Momentum diffusion most commonly refers to the diffusion, or spread of momentum between particles (atoms or molecules) of matter, often in the fluid state.
This transport of momentum can occur in any direction of the fluid flow.
Momentum diffusion can be attributed to either external pressure or shear stress or both.
This is because applying pressure on the fluid has caused momentum diffusion in that direction.
[1] A fluid flowing along a flat plate will stick to it at the point of contact and this is known as the no-slip condition.
This is an outcome of the adhesive forces between the flat plate and the fluid.
The attraction between the layers of the fluid is the result of cohesive forces, and viscosity is the property that explains the nature and strength of cohesive forces within a fluid.
The flat plate exerts an equal amount of force on the fluid.
(Newton's third law) Experiments on the fluid flow parallel to a flat plate reveal that the force, known as shear stress can be expressed mathematically as
Note this is valid only for one dimensional fluid flow in rectangular coordinates.
This is the precise reason why shear stress in a fluid can also be interpreted as the flux of momentum.