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
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: 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
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.