Russian Journal of Applied Chemistry, 2010, Vol. 83, No. 5, pp. 841−845.
Pleiades Publishing, Ltd., 2010.
Original Russian Text
Yu.V. Litovka, S.Yu. Denisov, 2010, published in Zhurnal Prikladnoi Khimii, 2010, Vol. 83, No. 5, pp. 789−793.
AND CORROSION PROTECTION OF METALS
Calculation of the Distribution of an Electroplated Coating
over the Surface of Large-Size Articles
Yu. V. Litovka and S. Yu. Denisov
Tambov State Technical University, Tambov, Russia
Received July 22, 2009
Abstract—Procedure for calculation of the distribution of an electroplated coating over the surface of large-size
articles was developed in order to make the coating more uniform.
Electroplated coatings ﬁ nd wide use in automobile,
aircraft, radioelectronic, and electronic industries.
The nonuniformity of the electric ﬁ eld in the course
of deposition of an electroplated coating leads to its
varying thickness over the surface of an article. If
a coating is thinner at some places than the prescribed
value (or, what is even worse, is lacking at all), rejects
are produced. An excessive thickness of a coating leads
to over-expenditure of the coating material and electric
power, which is economically inefﬁ cient. Thus, the
problem of making electroplated coatings more uniform
is important and topical.
To raise the coating uniformity, methods for
calculation of the electric ﬁ eld in the volume of
an electrolytic cell have been developed [1–4]. All
the known approaches assume that any point of the
article-cathode has the same potential. This assumption
is well justiﬁ ed for small articles. When, however,
a coating is deposited onto a large-size article having
a substantial length at a comparatively small cross-
sectional area (e.g., in chromium plating of long bores
in oil extraction, or electroplating of the inner surface of
long tubes with a wire anode), the current distribution
within the electrodes is nonuniform, which is caused
by the voltage drop on the body of the electrodes.
Therefore, a description of a system of this kind should
take into account the electric ﬁ eld distribution within
the metal of the electrodes. The aim of this study is to
develop a procedure for calculating the distribution of
an electroplated coating over the surface of a large-scale
article in order to make it more uniform.
The nonuniformity R of the coating distribution over
the article surface can be evaluated by the formula
is the cathode surface area; δ(x, y, z), coating
thickness at a cathode point with the coordinates (x, y, z);
, minimum coating thickness which must satisfy
the condition δ
, where δ
is the prescribed
To construct equations of the mathematical mode
of the electroplating process under consideration, we
make the following basic assumptions. (1) There are
no concentration and temperature gradients along the
linear coordinates. The electrical conductivity χ of the
electrolyte is independent of the coordinates x, y, z. The
assumption is based on the fact that the hydrodynamic
mode in industrial plating baths is close to the full
agitation mode because the electrolyte is bubble with
compressed air and hydrogen evolved at the cathode.
(2) Within the range of admissible variations of the
component concentrations and electrolyte temperature,
the electrical conductivity χ and the density ρ of the
electrolyte are independent of the concentration and
temperature. This assumption is based on the narrow
ranges of technologically acceptable variations of
the electrolyte concentration and temperature. (3)