Surprising Parameter Controls Solute Travel

Among the many factors that could control solute profiles in microfluidic systems, the pipe/channel aspect ratio alone governs the shape of the solute spread as it flows with the fluid down the tube, say Richard McLaughlin and Roberto Camassa, mathematics professors at the University of North Carolina at Chapel Hill (UNC) who worked on the project. Adjusting this ratio makes it possible to deliver solute with prescribed distributions, ranging from gradual buildup to sudden delivery, based only on the channel’s shape, they explain. Ratio selection thus offers a simple method to precisely control how fluids such as chemicals, medicine and pollutants travel downstream to their target. The ability to fine-tune this control in microfluidic devices is critical for optimizing the material’s effect, potency and lifespan, add the researchers.

In a recent Science article, the researchers report that thin channels (aspect ratio << 1) deliver solutes arriving with sharp fronts and tapering tails, whereas thick (aspect ratio ~ 1) channels produce the opposite effect. This occurs for rectangular and elliptical pipes regardless of initial distributions.

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“That was the big surprise,” says Camassa. “We stumbled upon this incredible disconnect between two different geometries. It’s one of nature’s universal principles governing the shape of solute spreading and it can be used to optimize results in many industries that deal with chemicals dissolved in fluid flows.”

“The control that we are envisioning is purely set by adjusting the aspect ratio: if you want symmetric delivery, then it’s best with something near the golden ratios. On the other hand, if you want a front-loaded delivery, a skinny cross-section will do the job, as opposed to if you want a gradual buildup followed by a rapid decrease in which case you would use a fat (more symmetric) cross-section. Whether this can be implemented on the fly or needs to designed as a switch is something that we will hope to explore in the future,” notes McLaughlin.

Flow Pattern

Figure 1. Solute is flowing from left to right in a square and skinny duct. The square case arrives with a gentler buildup (with more mass to the left), while the skinny case arrives with a more abrupt, sharper front. Source: Manuchehr Aminian, Francesca Bernardi, Roberto Camassa, Dan Harris and Richard McLaughlin, UNC

Results show that precision elliptical pipes, which may be difficult and expensive to manufacture, deliver fluid with calculated precision, but so too, given the right aspect ratio, do cheaper and easier-to-make rectangular ones. Rectangular ducts also stretch solute much less than ellipses, which can be critical when delivering more highly concentrated substances.

This new work can be used to optimize microfluidic devices for any particular goal. Tuning concentration gradients to improve output response could potentially help fine-tune reactions as well.

“We have been thinking about concentration-gradient-controlled chemical reactions, and in particular, how merging different solute streams from different shaped ducts could assist the careful tuning of concentrations at the merging location where a reaction could take place. This could be a potentially interesting application for manufacturing chemical compounds,” explains McLaughlin.

The team already is assessing more-complex geometries with many preliminary results theoretically and computationally obtained for various complex geometries. “We are starting to implement an experimental study of those domains,” says McLaughlin.

The researchers say they would like to hear from anyone that has suggestions for applications or how to apply their findings in a practical device.