O. Kodio, I. M. Griffiths and D. Vella, Lubricated wrinkles: imposed constraints affect the dynamics of wrinkle coarsening, Phys. Rev. Fluids 2, 014202 (2017). [ORA record] [arXiv]

Wrinkly isometry

Thin elastic objects are difficult to stretch, but easy to bend: they should deform whilst remaining close to isometries (deformations that do not stretch). Mathematically, such isometries should preserve the (Gaussian) curvature of the object; however, by wrinkling very thin sheets are able to change their apparent Gaussian curvature. Since wrinkling is a necessary pre-requisite for such these are sometimes called `wrinkly isometries' and the change in apparent length is achieved through `buffering by buckling'.

D. Vella, Buffering by buckling as a route for elastic, Nat. Rev. Phys. 1, 425-436 (2019)

D. Vella, H. Ebrahimi, A. Vaziri and B. Davidovitch, Wrinkling reveals a new isometry of pressurized elastic shells, EPL 112, 24007 (2015). [arXiv version] [ORA record]

D. Vella, J. Huang, N. Menon, T. P. Russell and B. Davidovitch, Indentation of ultrathin elastic films and the emergence of asymptotic isometry, Phys. Rev. Lett. 114, 014301 (2015). [arXiv version]

Static wrinkle patterns

Another primary aim of our research has been to understand the properties of the wrinkle patterns that form in extremely thin sheets, specifically the spatial extent of a wrinkle pattern and the number of wrinkles. The challenge in such problems is that the presence of wrinkles significantly modifies the forces acting on the sheet meaning that traditional buckling analyses are no longer valid.

D. Vella and B. Davidovitch, Regimes of wrinkling in an indented floating elastic sheet, Phys. Rev. E 98, 013003 (2018). [ORA Record] [arXiv]

F. Box, D. Vella, R. W. Style and J. A. Neufeld, Indentation of a floating elastic sheet: Geometry versus applied tension Proc. R. Soc. A 473, 20170335 (2017). [ORA record] [arXiv] [data]

M. Taffetani and D. Vella, Regimes of wrinkling in pressurized elastic shells Phil. Trans. R. Soc. 375, 20160330 (2017). [ORA record] [arXiv] [data]

P. S. Stewart, T. El-Sayed, S. L. Waters, D. Vella and A. Goriely, Wrinkling, creasing, and folding in fiber-reinforced soft tissues, Extr. Mech. Lett. 8, 22-29 (2016). [ORA record]

J. D. Paulsen, E. Hohlfeld, H. King, J. Huang, Z. Qiu, T. P. Russell, N. Menon, D. Vella and B. Davidovitch, Curvature-induced stiffness and the spatial variation of wavelength in wrinkled sheets, Proc. Natl. Acad. Sci. USA 113, 1144-1149 (2016). [ORA record]

S. Knoche, D. Vella, E. Aumaitre, P. Degen, H. Rehage, P. Cicuta and J. Kierfeld, Elastometry of Deflated Capsules: Elastic Moduli from Shape and Wrinkle Analysis, Langmuir 29, 12463-12471 (2013). [arXiv version]

R. D. Schroll, M. Adda-Bedia, E. Cerda, J. Huang, N. Menon, T. P. Russell, K. B. Toga, D. Vella and B. Davidovitch, Capillary deformations of bendable films, Phys. Rev. Lett. 111, 014301 (2013).

E. Aumaitre, S. Knoche, P. Cicuta and D. Vella, Wrinkling in the deflation of elastic bubbles, Eur. Phys. J. E 36, 22 (2013).

B. Davidovitch, R. D. Schroll, D. Vella, M. Adda-Bedia and E. Cerda, A prototypical model for tensional wrinkling in thin sheets, Proc. Natl Acad. Sci. USA 108, 18227 (2011).

D. Vella, A. Ajdari, A. Vaziri and A. Boudaoud, Wrinkling of pressurized elastic shells, Phys. Rev. Lett. 107, 174301 (2011).

D. Vella, M. Adda-Bedia and E. Cerda, Capillary wrinkling of elastic membranes, Soft Matter 6, 5778 (2010).

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Elasticity of thin objects

Connected to my work on wrinkling I have also worked on a number of problems in the elasticity of thin objects. This is distinct from my work on wrinkling in the sense that it is not always instability that concerns us. However, there is a large overlap between this work, my work on wrinkling and my work on `elasto-capillarity' (see below).

