Mathematical Modelling of Structures, Solids and Fluids
http://hdl.handle.net/2160/2918
20141025T09:31:25Z

Analysis of a model for foam improved oil recovery
http://hdl.handle.net/2160/14173
Analysis of a model for foam improved oil recovery
Grassia, P.; MasHernández, E.; Shokri, N.; Cox, S. J.; Mishuris, G.; Rossen, W. R.
During improved oil recovery (IOR), gas may be introduced into a porous reservoir filled with surfactant solution in order to form foam. A model for the evolution of the resulting foam front known as 'pressuredriven growth' is analysed. An asymptotic solution of this model for long times is derived that shows that foam can propagate indefinitely into the reservoir without gravity override. Moreover, 'pressuredriven growth' is shown to correspond to a special case of the more general 'viscous froth' model. In particular, it is a singular limit of the viscous froth, corresponding to the elimination of a surface tension term, permitting sharp corners and kinks in the predicted shape of the front. Sharp corners tend to develop from concave regions of the front. The principal solution of interest has a convex front, however, so that although this solution itself has no sharp corners (except for some kinks that develop spuriously owing to errors in a numerical scheme), it is found nevertheless to exhibit milder singularities in front curvature, as the longtime asymptotic analytical solution makes clear. Numerical schemes for the evolving front shape which perform robustly (avoiding the development of spurious kinks) are also developed. Generalisations of this solution to geologically heterogeneous reservoirs should exhibit concavities and/or sharp corner singularities as an inherent part of their evolution: propagation of fronts containing such 'inherent' singularities can be readily incorporated into these numerical schemes. © 2014 Cambridge University Press.
Grassia, P., MasHernández, E., Shokri, N., Cox, S. J., Mishuris, G., Rossen, W. R. (2014). Analysis of a model for foam improved oil recovery. Journal of Fluid Mechanics, 751, 346405
20140701T00:00:00Z

Statistical mechanics of twodimensional shuffled foams: Geometrytopology correlation in small or large disorder limits
http://hdl.handle.net/2160/14130
Statistical mechanics of twodimensional shuffled foams: Geometrytopology correlation in small or large disorder limits
Durand, Marc; Kraynik, Andrew M.; Van Swol, Frank; Käfer, Jos; Quilliet, Catherine; Cox, Simon; Ataei Talebi, Shirin; Graner, François
Bubble monolayers are model systems for experiments and simulations of twodimensional packing problems of deformable objects. We explore the relation between the distributions of the number of bubble sides (topology) and the bubble areas (geometry) in the low liquid fraction limit. We use a statistical model [M. Durand, Europhys. Lett. 90, 60002 (2010)EULEEJ0295507510.1209/0295 5075/90/60002] which takes into account Plateau laws. We predict the correlation between geometrical disorder (bubble size dispersity) and topological disorder (width of bubble side number distribution) over an extended range of bubble size dispersities. Extensive data sets arising from shuffled foam experiments, surface evolver simulations, and cellular Potts model simulations all collapse surprisingly well and coincide with the model predictions, even at extremely high size dispersity. At moderate size dispersity, we recover our earlier approximate predictions [M. Durand, J. Kafer, C. Quilliet, S. Cox, S. A. Talebi, and F. Graner, Phys. Rev. Lett. 107, 168304 (2011)PRLTAO0031900710.1103/ PhysRevLett.107.168304]. At extremely low dispersity, when approaching the perfectly regular honeycomb pattern, we study how both geometrical and topological disorders vanish. We identify a crystallization mechanism and explore it quantitatively in the case of bidisperse foams. Due to the deformability of the bubbles, foams can crystallize over a larger range of size dispersities than hard disks. The model predicts that the crystallization transition occurs when the ratio of largest to smallest bubble radii is 1.4. © 2014 American Physical Society.
Durand, M., Kraynik, A. M., Van Swol, F., Käfer, J., Quilliet, C., Cox, S., Talebi, S. A., Graner, F. (2014). Statistical mechanics of twodimensional shuffled foams: Geometrytopology correlation in small or large disorder limits. Physical Review E, 89(6), [062309]
20140619T00:00:00Z

Exact solution to a refined contact problem for biphasic cartilage layers
http://hdl.handle.net/2160/11052
Exact solution to a refined contact problem for biphasic cartilage layers
Argatov, Ivan; Mishuris, Gennady
Nithiarasu, P; Lohner, R; van Loon, R
We revisit the axisymmetric contact problem for a biphasic cartilage layer and consider a refined formulation taking into account the both normal and tangential displacements at the contact interface. The obtained analytical solution is valid for arbitrary time and increasing loading conditions. We compare it with the classic result and indicate cases where the difference could be pronounced.
Mishuris, G; Argatov I. Exact solution to a refined contact problem for biphasic cartilage layers. In proceedings of First International Conference on Computational and Mathematical Biomedical Engineering (CMBE09), Eds. P. Nithiarasu, R. Lohner, R. van Loon, ISBN:9780956291400 Swansea, Swansea, June 2009, pages 151  154.
20090601T00:00:00Z

Topological and geometrical disorder correlate robustly in twodimensional foams
http://hdl.handle.net/2160/10909
Topological and geometrical disorder correlate robustly in twodimensional foams
Cox, Simon; Kafer, J.; Rabaud, D.; Quilliet, C.; Graner, François; Ataei Talebi, S.
A 2D foam can be characterised by its distribution of bubble areas, and of number of sides. Both distributions have an average and a width (standard deviation). There are therefore at least two very different ways to characterise the disorder. The former is a geometrical measurement, while the latter is purely topological. We discuss the common points and differences between both quantities. We measure them in a foam which is sheared, so that bubbles move past each other and the foam is 'shuffled' (a notion we discuss). Both quantities are strongly correlated; in this case (only) it thus becomes sufficient to use either one or the other to characterize the foam disorder. We suggest applications to the analysis of other systems, including biological tissues.
Special Issue: Solid and Liquid Foams. In commemoration of Manuel Amaral Fortes C. Quilliet, S. Ataei Talebi, D. Rabaud, J. Kafer, S.J. Cox and F. Graner (2008) Topological and geometrical disorder correlate robustly in twodimensional foams. Sponsorship: We thank J. Legoupil for his participation in the simulations, K. Brakke for developing and maintaining the Surface Evolver code, A.F.M. Maree for developing the Potts model code used here, M.F. Vaz for providing references, I. Cantat for critical reading of the manuscript, Y. Bella¨ıche, R. Carthew and T. Hayashi for providing pictures of biological tissues, S. Courty for their analysis, P. Ballet for help in setting up the experiment, and participants of the Foam Mechanics workshop (Grenoble, January 2008) for many discussions. S.A.T. thanks Dr Ejtehadi for hospitality at the Institute of Physics and Mathematics, Tehran (Iran). S.J.C. thanks UJF for hospitality, and CNRS, EPSRC (EP/D048397/1, EP/D071127/1) and the British Council Alliance scheme for financial support.
20080101T00:00:00Z