In units where quick mixing is not desired, such as many analytical tests or separation systems, low Pe (of less than or around 1) is ideal. T-sensors, as shown in figure 2, are an example of a class of analytical devices that benefit from low Pe. T-sensors are used in many competitive immunoassays, where antigen and antibody are input into the T-sensor. Given the known diffusion pattern that are expected, as shown in figure 1, any deviation from this pattern indicate antibody binding. T-sensors can also be used in simpler cases, such as to quantify the diffusivities of the analyte and reaction kinetics since the effects of turbulence are neutered . Separation is also possible without the use of membranes in microfluidics, due to low Pe, as evidenced by the H filter, shown in figure 3. H-filter takes advantage of the fact that larger species have lower diffusion constants smaller ions. Proteins, for example, have diffusion coefficient three orders of magnitude larger than that of salt ions . separation can be achieved in a 'H' shaped channel, where a mixture will enter on the ends of the 'H' and a separation will occur such that the larger specie will exit the bottom of the same side, while the lighter specie will traverse the middle section of the H onto the other side.
In units where mixing is desired, such as reactors, Pe>>1 is necessary. Convection desired to produce large Pe can be provided with many methods
, such as stir bars , or with etched channels that induce vortices, as shown in a herringbone mixer , shown in figure 4
== References ==