Microfluidic devices such as those used in DNA sequencing typically involve the transport of a complex fluid through a geometry whose dimensions are on the order of the underlying microstructure (DNA molecules, blood cells, proteins, etc.) Consider, for example, the flow cell shown above, which was built in collaboration with D. C. Schwartz. In this case, the microstructure is fluorescently stained 300 micron DNA molecules. The width of the channel ranges from 50 microns down to 25 microns, or 1/12th of the length scale of the microstructure. When analyzing or designing these devices, one is concerned with overall fluid properties (pressure drop required for a given flow rate) as well as microstructural detail (wall adsorption, diffusion, and configuration of the microstructure).
In general, processes which involve the transport of complex materials contain a wide spectrum of time and length scales, and the level of description used to model the process depends on the information one wishes to obtain. Choices range from atomistic descriptions, which are unable to resolve the long length and time scales of realistic problems, to purely continuum descriptions, in which one ``gives up'' molecular detail in favor of a closed-form relation.
We, in collaboration
with Professor
Juan J. de Pablo , take an intermediate approach, in which the microstructure
is represented via Brownian dynamics, while the fluid is treated as a thermal
continuum which acts on the microstructure through the local velocity gradient
tensor and a sequence of random fluctuations. The microstructure
in turn acts on the fluid through its contribution to the stress tensor.
These multiscale, or ``Micro-Macro'', simulations allow one to retain important
molecular level information, and still resolve the time and length scales
of the overall process.
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