# Ideal liquids are viscous in nature

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### Basics of viscosity

The viscosity of the reaction mixture and the rheological behavior (rheology = study of the deformation and flow behavior of matter) must be taken into account when designing the pipeline system and the reactor for polymerisation reactions. The following principles apply to these.

The basic equation of hydrodynamics, the Bernoulli equation, applies to ideal liquids:

This results from the law of the conservation of mass and the law of the conservation of energy. Real liquids, however, are not frictionless, and this must be taken into account in the Bernoulli equation. This internal friction manifests itself as flow resistance. This is taken into account as an additional summand.

The internal friction of fluids is determined by their dynamic viscosity*η* described. The dynamic viscosity *η* of a fluid represents its resistance to a forced, irreversible change of location of its volume elements.

The plate B is displaced with the speed in the y-direction. Taking the case of laminar flow as a basis, a velocity gradient dv / dy is obtained within the fluid. Newton's law applies to ideal fluids:

Viscosity = proportionality factor between shear stress *τ* and shear rate dv / dy

In the case of Newtonian fluids, the dynamic viscosity is *η* thus independent of the shear rate dv / dy.

The dynamic viscosity of fluids depends not only on the flow condition but only on the temperature and pressure. In the case of gases, it increases with temperature (*η* proportional), because the momentum transport between the molecules increases with temperature. On the other hand, it decreases with liquids (*η* proportional to), because the interaction forces between molecules decrease with increasing temperature. The dependence on pressure is less pronounced and can mostly be neglected.

In macromolecular chemistry one usually encounters so-called real or non-Newtonian fluids, i.e. there is no linear relationship between the shear stress*τ* and the speed gradient dv / dy. The viscosity is no longer a material constant, but depends on the shear rate dv / dy. This is described by the Ostwald-de-Waele law

If n = 1, there is a Newton fluid.

The fluids can thus be classified according to their flow behavior (rheology).

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