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Péclet number (Pe) - Nishanth Saldanha

291 bytes removed, 06:10, 23 March 2017
[[Image:Tsensor.jpeg|150px|right|thumbnail|'''Figure 2''' Diffusion dominated mixing that occurs in a T-sensor makes it useful in florescence based analytical tests. The analyte (in blue) diffuses with the species in the channel as a function of the length of the middle channel. [5: http://faculty.washington.edu/yagerp/microfluidicstutorial/tsensor/tsensor.htm]]
[[Image:hfilterHfilter.jpegjpg|150px|right|thumbnail|'''Figure 3''' This is a microfluidic device that allows convenient extraction of small molecules from complex fluids into simpler buffer streams [6: http://www.nature.com/nature/journal/v442/n7101/fig_tab/nature05064_F4.html]]
The low inertial forces present within many microfluidic setups, due to low velocity and of the length scales, often yield low Reynolds number flows <sup>of the middle channel. [4]<5: http://sup>: low levels of turbulence can also be expected in these flow regimesfaculty. Thus convection is not prevalent in microfluidic setups, unless they are purposely inducedwashington. Most mixing that do occur in these devices occur due to diffusion [4edu/yagerp/microfluidicstutorial/tsensor/tsensor.htm]. Diffusion induced mixing is much slower than convective mixing, with mixing times in different order of magnitude. [4]
In units where quick mixing is not desired, such as many analytical tests or separation systems, low Pe is ideal[[Image:Herringbonemixer. T-sensors, as shown in figure 2, are an example jpg|150px|right|thumbnail|'''Figure 4''' Diagrams showing performance of a class of analytical devices that benefit staggered herringbone mixer. [7: Image by MIT OpenCourseWare. Adapted from low PeFigure 3 on p. T-sensors are used 649 in many competitive immunoassaysStroock, where antigen and antibody are input into the T-sensorA. D., S. K. W. Dertinger, A. Given the known diffusion pattern that are expectedAjdari, as shown in figure 1I. Mezi , any deviation from this pattern indicate antibody bindingH. A. T-sensors can also be used in simpler casesStone, such as to quantify the diffusivities of the analyte and reaction kinetics since the effects of turbulence are neutered [4]G. M. Whitesides. "Chaotic Mixer for Microchannels. Separation is also possible without the use of membranes in microfluidics" Science, New Series, due to low Pe295, as evidenced by the H filterno. 5555. (Jan. 25, shown in figure 32002): 647-651.]]
The molecules dissolved in the liquid also have an effect on Pe. Larger species (proteins for example) have lower diffusion constants than salt ions (by three orders of magnitude in um^2/s). These differences in diffusivities can be taken advantage of in separation systemslow inertial forces present within many microfluidic setups, as shown by the H-filter by Squires due to low velocity and Quake. Essentiallylength scales, species with lower diffusivities will not travel as far as species with higher diffusivities. Thus, 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 often yield low Reynolds number flows <sup>[4]</sup>: low mass specie will exit the bottom levels of the same side, while the lighter specie will traverse the middle section of the H onto the other side. Such a device turbulence can also help with buffer exchange or to separate non motile sperm from motile sperm, for example T-sensors are another class of devices that take advantage of the low Pe be expected in these flow regimes. In these systemsThus convection is not prevalent in microfluidic setups, two pure solutions enter on the top two ends of a 'T' junction, and then mix on the middle section of the 'T'unless they are purposely induced. Low Pe, means Most mixing that the mixing can be seen as function of the position on the middle section ->As one moves further down, more do occur in these devices occur due to diffusion occurs[4]. This also allows one to clearly view the differential Diffusion induced mixing is much slower than convective mixing that occurs, where the pure species are also visible. This can be helpful with mixing times in many analytical tests.  Both devices work in intermediate Pe range (Pe around 1), but differences in diffusivities among species is criticaldifferent order of magnitude.[4]
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 [4]. 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 [4]. 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.
At In units where mixing is desired, such as reactors, Pe>>1is necessary. Convection desired to produce large Pe can be provided with many methods, mixing can occursuch as stir bars, either due to convectively-stirred mixing or through Taylor dispersion mediated mixing.with etched channels that induce vortices, as shown in a herringbone mixer, shown in figure 4
== References ==

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