Viscosity

Resistance to flow

Viscosity measures a liquid's resistance to flow, arising from internal friction between layers of the fluid as they slide past one another. Strong intermolecular forces hold neighbouring layers together and resist this relative motion.

Laminar flow and the velocity gradient

When a liquid flows over a fixed surface, the very bottom layer — in direct contact with the surface — stays stationary, while each successive layer above it moves a little faster than the one below. This orderly build-up of speed from one layer to the next is called laminar flow (Fig. 5.16): any chosen layer is accelerated by the faster layer above it and retarded by the slower layer below it.

If the velocity changes by $du$ over a perpendicular distance $dz$, the velocity gradient is $\dfrac{du}{dz}$. Sustaining this layered flow requires a force $F$ that is proportional to both the area of contact $A$ between the layers and the velocity gradient:

Here $\eta$ (eta) is the proportionality constant, the coefficient of viscosity — numerically, the force needed when the velocity gradient and the contact area are both unity. So $\eta$ is the direct measure of a liquid's viscosity.

Units

• SI unit: $1\ \text{N s m}^{-2} = 1\ \text{pascal second (Pa s)} = 1\ \text{kg m}^{-1}\text{s}^{-1}$
• CGS unit: the poise, named after Jean Louis Poiseuille:

What controls viscosity …