THEORY OF VISCOPLASTIC FLOWS
The viscoplastic fluids are non-Newtonian fluids, it means that they
have a non-linear behaviour.
The viscous behaviour of most fluids is described by Stokes' law of
viscosity and such fluids are called Newtonian fluids.
The relation between the constrains and the deformation velocity
for a Newtonian fluid is linear and follows the equation :
where D is the deformation velocity tensor :
A lot of industrial flows are not Newtonian fluids so there is an important
bibliography on non-Newtonian flows.
Non-newtonian fluids don't follow the linear behaviour anymore,
the relation between viscosity and velocity depends of the fluid type :
pseudoplastic, viscoplastic, shear thinning, ... . There is several behaviour
laws to analyse the law of viscosity of non-Newtonian flows.
More precisely, Bingham fluids (see examples)
behaviour is modelised by :
For these type of flows, there is a yield value under which there
is no movement. Above it, they follow a Newtonian behaviour plus the constant
of yield value.