| Abstract: | A high-order finite difference scheme has been developed to approximate
the spatial derivative terms present in the unsteady Poisson-Nernst-Planck (PNP) equations
and incompressible Navier-Stokes (NS) equations. Near the wall the sharp solution
profiles are resolved by using the combined compact difference (CCD) scheme
developed in five-point stencil. This CCD scheme has a sixth-order accuracy for the
second-order derivative terms while a seventh-order accuracy for the first-order derivative
terms. PNP-NS equations have been also transformed to the curvilinear coordinate
system to study the effects of channel shapes on the development of electroosmotic
flow. In this study, the developed scheme has been analyzed rigorously through
the modified equation analysis. In addition, the developed method has been computationally
verified through four problems which are amenable to their own exact solutions.
The electroosmotic flow details in planar and wavy channels have been explored
with the emphasis on the formation of Coulomb force. Significance of different forces
resulting from the pressure gradient, diffusion and Coulomb origins on the convective
electroosmotic flow motion is also investigated in detail. |
