Russian Journal of Applied Chemistry, 2012, Vol. 85, No. 6, pp. 898−906.
Pleiades Publishing, Ltd., 2012.
Original Russian Text © L.A. Sanova, A.N. Lisitsyn, 2012, published in Zhurnal Prikladnoi Khimii, 2012, Vol. 85, No. 6, pp. 916−924.
OF SYSTEMS AND PROCESSES
Simulation of Foaming Ability, Multiplicity,
and Foam Stability of Shampoo
L. A. Sanova and A. N. Lisitsyn
VNIIZHirov, St. Petersburg, Russia
Received November 10, 2011
Abstract—Equations for a foam height, multiplicity, and foam stability of shampoo were suggested. Model
deriving was based on an assumption that foams was monodispersed systems consisting from cells of gas in the
form of pentagonal dodecahedra with liquid ﬁ lms created by two adsorption monolayers of surfactant monomers
Foaming ability, multiplicity, and foam stability are
main parameters . Nowadays quantitative assessment
of foams is performed by instrumental methods. No
information on calculation methods and rapid tests of
foam in the literature are given. This complicates the
choice of base surfactant in developing formulations of
shampoos and other foam cleansers.
The paper presents the results of the development of
computational equations of the quantitative assessing the
initial foam height, multiplicity, and foam stability of
shampoo based on a study of a structure of foam and its
relation to the colloid-chemical properties of surfactants.
1. FOAMING ABILITY
The foaming ability is quantiﬁ ed by volume (mL,
) or foam height (mm, cm) formed from a constant
volume of the solution under certain conditions in a
column for a speciﬁ ed time. In the National Standard of
the Russian Federation . as the foaming parameter of
the shampoo a number of foam was set, which should
be no less than 100 ml. Quantitatively this parameter
is determined in accordance with State Standard GOST
22567.1 and by the Ross–Miles device used as ISO
standard method (ISO 696:1975) for foam testing.
1.1. Hydraulic Model of Foam Layer
Initially, the foam in its formation in surfactant
solutions is very heterogeneous relative to a dispersion
of gas bubbles and their shape as well as to a thickness
of the liquid ﬁ lms separating the bubbles from each
other . At the stage of forming the gas bubble shape
in separating time is nearly spherical and surrounded by
a shell consisting of two adsorption monolayers of the
surfactant. A space inside these monolayers is ﬁ lled with
a liquid phase being in molecular dispersed or micellar
state (Fig. 1, 1). In the foam layer the bubble shape
changes from spherical to polyhedral, predominantly
in the form of regular pentagonal dodecahedra or
dodecahedra, whose any face is a regular pentagon
(Fig. 1, 2). These multi-faceted bubbles, usually called
cells (hence the term: cellular foams) are separated by
very thin ﬁ lms of liquid (Fig. 1, 3).
For foams with cells in the form of pentagonal
dodecahedron the faces of the ﬁ lms of adjacent cells
by their edges meet each other at an angle of 120°
forming Plateau triangular capillary channels with
a concave surface of the walls (Fig. 1, 4); at the vertices
of the dodecahedron the Plateau channels go into nodes
formed by four edges. The channels and nodes are ﬁ lled
Physical hydraulic model is underlain by the
following two assumptions.
(1) The foam layer is monodisperse and it is
a collection of gas cells in the form of pentagonal
dodecahedra with the side walls in the form of pentagonal