold in the egg-white picture, which is why a herringbone floor typically reaches a given degree of mixing in a shorter run than a serpentine that folds only sideways.
The price is manufacturing precision. The ridges need a controlled height, angle and spacing, and they sit at a different depth from the channel floor, so the block can no longer be cut at a single uniform depth. A coarser cutting or moulding process may not deliver that pattern consistently, and a poorly formed ridge pattern folds the flow unevenly, producing a channel that looks identical to a good one on a drawing while mixing measurably worse in use. A test with two differently dyed streams, photographed at the outlet, is the usual way to find out which of the two a batch of blocks has actually produced.
Choosing between them, or using both
Choosing between the two geometries, or combining them, is a real trade a manifold designer makes. A serpentine's simplicity and a herringbone's compactness pull in different directions depending on how much length the block can spare and how much manufacturing complexity the process can absorb. Where the block has room and the moulding process is coarse, a serpentine is usually the safer choice; where length is scarce and the process can hold fine features, the herringbone earns its extra difficulty. Some designs run a short herringbone section immediately after the junction where two streams first meet, where the layers are thickest and folding pays off most, and then let a gentler serpentine finish the job.
Both geometries accept the laminar nature of the flow completely. They spend the channel's available length folding the interface between two streams as many times as the geometry allows, and in doing so they turn a slow diffusion problem into one solved almost entirely by shape. Both also buy their mixing only within a manufacturing tolerance, and a designer who draws a herringbone without checking what the process can actually form has specified a mixer that may exist only on paper.