Snap-through dynamics

We have studied how elastic objects `snap' from one state to another. A key finding has been that this dynamics is slower than might be expected because of the nature of the transition.

M. Gomez, D. E. Moulton, and D. Vella, Dynamics of viscoelastic snap-through, J. Mech. Phys. Solids 124, 781-813 (2019). [ORA Record] [arXiv]

M. Gomez, D. E. Moulton and D. Vella, Passive control of viscous flow via elastic snap-through, Phys. Rev. Lett. 119, 144502 (2017). [ORA record] [arXiv] [data]

M. Gomez, D. E. Moulton, and D. Vella, Critical slowing down in purely elastic `snap-through' instabilities, Nat. Phys. 13, 142-145 (2017). [ORA Record] [arXiv] [SharedIt] [data]

A. Pandey, D. E. Moulton, D. Vella and D. P. Holmes, Dynamics of snapping beams and jumping poppers, EPL 105, 24001 (2014). [arXiv version]

Shell mechanics

We have obtained a number of new analytical results that describe the indentation (i.e. poking) of elastic shells (a thin elastic object that is naturally curved).

M. Taffetani, F. Box, A. Neveu, and D. Vella, Limitations of curvature-induced rigidity: How a curved strip buckles under gravity, Europhys. Lett. 127, 14001 (2019). [ORA Record] [arXiv]

M. Taffetani, X. Jiang, D. P. Holmes and D. Vella, Static bistability of spherical caps, Proc. R. Soc. A 474, 20170910 (2018). [ORA Record] [arXiv] [data]

M. Gomez, D. E. Moulton and D. Vella, The shallow shell approach to Pogorelov's problem and the breakdown of `mirror buckling', Proc. R. Soc. A 472, 20150732 (2016). [arXiv version] [ORA record]

D. Vella, H. Ebrahimi, A. Vaziri and B. Davidovitch, Wrinkling reveals a new isometry of pressurized elastic shells, EPL 112, 24007 (2015). [arXiv version] [ORA record]

H. Ebrahimi, A. Ajdari, D. Vella, A. Boudaoud and A. Vaziri, Anisotropic blistering instability of highly ellipsoidal shells, Phys. Rev. Lett. 112, 094302 (2014).

D. Vella, A. Ajdari, A. Vaziri and A. Boudaoud, Indentation of ellipsoidal and cylindrical elastic shells, Phys. Rev. Lett. 109, 144302 (2012).
Also highlighted as editor's suggestion and featured in Physics, 5^th October 2012

D. Vella, A. Ajdari, A. Vaziri and A. Boudaoud, The indentation of pressurized elastic shells: From polymeric capsules to yeast cells, J. R. Soc. Interface 9, 448 (2012).

Floating ice mechanics

Understanding the mechanics of floating sheets of ice (ice floes) is important for understanding how the ice cover in the polar regions evolves. We have studied some of the surprising patterns that form when floes collide and also shown that icebergs may breakup because of a new elastic mechanism.

T. J. W. Wagner, T. D. James, T. Murray and D. Vella, On the role of buoyant flexure in glacier calving, Geophys. Res. Lett. 43, 232-240 (2016). [ORA record]

T. J. W. Wagner, P. Wadhams, R. Bates, P. Elesogui, A. Stern, D. Vella, E. Abrahamsen, A. Crawford and K. Nicholls, The 'footloose' mechanism: Iceberg decay from hydrostatic stresses, Geophys. Res. Lett. 41 5522-5529 (2014).

D. Vella and J. S. Wettlaufer, Explaining the patterns formed by ice floe interactions, J. Geophys. Res. 113, C11011 (2008).

D. Vella and J. S. Wettlaufer, Finger rafting: A generic instability of floating elastic sheets, Phys. Rev. Lett. 98, 088303 (2007).

Effective elasticity

We have studied how an elasticity that is remarkably close to that of a rod emerges from the interactions between magnetic dipoles. This can be seen by playing with popular toys like the NeoCube and BuckyBalls, though be warned that these now seem to be deemed a saftety hazard!

