When solving differential equations on macroscopic lenght scales, we usually impose the trivial no-slip boundary condition, which assumes zero fluid velocity relative to any boundaries. However, since fluids consist of moving particles which generally scatter from boundaries in an asymmetric manner, the aforementioned boundary condition only holds true as a spatial average and does not fully describe the effects of boundary properties on fluid flows.
Theoretical methods were used to determine expressions for macroscopic quantities at solid boundaries. We assumed the fluid to behave as an ideal gas, with gas particles behaving classically. The boundary was modeled as the surface of a semi-infinite monocrystalline solid, with the potential energy field determining its shape varying in position as a periodic function or periodic function series. Using theoretical scattering models and the formalism of the kinetic theory of fluids, we derived expressions describing statistical averages of velocity and stress tensor elements at the boundary. We demonstrated that these quantities are also periodic functions of position, which together represent a non-trivial boundary condition. Such boundary conditions were accounted for in the analysis of fluid stability, which allowed us to determine their influence on instability onset. Results were compared to findings available in literature.
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