Newton's Laws of fluid motion

Question

Can someone explain the similarity between friction and viscous force?

This is what I have understood:

Friction and viscous force come into play in presence of relative motion. They are dissipative and both are dependent on a constant ,unique for a medium.

1. The very famous saying "A body is accelerated if there is an external force acting on it". Is it violated for liquids ? Every layer is acted upon by an external force (viscous friction) but the acceleration of a particular layer is nil.

2. Now why does friction brings a body to rest but viscous drag doesn't stop a liquid completely ?

3. Friction doesn't maintain the velocity of a body but viscous force does not change the velocity of a particular layer.

4. Why does viscous force depend on area and velocity but friction is independent of it?

Assistance using simple terms will be appreciated.

Answer 1

1. What you call "external" is a matter of taste. Fluid layers interact with each other through viscosity, so whether one layer is "external" to another is not really relevant physically, so this term is primarily a means of communication. As to acceleration: infinitesimally close fluid layers are only accelerated infinitesimally relative to each other. So in the limit of zero distance relative acceleration is, of course, zero, but for finite distance of the layers, relative acceleration is actually non-zero. What really matters, however, is the derivative of force and relative acceleration with respect to distance, and this is also non-zero. This derivative of force is called shear stress, which is the nature of viscosity.

2. Friction (in the naive sense) is a constant force, and hence brings a body to rest with a constant acceleration until the friction breaks down at rest (a half parabola in the $x(t)$ diagram). By contrast, viscous forces are not constant but proportional to velocity, so the smaller the velocity has already become, the smaller the "braking" forces get, and so the motion never stops (a decaying exponential in the $x(t)$ diagram). Actually both, friction and viscosity (applied to macroscopic bodies instead of fluids) can both be put under the umbrella of nonlinear velocity dependent forces. For viscosity the "nonlinearity" is just "linear". For friction, the dependency is constant up to a small threshold velocity where sliding friction breaks down and (usually higher) sticking friction begins to take over. In the sticking regime, elasticity starts to become more important, so there is a more or less smooth transition in the $F(v)$ diagram between stick and slip. This causes challenging stick-slip phenomena (also in the numerical treatment) in technical systems, that cause vibrations (think e.g. of a wine glass, the rim of which you rub with your wet finger, causing a tone). For these more accurate models of friction, see for example this page

3. see 1), relative acceleration is only zero in the limit of zero distance of the layers. For finite distance there IS relative acceleration.

4. That is not easy to answer, AFAIK. It relates to the microscopic properties of friction and viscosity. For friction you can think of zooming in to the microscopic surface structure and visualize it as two horizontal tooth racks locked into each other. If you move the two racks laterally against each other, you will also lift them vertically (remove the teeth from each other). Since the teeth have a certain slope, and there is a certain vertical force acting on them (e.g. gravity), you have to apply a lateral force that depends on the vertical force, just like for an inclined plane. This force only depends on the slope of the teeth, not on their number (corresponding to area). For viscosity in the microscopic picture, the force depends on the number of molecules that go astray from their own layer and collide with an adjacent layer. You can imagine that the probability of such collisions grows with the number of molecules in the layer and hence, the contact area between layers. These are just quick visualizations, I am no expert in the microscopic foundation of neither friction nor viscosity.