rheology - Scope, Dimensionless numbers in rheology

The study of the deformation and flow of materials subjected to force. It includes the viscosity of liquids and gases, strain and shear due to stresses in solids, and plastic deformation in metals.

Continuum mechanics

General

Classical mechanics Stress Tensor Conservation of mass Conservation of momentum

Solid mechanics

Solids Elasticity Plasticity Hooke's law Rheology

Fluid mechanics

Fluids Fluid statics Fluid dynamics Navier-Stokes equations Viscosity Newtonian fluids Non-Newtonian fluids

Rheology is the study of the deformation and flow of matter under the influence of an applied stress.

Scope

In practice, rheology is principally concerned with extending the "classical" disciplines of elasticity and (Newtonian) fluid mechanics to materials whose mechanical behaviour cannot be described with the classical theories.

Continuum mechanics	Solid mechanics or strength of materials	Elasticity
		Plasticity	Rheology
	Fluid mechanics	Non-Newtonian fluids
		Newtonian fluids

Rheology unites the seemingly unrelated fields of plasticity and non-Newtonian fluids by recognising that both these types of materials are unable to support a shear stress in static equilibrium.

Liquid and solid characters are long-time properties

Let us attempt to deform the material by applying a continuous, weak, constant stress:

if the material, after some deformation , eventually resists further deformation, it is a solid ; By contrast, elastic and viscous characters (or intermediate, viscoelastic behaviours) appear at short times

Again, let us attempt to deform the material by applying a weak stress varying in time:

if the material deformation follows the applied force or stress, then the material is elastic; If a high stress is applied, a material that behaves as a solid under low applied stresses may start to flow.

Dimensionless numbers in rheology

Deborah number

When the rheological behaviour of a material includes a transition from elastic to viscous as the time scale increase (or, more generally, a transition from a more resistant to a less resistant behaviour), one may define the relevant time scale as a relaxation time of the material. Small Deborah numbers correspond to situations where the material has time to relax (and behaves in a viscous manner), while high Deborah numbers correspond to situations where the material behaves rather elastically.

Note that the Deborah number is relevant for materials that flow on long time scales (like a Maxwell fluid) but not for the reverse kind of materials (like the Voigt or Kelvin model) that are viscous on short time scales but solid on the long term.