D. Vella, E. du Pontavice, C. L. Hall and A. Goriely, The Magneto-elastica: From self-buckling to self-assembly, Proc. R. Soc. A 470, 20130609 (2014). [arXiv version]

C. L. Hall, D. Vella and A. Goriely, The mechanics of a chain or ring of spherical magnets, SIAM J. Appl. Math. 73, 2029-2054 (2013). [arXiv version]

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Elastocapillarity

Small, thin elastic objects are so flexible that surface tension is strong enough to bend them. This interaction between elasticity and capillarity (elasto-capillarity) is important at small scales and also overlaps with many of the classic concepts in adhesion science.

M. Butler, F. Box, T. Robert and D. Vella, Elasto-capillary adhesion: The effect of deformability on adhesion strength and detachment, Phys. Rev. Fluids 4, 033601 (2019). [ORA Record] [arXiv] [data]

A. T. Bradley, F. Box, I. J. Hewitt and D. Vella, Wettability-independent droplet transport by Bendotaxis, Phys. Rev. Lett. 122 074503 (2019). [ORA Record] [arXiv]

B. Davidovitch and D. Vella, Partial wetting of thin solid sheets under tension, Soft Matter 14, 4913-4934 (2018). [ORA Record] [arXiv]

A. Hadjittofis, J. R. Lister, K. Singh and D. Vella, Evaporation effects in elastocapillary aggregation, J. Fluid Mech. 792, 168-185 (2016). [arXiv version] [ORA record]

K. Singh, J. R. Lister and D. Vella, A fluid-mechanical model of elastocapillary coalescence, J. Fluid Mech. 745, 621-646 (2014). [arXiv version]

T. J. W. Wagner and D. Vella, Switch on, switch off: Stiction in nanoelectromechanical switches, Nanotechnology 24, 275501 (2013).

T. J. W. Wagner and D. Vella, The `Sticky Elastica': Delamination blisters beyond small deformations, Soft Matter 9, 1025 (2013).

M. Taroni and D. Vella, Multiple equilibria in a simple elastocapillary system, J. Fluid Mech. 712, 273 (2012).

T. J. W. Wagner and D. Vella, The sensitivity of Graphene `Snap-through' to substrate geometry, Appl. Phys. Lett. 100, 233111 (2012). [arXiv version]
Also selected to appear in Virtual Journal of Nanoscale Science and Technology, 18^th June 2012

T. J. W. Wagner and D. Vella, Floating carpets and the delamination of elastic sheets, Phys. Rev. Lett. 107, 044301 (2011).

D. Vella, A. Boudaoud and M. Adda-Bedia, Statics and Inertial Dynamics of a Ruck in a Rug, Phys. Rev. Lett. 103, 174301 (2009).

D. Vella, J. Bico, A. Boudaoud, B. Roman and P. M. Reis, The Macroscopic Delamination of Thin Films from Elastic Substrates, Proc. Natl. Acad. Sci. USA 106, 10901 (2009).

J. Chopin, D. Vella and A. Boudaoud, The Liquid Blister Test, Proc. R. Soc. A 464, 2887 (2008).

D. Vella and L. Mahadevan, A simple microscopic model for the dynamics of adhesive failure, Langmuir 22, 163 (2006). [arXiv version]

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Complex Interfaces and Fluids

Interfacial Rheology

When a liquid interface is covered with many objects (small particles or large molecules) the behaviour changes to become reminiscent of an elastic sheet. We have characterized the elastic properties of these interfaces and also studied how the elasticity can cause surprising results when using conventional measurement techniques.

S. Knoche, D. Vella, E. Aumaitre, P. Degen, H. Rehage, P. Cicuta and J. Kierfeld, Elastometry of Deflated Capsules: Elastic Moduli from Shape and Wrinkle Analysis, Langmuir 29, 12463-12471 (2013). [arXiv version]

E. Aumaitre, S. Wongsuwarn, D. Rossetti, N. D. Hedges, A. R. Cox, D. Vella and P. Cicuta, A viscoelastic regime in dilute hydrophobin monolayers, Soft Matter 8, 1175 (2012).

E. Aumaitre, D. Vella and P. Cicuta, On the measurement of the surface pressure in Langmuir films with finite shear elasticity, Soft Matter 7, 2530 (2011).

