Russian Journal of Applied Chemistry, 2011, Vol. 84, No. 4, pp. 628−631.
Pleiades Publishing, Ltd., 2011.
Original Russian Text © O.S. Ivanov, M.S. Vasilishin, 2011, published in Zhurnal Prikladnoi Khimii, 2011, Vol. 84, No. 4, pp. 591−594.
PROCESSES AND EQUIPMENT
OF CHEMICAL INDUSTRY
Evaluation of Energy Expenditure in “Wet” Grinding
of a Dispersed Material
O. S. Ivanov and M. S. Vasilishin
Institute for Problems of Chemical–Energetic Technologies, Siberian Branch,
Russian Academy of Sciences, Biisk, Altai krai, Russia
Received September 10, 2010
Abstract—Equation relating the physicochemical properties of a material being ground to technological parameters
of the process is derived. The equation makes it possible to evaluate the energy expenditure for grinding.
Grinding is a process that is widely used in techno-
logical cycles of numerous plants for production of, e.g.,
pigments  or construction materials  and is distin-
guished by a considerable power intensity .
Recently, the so-called “wet” grinding in a wide
variety of apparatus has found use in industrial practice
, together with “dry” grinding. It is known [5, 6] that
some liquids well wet powder particles, i.e., reduce
the surface tension at the l–s phase boundary. These
liquids, named dispersants, can substantially facilitate
the grinding process and preclude coagulation and
aggregation of the already milled particles . Of no
small importance is that dust formation leading to
deterioration of working conditions and potentially
causing industrial accidents is entirely absent in the case
of grinding in the liquid phase.
An important task in designing an apparatus for wet
grinding is to ﬁ nd the calculation relation between the
size of resulting particles and energy expenditure for
the technological process. Finding a relationship of
this kind enables an objective evaluation of the energy
expenditure and a substantiated choice of an appropriate
The process of ﬁ ne grinding of materials is rather
precisely described by P. Rittinger’s theory  according
to which the expended energy is proportional to the
area of a newly formed surface. At the same time it is
known that any change in the particle size, including
that in grinding, changes the free (surface) energy of
the system, E
(J), in accordance with U. Thomson’s
where σ is the surface tension at the interface between
particles being ground and the ambient (J m
volume of the particles (m
, initial particle radius
(m); and r
, ﬁ nal particle radius (m).
Assuming that the particles are spherical and
expressing the radii of these particles, r
terms of their speciﬁ c surface areas, S
), we obtain
On substituting expressions (2) into formula (1), we
In formula (3) we have 2σ that symbolizes the
surface energy associated with the formation of two new
surfaces that develop as a result of microcrack growth.
However, the case in which only two new surfaces are
formed as a result of grinding is idealized and can only be
observed in some particular cases, e.g., in disintegration
of metals. Therefore, a dimensionless parameter is used