Interdisciplinary Applied Mathematics

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In summary,    by    investigating    the    behavior    of water    and    ions    (or    elec


trolytes) and their interactions in carbon nanotubes and functionalized carbon nanotubes and other nanopores, it is possible to create nanofluidic devices that open new opportunities for sensing, detection, and probing matter at nanoscales.


Part III:


Simulation Techniques

14

Numerical Methods for Continuum Simulation


Full-system simulation of microsystems typically involves simulations of coupled electrical, mechanical, thermal, and fluid domains. Even within the fluid domain only, in applications such as multiphase microflows, different subdomains are required to handle the stationary and moving components. It is clear that in order to reduce computational complexity, the numerical discretizations employed should be both highly efficient as well as robust. The significant geometric complexity of flows in microsystems suggests that finite elements and boundary elements are more suitable than finite differences for efficient discretization. Because of the nonlinear effects, either through convection or boundary conditions, boundary element methods are also limited in their application range despite their efficiency for linear flows. However, they have been used routinely for efficient computation of the electrostatics. A particularly promising approach for microflows makes use of meshless techniques, where particles are “sprinkled” almost randomly into the flow and boundary. This approach handles the geometric complexity of microflows effectively, but the issues of accuracy and efficiency have not yet been fully resolved. As regards nonlinearities, one may argue that at such low Reynolds numbers the convection effects should be neglected, but in complex geometries with abrupt turns the convective acceleration terms may be substantial, and thus they need to be taken into account. The same is true for particulate microflows, where nonlinear effects are important, and thus Stokesian dynamics — a very effective simulation approach — may be limited for simulation of biofluidic applications, since it can simulate only zero Reynolds number flows. Also, flows in micronozzles and other aerospace applications may result in large Reynolds numbers, exceeding one thousand!

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