Fluid Dynamics and Braess’s Paradox
Braess’s Paradox is the phenomena whereby adding more throughput capacity to a network can actually result in a worse (i.e., less socially advantageous) Nash equilibrium solution. In class, we considered the application of Braess’s Paradox to traffic networks and noted how the addition of roads could actually increase travel time. However, the application of Braess’s Paradox is not limited to just traffic networks.
Microfluidics is a novel technology being employed to separate liquids on a microscopic scale. It works by pumping minute quantities of liquid through a series of interweaving corridors formed from silica. The corridors and their correspondent array of pumps and mixing chambers collectively comprise a microfluidics chip. In order to function, the microfluidics chip relies on an integrated circuit that manages the chip’s pumps and controls access to various corridors. This circuit, while critical to the chip’s function, results in added bulk and complexity. Therefore, researchers wanted to construct a new type of chip that would retain the functionality of the original but without the appended circuitry.
A team of scientists at Northwestern University were able to achieve this goal thanks in part to Braess’s Paradox. Microfluidics chips as initially conceived exhibited linear flow. When pressure was increased, there would be a corresponding increase in liquid flow. The new design, however, leverages a nonlinear flow. To achieve this, the scientists constructed corridors in an H-shape with two long vertical pathways adjoined by a short horizontal pathway. The bottom of one of the horizontal pathways was fitted with obstacles to introduce resistance. The scientists found that by manipulating the pressure between the top and bottom of the system, they could control the direction of flow. However, they found that to achieve optimal flow, they sometimes had to restrict access to the horizontal channel. In other words, flow was greatest when there were fewer routes available. As stipulated by Braess’s Paradox, getting rid of certain routes (in this case the intermediary) can increase the efficiency of the system.
The research has implications for other microfluidic networks. It suggests other networks’ efficiency may be hindered by Braess’s Paradox, and that researchers using these technologies should better scrutinize them for Braess’s Paradox.