Identities for droplets with circular footprint on tilted surfaces.

Exact mathematical identities are presented between the relevant parameters of droplets displaying circular contact boundary based on flat tilted surfaces. Two of the identities are derived from the force balance, and one from the torque balance. The tilt surfaces cover the full range of inclinations for sessile or pendant drops, including the intermediate case of droplets on a wall (vertical surface).

Pinning of a drop by a junction on an incline.

The shape of a drop pinned on an inclined substrate is a long-standing problem where the complexity of real surfaces, with heterogeneities and hysteresis, makes it complicated to understand the mechanisms behind the phenomena. Here we consider the simple case of a drop pinned on an incline at the junction between a hydrophilic half plane (the top half) and a hydrophobic one (the bottom half). Relying on the equilibrium equations deriving from the balance of forces, we exhibit three scenarios depending on the way the contact line of the drop on the substrate either simply leans against the junction or overfills (partly or fully) into the hydrophobic side.

Contact angles of a drop pinned on an incline.

For a drop on an incline with small tilt angle α, when the contact line is a circle of radius r, we derive the relation mgsinα=γrπ/2(cosθ^{min}-cosθ^{max}) at first order in α, where θ^{min} and θ^{max} are the contact angles at the back and at the front, m is the mass of the drop and γ the surface tension of the liquid. We revisit in this way the Furmidge model for a large range of contact angles. We also derive the same relation at first order in the Bond number B=ρgR^{2}/γ, where R is the radius of the spherical cap at zero gravity.

Is superhydrophobicity robust with respect to disorder?

We consider theoretically the Cassie-Baxter and Wenzel states describing the wetting contact angles for rough substrates. More precisely, we consider different types of periodic geometries such as square protrusions and disks in 2D, grooves and nanoparticles in 3D and derive explicitly the contact angle formulas. We also show how to introduce the concept of surface disorder within the problem and, inspired by biomimetism, study its effect on superhydrophobicity.

Pareto genealogies arising from a Poisson branching evolution model with selection.

We study a class of coalescents derived from a sampling procedure out of N i.i.d.

On the extended Moran model and its relation to coalescents with multiple collisions.

We study the asymptotics of the extended Moran model as the total population size N tends to infinity. Two convergence results are provided, the first result leading to discrete-time limiting coalescent processes and the second result leading to continuous-time limiting coalescent processes. The limiting coalescent processes allow for multiple mergers of ancestral lineages (Λ-coalescent).