What is the normal viscous force(stress)?
 

Hello,

I understand the tangential shear stresses (or forces) acting on a fluid element due to friction between moving fluid layers, but I can't imagine how viscosity might cause a normal force (on a fluid element), Doesn't it always have a tangential effect? .... explain please!

are you talking about the relevance of the bulk viscosity? In general, a second viscosity coefficent increments the normal stress due to pressure, but often this contribution is disregarded within the Stokes hypothesis

I think gradients are harder to picture in the normal direction because we can really only experience a sliding type of friction when we a moving tangential to a surface, we can't really have a normal gradient in velocity because we are solids. It might help to imagine the friction in a tangential shear stress and rotate it into a normal stress. You still have particles sliding past each other just in a different and harder to understand way. You can also relate it to the diffusion of momentum in analogy with heat and mass transfer starting from ideal gas theory but that's a bit complicated to.