P. Cicuta and D. Vella, Granular Character of Particle Rafts, Phys. Rev. Lett. 102, 138302 (2009).

D. Vella H.-Y. Kim, P. Aussillous and L. Mahadevan, Dynamics of surfactant-driven fracture of particle rafts, Phys. Rev. Lett. 96, 178301 (2006). [arXiv version]

D. Vella, P. Aussillous and L. Mahadevan, Elasticity of an interfacial particle raft, Europhys. Lett. 68, 212 (2004). [arXiv version]

Ionic Liquids

A. A. Lee, S. Kondrat, D. Vella, and A. Goriely, Dynamics of ion transport in ionic liquids, Phys. Rev. Lett. 115, 106101 (2015). [arXiv version]

A. A. Lee, D. Vella, S. Perkin and A. Goriely, Are room temperature ionic liquids dilute electrolytes?, J. Phys. Chem. Lett. 6, 159-163 (2015). [arXiv version]

A. A. Lee, D. Vella, S. Perkin and A. Goriely, Unravelling nanoconfined films of ionic liquids, J. Chem. Phys. 141, 094904 (2014). [arXiv version]

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Floating objects: The Cheerios effect and Archimedes' Principle

Floating vs sinking

The surface tension of an interface allows objects that are significantly more dense than the liquid to float. We have studied the conditions under which surface tension is strong enough to keep such particles afloat and the dynamics by which they sink if not.

C. Y. H. Wong, M. Adda-Bedia and D. Vella, Non-wetting drops at liquid interfaces: From liquid marbles to Leidenfrost drops, Soft Matter 13, 5250-5260 (2017). [ORA Record] [arXiv]

H. Cooray, P. Cicuta and D. Vella, Floating and sinking of a pair of spheres at a liquid-fluid interface, Langmuir 33, 1427-1436 (2017). [ORA Record]

D.-G. Lee, P. Cicuta and D. Vella, Self-assembly of repulsive interfacial particles via collective sinking, Soft Matter 13, 212-221 (2017). [ORA record] [arXiv]

M. Adda-Bedia, S. Kumar, F. Lechenault, S. Moulinet, M. Schillaci and D. Vella, Inverse Leidenfrost Effect: Levitating Drops on Liquid Nitrogen, Langmuir 32, 4179-4188 (2016). [ORA record]

D. Vella, Floating versus Sinking, Annu. Rev. Fluid Mech. 47, 115-135 (2015).
[Complimentary one-time access to this article as a PDF file is for personal use (courtesy of Annual Reviews).]

D. Vella and J. Li, The impulsive motion of a small cylinder at an interface, Phys. Fluids 22, 052104 (2010).

D. Vella, Floating Objects with Finite Resistance to Bending, Langmuir 24, 8701 (2008).

D. Vella and P. D. Metcalfe, Surface tension dominated impact, Phys. Fluids 19, 072108 (2007).
Also selected to appear in Virtual Journal of Biological Physics Research, 1^st August 2007

D. Vella and H. E. Huppert, The waterlogging of floating objects, J. Fluid Mech. 585, 245 (2007).

D. Vella, D.-G. Lee and H.-Y. Kim, The load supported by small floating objects, Langmuir 22, 5979 (2006).

D. Vella, D.-G. Lee and H.-Y. Kim, Sinking of a horizontal cylinder, Langmuir 22, 2972 (2006).

D. Vella, P. D. Metcalfe and R. J. Whittaker, Equilibrium conditions for the floating of multiple interfacial objects, J. Fluid Mech. 549, 215 (2006). [arXiv version]

The Cheerios effect

Floating objects that are sufficiently close together `attract' one another because of the meniscus deformation that they each cause. We have quantified this force in some new situations, used numerical techniques to test the validity of existing approximations and some of the dynamics of the attraction.

D.-G. Lee, P. Cicuta and D. Vella, Self-assembly of repulsive interfacial particles via collective sinking, Soft Matter (in revision). [arXiv version]

H. Cooray, P. Cicuta and D. Vella, The capillary interaction between two vertical cylinders, J. Phys. Cond. Mat. 24, 284104 (2012).

