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I just started working in a lab that is trying to design microfluidics devices to trap and manipulate colonies of E. coli cells. Given a 3D model of such a device created in Autodesk Inventor (or a similar program), and leaving out the cells, what would be the best way to simulate fluid flow through the channels of the device? The flows are completely laminar, so it seems like a computationally tractable-ish problem.

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Given the small dimensions in microfluidics, flow is well described by the Stokes equations. There are a number of commercial packages that I'm sure can simulate this kind of flow.

Most available open source finite element packages can also do this, though likely with less ease. For example, in deal.II (that's a package of which I'm one of the principal developers), there's a tutorial program that shows how to do that: http://www.dealii.org/developer/doxygen/deal.II/step_22.html . I'm sure FEniCS and libMesh have similar capabilities to solve the Stokes equations.

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Autodesk has multiple CFD offerings (Simulation CFD, NASTRAN) that would integrate well with your Inventor based workflow. If you are a student you can have free access to these tools following a simple registration process (http://www.autodesk.com/education/free-software/simulation-cfd).

Aside from the selection of the appropriate fluid model, would you like to model the interaction with the cells as well? For this purpose a Lagrangian (particle based) model for the E.coli might be suitable.

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