Article

A simple microstructural viscoelastic model for flowing foams

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Abstract and Figures

The numerical modelling of forming processes involving the flow of foams requires taking into account the different problem scales. Thus, in industrial applications a macroscopic approach is suitable, whereas the macroscopic flow parameters depend on the cellular structure: cell size, shape, orientation, etc. Moreover, the shape and orientation of the cells are induced by the flow. A fully microscopic description remains useful to understand the foam behaviour and the topological changes induced by the cell elongation or distortion, however, from an industrial point of view, microscopic simulations remain challenging to address practical applications involving flows in complex 3D geometries. In this paper, we propose a viscoelastic flow model where the foam microstructure is represented from suitable microstructure descriptors whose evolution is governed by the macroscopic flow kinematics.
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https://doi.org/10.1007/s12289-018-1417-4
ORIGINAL RESEARCH
A simple microstructural viscoelastic model for flowing foams
Rub´
en Ib´
a˜
nez1·Adrien Scheuer1,4 ·Emmanuelle Abisset-Chavanne1·Francisco Chinesta2·Antonio Huerta3·
Roland Keunings4
©Springer-Verlag France SAS, part of Springer Nature 2018
Abstract
The numerical modelling of forming processes involving the flow of foams requires taking into account the different problem
scales. Thus, in industrial applications a macroscopic approach is suitable, whereas the macroscopic flow parameters depend
on the cellular structure: cell size, shape, orientation, etc. Moreover, the shape and orientation of the cells are induced by the
flow. A fully microscopic description remains useful to understand the foam behaviour and the topological changes induced
by the cell elongation or distortion, however, from an industrial point of view, microscopic simulations remain challenging
to address practical applications involving flows in complex 3D geometries. In this paper, we propose a viscoelastic flow
model where the foam microstructure is represented from suitable microstructure descriptors whose evolution is governed
by the macroscopic flow kinematics.
Keywords Flowing foams ·Viscoelasticity ·Conformation ·Microstructural description
Francisco Chinesta
Francisco.Chinesta@ensam.eu
Rub´
en Ib´
a˜
nez
Ruben.Ibanez-Pinillo@eleves.ec-nantes.fr
Adrien Scheuer
Adrien.Scheuer@uclouvain.be; Adrien.Scheuer@ec-nantes.fr
Emmanuelle Abisset-Chavanne
Emmanuelle.Abisset-Chavanne@ec-nantes.fr
Antonio Huerta
Antonio.Huerta@upc.edu
Roland Keunings
Roland.Keunings@uclouvain.be
1ICI - High Performance Computing Institute at Ecole Centrale
de Nantes, ESI GROUP Chair on Advanced Modeling and
Simulation of Manufacturing Processes, 1 rue de la Noe,
44300 Nantes, France
2PIMM, ENSAM ParisTech, ESI GROUP Chair on Advanced
Modeling and Simulation of Manufacturing Processes, 151
Boulevard de l’Hˆ
opital, 75013, Paris, France
3Laboratori de C`
alcul Num`
eric, Universitat Polit`
ecnica de
Catalunya, BarcelonaTech, 08034 Barcelona, Spain
4ICTEAM, Universit´
e catholique de Louvain, Av. Georges
Lemaitre 4, 1348, Louvain-la-Neuve, Belgium
Introduction
Aqueous foams are concentrated dispersions of gas bubbles
in a surfactant solution. Their structures are organized over
a large range of length scales and complex flows take place
at different scales [6].
The proposal of macroscopic constitutive equations
allows for the efficient modelling and simulation of indus-
trial processes involving the flow of foams [1,4]. Usu-
ally, such descriptions remain however too phenomeno-
logical, and even though they predict accurately the flow
kinematics, microstructure information remains often unac-
cessible. On the opposite side, fully microscopic simu-
lations allow for very detailed descriptions of the foam
microstructural evolution [2]. However such approaches
fail to address scenarios of industrial interest that usually
involve the flow of foams in very large and complex 3D
geometries.
The macroscopic flow model is expected to depend on
the cellular structure: cell size, shape and orientation, as
well as on the fluid rheology and the surface tension.
Moreover, cell shape and orientation are induced by the
flow. This microscopic information could be introduced
into a macroscopic flow model by using standard upscaling
and homogenization techniques. Thus inspired by [7],
at some locations in the domain in which an effective
homogeneous fluid flows, we could attach a representative
International Journal of Material Forming (2019) 12:295–306
Received: 21 October 2017 / Accepted: 26 March 2018 / Published online: 28 April 2018
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
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