Péclet number (Pe) - Nishanth Saldanha: Difference between revisions

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[[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: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:hfilter.jpeg|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]]
[[Image:Hfilter.jpg|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 length scales, often yield low Reynolds number flows <sup>[4]</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 [4]. Diffusion induced mixing is much slower than convective mixing, with mixing times in different order of magnitude. [4]
of the length of the middle channel. [5: http://faculty.washington.edu/yagerp/microfluidicstutorial/tsensor/tsensor.htm]]


In units where quick mixing is not desired, such as many analytical tests or separation systems, low Pe 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.
[[Image:Herringbonemixer.jpg|150px|right|thumbnail|'''Figure 4''' Diagrams showing performance of staggered herringbone mixer. [7: Image by MIT OpenCourseWare. Adapted from Figure 3 on p. 649 in Stroock, A. D., S. K. W. Dertinger, A. Ajdari, I. Mezi , H. A. Stone, and G. M. Whitesides. "Chaotic Mixer for Microchannels." Science, New Series, 295, no. 5555. (Jan. 25, 2002): 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 systems, as shown by the H-filter by Squires and Quake. Essentially, 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 low mass 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. Such a device can also help with buffer exchange or to separate non motile sperm from motile sperm, for example
The low inertial forces present within many microfluidic setups, due to low velocity and length scales, often yield low Reynolds number flows <sup>[4]</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 [4]. Diffusion induced mixing is much slower than convective mixing, with mixing times in different order of magnitude. [4]
 
T-sensors are another class of devices that take advantage of the low Pe regimes. In these systems, two pure solutions enter on the top two ends of a 'T' junction, and then mix on the middle section of the 'T'. Low Pe, means that the mixing can be seen as function of the position on the middle section ->As one moves further down, more diffusion occurs. This also allows one to clearly view the differential mixing that occurs, where the pure species are also visible. This can be helpful in many analytical tests.
 
Both devices work in intermediate Pe range (Pe around 1), but differences in diffusivities among species is critical.


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 Pe>>1, mixing can occur, either due to convectively-stirred mixing or through Taylor dispersion mediated mixing.
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 ==
== References ==
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