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→Applications to Microfluidics
[[Image:Herringbonemixer.jpg|150px|right|thumbnail|'''Figure 4''' Diagrams showing performance of staggered herringbone mixer. Image by MIT OpenCourseWare. Adapted from Figure 3 on p. 64 in Stroock et al. <sup></sup>]]
The low inertial forces present within many microfluidic setups, due to low velocity and length scales, often yield low Reynolds number flows <sup></sup>: low levels of turbulence can also be expected in these flow regimes. Thus convection is not prevalent in microfluidic setups, unless
they are purposely induced. Most mixing that do occur in these devices occur due to diffusion <sup></sup>. Diffusion induced mixing is much slower than convective mixing, with mixing times in different order of magnitude. <sup></sup>
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 2''', 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 <sup></sup>. 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 <sup></sup>. 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 using stir bars or using etched channels that induce vortices, as shown in a herringbone mixer in '''Figure 4'''.