Scattering dynamics and viscosity

[Archer]

I have been studying the statistical mechanics' viewpoint of fluid dynamics by considering the derivation of Navier-Stokes' equations from the Boltzmann equation involving the whole Chapman-Enskog expansion. It is clear that through this process, it is possible to account for the dependence of material constants on particle dynamics and collision parameters.

If we define a wall as a solid boundary or a potential field with infinite potential in an area extending over some boundary, then we can claim that interactions between particles and wall should in general be described by different characteristic parameters, say the angle between pre and post-collisional velocities, compared to interparticle interactions. Following this reasoning, it means material constants should differ near wall/boundaries, i.e. domains where molecular dynamics are distinctly different?

 

[Valerie Park]

Can the above mentioned Chapman-Enskog approach provide an insight into this?Yes, the Chapman-Enskog expansion can provide insight into how material constants depend on particle dynamics near boundaries or walls. This is because the expansion allows us to identify the different terms of the flow equation that are responsible for the behavior of the material constants. For example, the first-order velocity terms are related to the viscosity and the higher-order terms are related to the thermal conductivity. By identifying these terms and the parameters associated with them, we can determine how the material constants depend on particle dynamics near walls or boundaries. Additionally, we can use the Chapman-Enskog expansion to obtain the Navier-Stokes equations in the presence of walls or boundaries, which provide an understanding of the effects of different wall/boundary conditions on the flow field.