Planar flows in nanoscale regions

Last years, fluid flows in nano-sized domains are intensively studied due to nontriviality of observed effects and practical importance of this part of hydrodynamics. At present, there are no general equations of nano-hydrodynamics. Usually, the molecular dynamics is used for computations. As for analytical approaches, the simplest one involves introducing the slip condition at the boundary together with classical hydrodynamics equations. The small scale of nanochannels gives us the possibility to use, in some cases, the Stokes approximation for motion equations. In this work we apply the planar Stokes model with slip boundary conditions for describing nano-flows. We have developed a method of flow calculation, which is based on the expansion of pressure in a complete system of harmonic functions. Using the pressure distribution, we calculate the velocity field and stress on the boundary. This method can be used for description of various problems of nanofluidics: hydrodynamics of nanochannels, flows along superhydrophobic surfaces, etc.