Russian Journal of Applied Chemistry, 2013, Vol. 86, No. 8, pp. 1212−1219.
Pleiades Publishing, Ltd., 2013.
Original Russian Text © V.O. Yablonskii, 2013, published in Zhurnal Prikladnoi Khimii, 2013, Vol. 86, No. 8, pp. 1236−1243.
OF SYSTEMS AND PROCESSES
Hydrodynamics of Nonlinear Viscoplastic Fluid
in Cylindrical Hydrocyclone
V. O. Yablonskii
Volgograd State Technical University, Volgograd, Russia
Received May 16, 2013
Abstract— A ﬂ ow of non-linear viscoplastic ﬂ uid ﬁ lm in a cylindrical hydrocyclone was simulated. The distribution
of the velocity component and also a dependence of a ﬂ uid ﬁ lm thickness on an axial coordinate were determined
by numerical solution of a set of rheodynamic model equations for various rheological properties of the liquid
and dimensionless quantities. An inﬂ uence of plastic properties of the liquid on damping of the circumferential
component of the velocity was examined. The results were physically substantiated.
The hydrocyclone due to its simplicity of design,
high reliability, and compact size is one of the widely
used devices for separating liquid heterogeneous
systems. Hydrocyclones are used in the mining and
mineral processing industry as well as in mud cleaning
systems from drilling cuttings in oil and gas production.
In the chemical industry hydrocyclones can be used to
treat wastewater of suspension and emulsion polyvinyl
chloride production, degassing of the reaction mixture of
polyvinyl chloride, for degassing and pressure ﬂ otation
in production of protein feed Gaprin, biomass, glaze.
Suspensions with non-linear viscoplastic properties,
in particular, aqueous solutions of bentonite are typically
used as drilling ﬂ uids.
Hydrodynamics of swirling ﬂ ows of the pseudoplastic
ﬂ uid was examined in [1, 2]. This ﬂ ow is described
by the Ostwald de Waele rheological law with respect
to the swirling ﬂ ow of oil bitumen in the cylindrical
channel and puriﬁ cation of oil-contaminated soil in
The mathematical investigation of the ﬂ ow in
a hydrocyclone of viscoplastic drilling solutions,
rheological properties of which are described by the
Shvedov–Bingham linear model, was carried out in .
However, an effect of gravitational forces on
a medium separated in a hydrocyclone was not
accounted for in [1–3], so it is unclear to what values of
a separation factor these models can be applied.
Studies [4, 5] are devoted to investigation by
a numerical method of development of rotating the ﬁ lm
ﬂ ow of non-Newtonian ﬂ uid in a cylindrical continuous-
ﬂ ow hydrocyclone. The rheological properties of the
separated medium are described by the Ostwald-de
Results of numerical modeling and experimental
studies of non-Newtonian ﬂ uid ﬂ ow in a hydrocyclone
are presented in [6–8]. The results show a clear difference
in the velocity distribution in the hydrocyclone for ﬂ ow
of pseudoplastic ﬂ uids compared with Newtonian.
In these works it was assumed that values of a ﬂ uid
velocity in inlet and outlet cross-sections of the ﬂ ow is
constant and a radius of an air column is also constant
along a hydrocyclone height. These assumptions can
cause signiﬁ cant non-precision in the simulation results.
Insufﬁ cient compliance of these mathematical
models with real hydrodynamic conditions and the lack
of solutions for hydrocyclone separation of media with
both non-linear and viscoplastic rheological properties,
e.g., drilling solutions, reduce a scope of application of
the simulation results. Therefore, consideration of the