S. Gart, D. Vella and S. Jung, The collective motion of nematodes in a thin liquid layer, Soft Matter 7, 2444 (2011).

D. Vella and L. Mahadevan, The 'Cheerios effect', Am. J. Phys. 73, 817 (2005). [arXiv version]

D. Vella, H.-Y. Kim and L. Mahadevan, The wall-induced motion of a floating flexible train, J. Fluid Mech. 502, 89 (2004).

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Flow in Porous Media

Brain edema

G. E. Lang, D. Vella, S. L. Waters and A. Goriely, Propagation of damage in brain tissue: Coupling the mechanics of Edema and oxygen delivery, Biomech. Model. Mechanobiol. 14, 1197-1216 (2015).

G. E. Lang, P. S. Stewart, D. Vella, S. L. Waters and A. Goriely, Is the Donnan effect sufficient to explain swelling in brain tissue slices?, J. R. Soc. Interface 11, 20140123 (2014).

Water filtration

Many techniques for filtering water rely on passing the water through a porous medium in such a way that the junk gets left behind. We have developed mathematical models of this process.

J. G. Herterich, D. Vella, R. W. Field, N. P. Hankins and I. M. Griffiths, Tailoring wall permeabilities for enhanced filtration, Phys. Fluids 27, 053102 (2015).

A. Eisenträger, D. Vella and I. M. Griffiths, Particle Capture Efficiency in a Multi-Wire Model for High Gradient Magnetic Separation, Appl. Phys. Lett. 105, 033508 (2014).

J. G. Herterich, I. M. Griffiths, R. W. Field and D. Vella, The effect of a concentration-dependent viscosity on particle transport in a channel flow with porous walls, AIChE J. 60, 1891-1904 (2014).

Carbon sequestration

One way by which the harmful effects of atmospheric carbon dioxide can be mitigated is to remove it and bruy it underground in aquifers (carbon sequestration). We have studied how the carbon dioxide spreads when underground and whether cracks in the caprock that overlies aquifers would be terminal for the efficacy of storage.

P. J. Zimoch, J. A. Neufeld and D. Vella, Leakage from inclined porous reservoirs, J. Fluid Mech. 673, 395 (2011).

D. Vella, J. A. Neufeld, H. E. Huppert and J. R. Lister, Leakage from gravity currents in a porous medium. Part 2. A line sink, J. Fluid Mech. 666, 414 (2011).

J. A. Neufeld, D. Vella, H. E. Huppert and J. R. Lister, Leakage from gravity currents in a porous medium. Part 1. A localized sink, J. Fluid Mech. 666, 391 (2011).

J. A. Neufeld, D. Vella and H. E. Huppert, The effect of a fissure on storage in a porous medium, J. Fluid Mech. 639, 239 (2009).

D. Vella and H.E. Huppert, Gravity currents in a porous medium at an inclined plane, J. Fluid Mech. 555, 353 (2006). [arXiv version]

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Miscellaneous

I sometimes get involved with other problems in Applied Mathematics that do not fit into the broad areas described above.

Archaeology

Archaeologists often use isotope meaurements from animal teeth to make statements about the diet and movements of those animals. We develop a simple model for how non-constant tooth growth should be taken into account when making such inferences.

R. Bendrey, D. Vella, A. Zazzo, M. Balasse and S. Lepetz, Exponentially decreasing tooth growth rate in horse teeth: Implications for isotopic analyses, Archaeometry 57, 1104-1124 (2015).

A. Zazzo, R. Bendrey, D. Vella, A. P. Moloney, F. J. Monahan and O. Schmidt, A refined sampling strategy for intra-tooth stable isotope analysis of mammalian enamel, Geochim. Cosmochim. Acta 84, 1 (2012).

The Percus-Yevick equation

The Percus-Yevick approximation is a popular closure relation for the problem of gases at non-vanishing densities. We developed a new technique for solving the resulting equations.

(Several groups have contacted us asking for numerical data we obtained as part of our solution of the Percus-Yevick equation. A webpage with links to this data (with instructions on how to use it) can be found here.)

M. Adda-Bedia, E. Katzav and D. Vella, Solution of the Percus-Yevick equation for hard hyperspheres in even dimensions, J. Chem. Phys. 129, 144506 (2008).

M. Adda-Bedia, E. Katzav and D. Vella, Solution of the Percus-Yevick equation for hard disks, J. Chem. Phys. 128, 184508 (2008).

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