I have been reading about the differences between momentum and mass diffusivity. I understand that mass diffusion occurs because of the "random walk" of individual molecules which over time will smooth out gradients in species. That makes sense to me. The random motion of the molecules cause it and there is no preference in direction so over time it should equililbriate.
I am having more trouble understanding momentum diffusivity or viscosity. I have read here (last paragraph on page 11 of 15) and here (last paragraph on page 7 of 22) that it can occur WITHOUT the motion of individual particles and that is the part I am having trouble understanding. It seems to contradict explanations like the one here (page 3 of 8) which states that momentum transfer occurs because molecules with more or less momentum move back and forth between regions of high and low momentum.
Intuitively I can follow the explanation using a boundary layer in fully developed pipe flow for example. We know in that case that $v=0$ (y direction) and that the shear stress (which is a vector quantity) is equal to $\vec{\tau} = \mu \, du / dy$ and is in the direction perpendicular to flow. But how is that momentum moving perpendicular to the direction of flow ($u$ direction)? That is what I am struggling to understand.
