Have you ever been asked to define how solids are different from liquids? Is it the density or rather the pressure difference acting on them? Maybe whether the two matters are compressible? Not quite...
The most important difference between solids and liquids, from fluid mechanical point of view, is in its' stresses.
When talking about solids; the stresses are depending on the deformation. If one is applying force to an object, it'll have inner stresses generated inside the molecules. If the same force would be applied to a liquid, it will probably not generate anything, and will not affect much the state. In case of liquids, the different source of stresses are achieved by the velocity of deformation.
One can write the constitutive equation, for a Newtonian fluid:
Where: T - stress tensor, I - identity matrix, μ - viscosity term
D - divergence of velocity / deformation velocity tensor, expressed as:
The reason, why liquids flow lies in the above equation. The stress does not depend on deformation but depends on deformation of velocity. In all kinds of fluids (except for superfluids), any change in deformation increases the viscous forces within the matter, due to the friction between the adjacent particles. The stress state tensor is describing these stress changes at any point of the fluid domain.
- Computational Fluid Dynamics lecture - dr Jacek Rokicki