A SYNERGETIC ANALYSIS OF THE EFFICIENCY
OF GRINDING PROCESSES
I. A. Trubnikov
and E. A. Kandyusheva
Translated from Novye Ogneupory, No. 5, May, 2005, pp. 45 – 51.
A synergetic approach based on irreversible thermodynamics is applied to the description of particle size re
duction of raw materials and related technological implications.
The controlled disintegration of raw materials and
semi-finished products is a necessary step in the production
technology of a vast range of technical ceramics and
refractories. The grinding has become a special concern be-
cause of the increasingly stringent requirements placed on
the product quality as well as of environmental consider-
ations. One will recall that the surface S
particles is proportional to the energy E spent on grinding:
is a coefficient which takes account of the dissipa
tion of useful mechanical energy associated with effects due
to friction, bending, pressure, heat, and vibration.
Fine milling of materials of moderate and high hardness
is attained using ball mills, impact-rod mills, also vibratory
and colloidal mills which allow the particle size reduction to
several micrometers. In these facilities, the material is re
duced in size under the action of impact, crushing, or attri
Most actual processes involved are in fact non-equilib
rium ones exhibiting cooperative, dissipative, or nonlinear
effects. The modern synergetics  (the term “synergetics”
derives from a Greek “sun-ergatikoz” which signifies
“mutual action”) as a science that has to deal with such pro
cesses makes use of the formalism of nonlinear dynamics
and nonequilibrium thermodynamics. Our goal in this study
was to show how synergetic methods can be applied to ex
plore the processes of disintegration of solids.
FLUXES AND TRANSFER PHENOMENA
In mathematics (in the field theory), the vector field flux
R through the surface S is expressed (except for sign) by the
(, ) ( )
a n dS a dydz a dzdx a dxdy
is a unit vector normal to surface
In practical engineering, the transfer phenomenon is a
particularly important concern which allows one, in terms of
molecular physics, to formulate the concept of a flow of sub
stance . The substance Y is understood to mean a physical
quantity which obeys laws of conservation (mass, material
, electrical charge, enthalpy, or momentum); the
term “flow” is used to characterize the change of a particular
quantity over time.
In 1822, Jean Batiste Fourier was the first to introduce,
in his work “An Analytical Theory of Heat,” the concept of a
flow and considered theoretically the phenomenon of heat
conduction. Also, Georg Ohm used this method to derive his
famous law. A similar approach was used by Louis Navier in
describing the viscous flow of a fluid. Later, in 1855, Adolph
Fick developed a theory of the diffusion process using meth
ods of J.-B. Fourier and S. Poisson applied to special prob
lems of transfer in gases.
The flow and the rate of growth of entropy
Refractories and Industrial Ceramics Vol. 46, No. 4, 2005
1083-4877/05/4604-0239 © 2005 Springer Science+Business Media, Inc.
Rostov State University, Rostov, Russsia.
In a chemical reaction, these are atoms.