J Elast (2010) 101: 77–99
DOI 10.1007/s10659-010-9252-y
A Continuum Model for Fluid Foams
Cesare Davini
Received: 27 October 2009 / Published online: 26 March 2010
© Springer Science+Business Media B.V. 2010
Abstract A continuum theory of fluid foams regarded as a continuum of hexagonal micro
cells with fluid walls is derived and some qualitative aspects of the equilibrium problem are
discussed.
Keywords Foams · Honeycomb cells · Microstructured fluids
Mathematics Subject Classification (2000) 74A60 · 74N15 · 76A02
1 Introduction
Fluid foams are complex fluids consisting of small gas bubbles separated by thin liquid walls
in such a proportion that the volume fraction of the liquid phase is small. Walls are stabilized
by means of chemicals (surfactants) that render the whole system rather persistent in spite
of a natural trend to change its state with time. The physics of foams is determined by the
interfacial forces that occur at the film level. The result is a rather rich phenomenology that
under certain circumstances includes solid-like behaviour and that, more generally, exhibits
“the whole panoply of mechanics and rheology”, to use words of Weaire and Fortes [21].
The peculiar feature of the foams makes them precious in a variety of applications, from
fire fighting to the transport of particulates in well drilling and clean-out operations in the
oil and gas industry [11]. So, apart from pure speculation, there are strong practical reasons
for studying them. The interest for the subject dates back to the late 19th century with
the celebrated work of Plateau, but a thorough study began only a thirty years ago and it
has given rise to an intense activity of research covering both experimental and theoretical
aspects. The work done is well reviewed in the above cited articles; with different focusses,
the monographs Weaire and Hutzler [22], Ekserova and Krugliakov [7] give an introduction
to the main aspects involved.
C. Davini ( )
Dipartimento di Georisorse e Territorio, Università di Udine, Via del Cotonificio 114, 33100 Udine,
Italy
e-mail: davini@uniud.it