ELECTROCHEMISTRY AND OTHER
PROCESSES OF CHEMICAL TECHNOLOGY
Russian Journal of Applied Chemistry, 2013, Vol. 86, No. 7, pp. 1046−1055.
Pleiades Publishing, Ltd., 2013.
Original Russian Text © A.G. Laptev, T.M. Farakhov, O.G. Dudarovskaya, 2013, published in Zhurnal Prikladnoi Khimii, 2013, Vol. 86, No. 7, pp. 1112−1121.
Models of Turbulent Viscosity and Mixing in Channels
and Packed Flow-Through Mixers
A. G. Laptev
, T. M. Farakhov
, and O. G. Dudarovskaya
Kazan State University of Power Engineering, Kazan, Tatarstan, Russia
Inzhekhim Engineering and Promotion Center, Limited Liability Company, Kazan, Tatarstan, Russia
Received July 4, 2013
Abstract—The use of packed ﬂ ow-through mixers for intense mixing of liquid media and of liquids with a ﬁ nely
dispersed phase is considered. Ways to determine the mixing and turbulent exchange coefﬁ cients for evaluating
the mixing efﬁ ciency in channels and in packed ﬂ ow-through mixers are presented. The results are consistent
with the experimental data on turbulent viscosity in pipes. An expression is obtained for calculating the turbulent
viscosity coefﬁ cient in a packing bed. Comparative characteristics of mixers with Raschig rings and Inzhekhim
packing are presented. The calculated values of the Peclet number for various packings in relation to the Reynolds
number are given.
The use of small flow-through static mixers is a
promising line in the development of compounding pro-
cesses. They are used for simple mixing of a wide range
of mutually soluble liquids, suspensions, and emulsions,
in processes involving heat and mass exchange, and as
chemical reactors. Static mixers are used today in instal-
lations for introducing additives into fuel to improve its
quality, ﬂ occulants into suspensions, and acids into liquids
for their neutralization, and also for diluting concentrates
of additives prior to their feeding to process streams.
Flow-through mixers are installed on pipelines feeding
the components being mixed and taking off the mixtures.
Such mixers are easy in fabrication and operation and
ensure high performance. Static mixers allow maximal
utilization of the pressure head spent for mixing to aver-
age the concentrations of the phases being mixed.
There are numerous designs of static mixers: with
screw parts, with intermediate chambers, with plate and
corrugated parts. Flow-through packed mixers with ir-
regular packing are used for increasing the contact area
of the mixture components by shear ﬂ ow and chaotic
reorientation of liquid streams.
To evaluate the efﬁ ciency of mixing of liquid media
and of liquids with a ﬁ nely dispersed phase, we consid-
ered in this study the approaches to determination of the
mixing and turbulent exchange coefﬁ cients in channels
and in ﬂ ow-through mixers with disordered packing.
Theoretical principles of modeling. In industrial ap-
paratuses of chemical technology and power engineering,
the ﬂ ow of gases (vapors) and liquids is almost always
turbulent. Therefore, reliable calculation of turbulent
ﬂ ows is important for the improvement of chemical and
power engineering equipment.
The ﬁ rst fundamental studies of turbulent ﬂ ows were
performed as early as XIX century by G. Hagen, O. Reyn-
olds, J. Boussinesq, and G. Lorenz and were extensively
developed in the beginning of the XX century (L Prandtl,
T. von Karman, V. Eckman, J. Burgers, A. Kolmogorov,
H. Dryden, F.H. Clauser, G.I. Taylor, H. Schlichting,
L. Loitsyanskii, et al.). Various semiempirical theories
of near-wall turbulence and detaching ﬂ ows have been
developed. The Reynolds averaging of the equations of
viscous liquid dynamics leads to the system of Reyn-
olds equations termed ﬁ rst-momentum equations. In the
general case, the problem of closure of these equations