Research Interests

My main research interests lie in the general area of continuum mechanics with particular interest in surface tension driven fluid flows and the elasticity of thin objects. Each of the pictures below links to a table describing my work in that area with preprints of relevant papers.

For further information, try the News tab (top), which contains links to various popular science articles about my research that may be of interest.

If this page seems out of date my list of publications should remain reasonably current.

To search the arxiv for things by me, click here.

To view my researcherid profile, click here. (This has citation statistics for those who are interested in such things.)

I am also interested in some elementary problems in number theory. In particular, I have studied some properties of Fibonacci sequences and Pythagorean triples. If you are interested in these kinds of subjects then you can find more details here.

Elasticity of thin objects

Recently, I have become interested in a variety of problems. These have the loose connection that they all involve thin elastic sheets. You may also like to look at the adhesion table, which also contains related papers.

Title	Main Idea	Published?	Co-worker(s)
Statics and inertial dynamics of a ruck in a rug	We study when a ruck in a rug is stabilized by friction and the speed of motion of a ruck when one end of a rug is wiggled.	Phys. Rev. Lett. 103 (2009), 174301 arXiv:0905.2952	Arezki Boudaoud and Mokhtar Adda-Bedia
Explaining the Patterns Formed by Ice Floe Interactions	We give conditions on the thickness and strength of two floating sheets of ice to determine the pattern they form on collision.	J. Geophys. Res. 113 (2008), C11011 JGR copy	John Wettlaufer
Finger rafting: A generic instability of floating elastic sheets	We study the strange pattern that sometimes occurs when two floating sheets of ice collide.	Phys. Rev. Lett. 98 (2007), 088303 PRL copy	John Wettlaufer

Adhesion

I have spent some time thinking about adhesion: the patterns that form and how they can be quantified. Often this involves using some of the same techniques as we use to model thin elastic sheets.

Title	Main Idea	Published?	Co-worker(s)
The Macroscopic Delamination of Thin Films from Elastic Substrates	We study a macroscopic model for the delamination of sticky sheets from elastic substrates. This is a model of a microscopic technique for creating stretchable electronic devices.	Proc. Natl. Acad. Sci. 106 (2009), 10901 PNAS Copy	José Bico, Arezki Boudaoud, Benoit Roman and Pedro Reis
The liquid blister test	We study a variant of the classic blister test, which is used to characerize adhesives. We use a liquid as the adhesive and find interesting new regimes.	Proc. R. Soc. A 464 (2008), 2887 arxiv:0803.0712	Julien Chopin and Arezki Boudaoud
A simple microscopic model for the dynamics of adhesive failure	We suggest that the second peak observed in the stress-strain curves for adhesives loaded at constant velocity may be due to finite bond length effects.	Langmuir 22 (2006), 163 arXiv:cond-mat/0506717	L. Mahadevan

Flow in Porous Media

I am also interested in how fluids flow in porous media. This work is particularly motivated by applications to storing Carbon Dioxide deep underground in naturally occuring reservoirs.

Title	Main Idea	Published?	Co-worker(s)
The effect of a fissure on storage in a porous medium	We show that long term carbon sequestration can be badly compromised by the presence of a fault in the overlying rock and determine what `long term' means in this context.	J. Fluid Mech. 639 (2009), 239 JFM copy	Jerome Neufeld and Herbert Huppert
The waterlogging of floating objects	We study how a very porous body (such as a piece of pumice) sucks water in, becomes denser and ultimately sinks. This allows to estimate how long the 'pumice rafts' formed sometime formed after volcanic eruptions should be expected to float.	J. Fluid Mech. 585 (2007), 245 JFM copy	Herbert Huppert
Gravity currents in a porous medium at an inclined plane	We study how a dense fluid spreads through a porous medium along an inclined plane.	J. Fluid Mech. 555 (2006), 353 arXiv:physics/0512168	Herbert Huppert

Particle Rafts

With a large number of particles floating at an air-water interface, the cheerios attraction causes a qualitative change in the behaviour of the interface: it looks more like an elastic solid than a fluid. The rheology of these interfaces is complicated, however. I am interested in characterizing and understanding it better.

