# Interdisciplinary Applied Mathematics

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valid for electroosmotic flow in a 0.95-nm-wide channel. However, continuum theory can be used to describe flow in channels wider than 2.22 nm, provided that    viscosity    variation near    the    channel    wall    is    taken    into    ac

count. It is, however, very difficult to obtain a closed-form expression for viscosity variation near the channel wall. To simulate electroosmotic flow in wide channels, where MD simulation can be very expensive, one possible way is to first perform an MD simulation in a smaller channel under similar conditions (e.g., using the same wall structure and charge density as in a wider channel) and then extract the viscosity from the MD data. The extracted viscosity can then be used in continuum theory to model flow in a wider channel. In this approach, one assumes that the viscosity near the channel wall would not change appreciably when the channel width increases. This assumption typically holds, since viscosity depends on the fluid properties and ion concentrations near the channel wall, and these parameters would not change significantly when the channel width changes, provided that other operating conditions (e.g., wall structure and wall charge density) do not change significantly or remain the same. The evaluation of viscosity from molecular dynamics data can be difficult, since one needs to compute the derivative of the velocity obtained from MD data. Since the velocity obtained from the MD simulation is usually very noisy, unless the simulation is carried out for a very long time, the derivative of the velocity would be even noisier, leading to significant noise in the extracted viscosity. It is possible to smooth the velocity data using a filter, but this may introduce additional errors into the viscosity estimation. An alternative approach is to use the embedding multiscale approach, in

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