# Interdisciplinary Applied Mathematics

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4. Boundary Condition Treatment: Especially the inflow/outflow boundary conditions can become important in a microfluidic simulation. A subsonic microchannel flow simulation may require specification of inlet and exit pressures. Based on the apparent viscosity of the fluid, the flow will develop under this pressure gradient, and result in a certain mass flowrate. During such a simulation, specification of back-pressure for subsonic flows becomes a problem. For this case we have implemented and recommend a DSMC algorithm mimicking the characteristic treatment of subsonic compressible flow algorithms in the following fashion: At the entrance of the channels we specified the number density, temperature, and average velocity of the molecules. At the outflow region we specified the desired number density and temperature (for a given pressure drop) as well as the corresponding average velocity of the molecules that are entering the computational domain from the outflow boundary. By this treatment we were able to significantly reduce the spurious numerical boundary layers at the inflow and outflow regions.

Also, for high Knudsen number flows (i.e., Kn > 1) in a channel with blockage (such as a sphere in a pipe) we have observed that the location of the inflow and outflow becomes important. For example, the molecules    reflected    from    the    front    of    the    body    may    reach    the

inflow region with very few intermolecular collisions. This creates a largely diffused flow at the front of the bluff body (Liu et al., 1998).

5. Uncertainties in the Physical Input Parameters: These include typically the input for molecular collision cross-section models such as the hard sphere (HS), variable hard sphere (VHS), and variable soft sphere (VSF) models; see (Oran et al., 1998; Vijayakumar et al.,    1999),    and    the    references    therein.    The    hard sphere    model    is

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