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Copyright Brian J. Kirby. With questions, contact Prof. Kirby here. This material may not be distributed without the author's consent. When linking to these pages, please use the URL http://www.kirbyresearch.com/textbook.

This web posting is a draft, abridged version of the Cambridge University Press text. Follow the links to buy at Cambridge or Amazon or Powell's or Barnes and Noble. Contact Prof. Kirby here. Click here for the most recent version of the errata for the print version.

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Jump To: [Kinematics] [Couette/Poiseuille Flow] [Fluid Circuits] [Mixing] [Electrodynamics] [Electroosmosis] [Potential Flow] [Stokes Flow] [Debye Layer] [Zeta Potential] [Species Transport] [Separations] [Particle Electrophoresis] [DNA] [Nanofluidics] [Induced-Charge Effects] [DEP] [Solution Chemistry]

4.5 Laminar flow patterning in microdevices [flow patterning/microfluidic mixing top]

VIDEO: Concept map of laminar flow patterning and relation to Re and Pe.

In thehigh-Pe, low-Re limit, laminar flow patterning can be used to control the spatial position of chemical species because multiple solutions can be brought into contact without their chemical components mixing. Simple arguments regarding the flow rate of each solution dictate the area occupied by each component when traveling through a microfluidic channel.

Consider a microchannel system as a resistor network with nodes, as described in Chapter 3. Consider two channels that generate miscible input flows into a node, the first with flowrate Q1 of a solution of species A and the second with flowrate Q2 of a solution of species B. If the mixing between these two species is slow and the channel is shallower than it is wide, then there will be a clear interface between the two streams, and the location of the interface between these two solutions can be predicted with simple flowrate arguments.

Far from the channel junction or node, the depth-averaged velocity is uniform across the width of the channel (but of course varies strongly along the depth axis). In this case, we can use conservation of species to infer what the cross-sectional areas of each flow is. From this argument, we can show that the fraction of the channel filled with species A is given by Q1(Q1 +Q2). Similar relations can be derived for the other species, or for each species in a multicomponent system. An example configuration is shown in Figure 4.8.


microfluidics textbook nanofluidics textbook Brian Kirby CornellFigure 4.8: Domain geometries as predicted by inlet flow rates.


Practically speaking, this result means that, if the device and fluids are designed properly, meaning that the channels are wider than they are deep, the Reynolds number is low, and the mass transfer Peclet numberis high, then the distribution of the species in a channel can be controlled simply by controlling the input flow rates of each, either through control of channel depths, channel widths, or input pressures.

VIDEO: Two examples of laminar flow patterning in microdevices.

The microfluidics community often uses the terms “laminar flow” or “the technique of laminar flow” to imply laminar flow patterning—the control of species distributions in a channel in the limit in which flow rates directly control interfacial positioning. This is common shorthand that has permeated the community, though it obscures an important distinction—laminar flow implies a specific flow regime at low Re characterized by stable sheetlike flow structures, while laminar flow patterning implies a technique for controlling the location of fluids in long, narrow channels at low Re and high Pe.


microfluidics textbook nanofluidics textbook Brian Kirby Cornell



microfluidics textbook nanofluidics textbook Brian Kirby Cornell


[Return to Table of Contents]



Jump To: [Kinematics] [Couette/Poiseuille Flow] [Fluid Circuits] [Mixing] [Electrodynamics] [Electroosmosis] [Potential Flow] [Stokes Flow] [Debye Layer] [Zeta Potential] [Species Transport] [Separations] [Particle Electrophoresis] [DNA] [Nanofluidics] [Induced-Charge Effects] [DEP] [Solution Chemistry]

Copyright Brian J. Kirby. Please contact Prof. Kirby here with questions or corrections. This material may not be distributed without the author's consent. When linking to these pages, please use the URL http://www.kirbyresearch.com/textbook.

This web posting is a draft, abridged version of the Cambridge University Press text. Follow the links to buy at Cambridge or Amazon or Powell's or Barnes and Noble. Contact Prof. Kirby here. Click here for the most recent version of the errata for the print version.


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