Title	Main Idea	Published?	Co-worker(s)
Granular character of particle rafts	We show that, according to certain tests, particle rafts demonstrate granular (as well as elastic) characteristics	Phys. Rev. Lett. 102 (2009), 138302 arxiv:0901.2801	Pietro Cicuta
Dynamics of surfactant-driven fracture of particle rafts	We study how a particle raft fractures when you add a drop of surfactant to the raft.	Phys. Rev. Lett. 96 (2006), 178301 arXiv:cond-mat/0509781	H.-Y. Kim, P. Aussillous and L. Mahadevan
Elasticity of particle rafts	We characterize the elastic properties of a dense assembly of particles at an interface	Europhys. Lett. 68 (2004), 212 arXiv:cond-mat/0406723	P. Aussillous and L. Mahadevan

The Cheerios Effect

When two, or more, objects of the same type float on water, they attract one another because of their weight and the surface tension of the interface. This is often referred to as the 'Cheerios effect' since it is often observed in breakfast cereals but can equally be seen in a glass of sparkling water or many other situations. The dynamics of the interaction have not been studied in any detail, but we showed that a very simple model of the dynamics gives reasonably good agreement with simple experimental results.

Title	Main Idea	Published?	Co-worker(s)
The 'Cheerios effect'	A pedagogical article looking at the aggregation of floating objects. We explore a series of classic calculations bearing in mind the physical picture of the Cheerios interaction.	Am. J. Phys. 73 (2005), 814 arXiv:cond-mat/0411688	L. Mahadevan
The wall-induced motion of a floating flexible train	We study with theory and experiment the zippering motion of a flexible train of rods at an interface	J. Fluid Mech. 502 (2004), 89 PDF (276 KB)	H.-Y. Kim and L. Mahadevan

How to Sink Things

My PhD Thesis was largely concerned with when surface tension allows small, dense objects to float at an interface. My thesis (entitled `The Fluid Mechanics of Floating and Sinking') can be obtained here. The papers that made up this thesis are listed in the table below, along with some extras.

Title	Main Idea	Published?	Co-worker(s)
Floating Objects with Finite Resistance to Bending	We show how an object's flexibility can compromise its ability to float with particular reference to the long, thin legs of pond skaters (water striders).	Langmuir 24 (2008), 8701 Langmuir copy	None
Surface tension dominated impact	We study the impact of a very small object onto an interface at high Reynolds number and determine quantitatively how as the impact speed increases the maximum weight the object can have and still float decreases.	Phys. Fluids 19 (2007), 072108 Phys. Fluids copy	P. D. Metcalfe
The load supported by small floating objects	We give conditions on the density and radius of a small object for it to be able to float. In particular, we study how the hydrophobicity of the object affects the critical density at which sinking occurs.	Langmuir 22 (2006), 5979 Langmuir copy	D. G. Lee and H.-Y. Kim
Equilibrium Conditions for the Floating of Multiple Interfacial Objects	We give conditions under which multiple objects can remain afloat at an interface. In particular, we look at two parallel strips and then generalise this to a continuum raft of strips.	J. Fluid Mech. 549 (2006), 215 arXiv:physics/0509009	P. D. Metcalfe and R. J. Whittaker
Sinking of a horizontal cylinder	This is a first attempt to model the dynamics of sinking. The model is a bit naive but is in good agreement with experiments.	Langmuir 22 (2006), 2972 Langmuir copy	D. G. Lee and H.-Y. Kim
The Physics of Floating	A pedagogical article outlining the generalisation of Archimedes' Principle to include surface tension. This is used to calculate the maximum density of a cylinder that can remain afloat for various values of the radius.	Eureka 57 (2005), 26 PDF (160 KB)	None

This page was most recently updated on the 7^th of January, 2010.