The yield stress ([t.sup.0]) and plastic viscosity ([[mu].sub.pl.]) were determined in the course of linear approximation of flow curves (dependence between shear stress ([tau]) and shear rate ([gamma]) in the range from 0.1 to 100 [s.sup.-1] based on the Bingham model
. The Bingham model
is a more widely used model for description of flow behavior of cement systems, which is expressed by following equation:
Cazacliu, "Analysis of a regularized Bingham model
with pressure-dependent yield stress," Journal of Mathematical Fluid Mechanics, vol.
. The Bingham and Herschel-Bulkley models are commonly applied in paste rheology.
We assume that the debris flow impinging on an obstacle is 2-dimensional (2D), based on Bingham Model
and unaffected by the dynamics of run-up on the obstacle.
Under the effect of magnetic field, MRF is a kind of plastic fluid and confirms to Bingham model
. Similarly, magnetic liquid also conforms to Bingham model
The Ishlinsky model also transforms itself into the Bingham model
on the same condition, i.e.
As far as Bingham model
is adequate to characterize rheological properties of fresh mortar and concrete, characterization of rheological properties of cement paste demands more complex models.
If in the Bingham model
we do not take into account the damping force and take into account the constant force P in one direction--in compression phase, the tensile stress does not appear.
To describe concrete flow behavior, both yield stress and plastic viscosity, as defined by the Bingham model
, are key properties that should be determined.
The Herschel-Bulkley model is a generalized form of the Bingham model
, where the linear shear-rate dependence is replaced by a power-law behaviour.
In previous studies, paste-like tailings slurry (PLTS) was simplified as a Bingham plastic fluid, whose flow properties were time-independent, and the existing empirical formulas for calculating the hydraulic gradient of a paste-like flow were derived based on the time-invariant Bingham model
It is also observed while dealing with Bingham Model
; three different zones in the flow domain can be identified