Some Isoperimetric Inequalities in Electrochemistry and Hele Shaw Flows

Isoperimetric inequalities are applied to a moving-boundaryproblem for doubly-connected domains. This problem occurs forexample in electrochemistry, in which case the domains in questionare the electrolyte of an electrolytic cell. The two electrodessurrounding the electrolyte are assumed to grow or dissolve,at different rates in general, by electrochemical reaction.We obtain optimal estimates showing, for example, that the leastchange in volume of each electrode always occurs in sphericalsymmetry.     

The flow of an Oldroyd fluid around a sharp corner

A similarity solution is constructed for the flow of an Oldroyd-B fluid around a 270° re-entrant comer. The velocity is found to vanish like r^5/9 and the stress to be singular like r^−2/3. A simple expression is found for the streamfunction.     

Tackiness and cohesive failure of granular pastes: Mechanistic aspects

Granular pastes are dense dispersions of non-colloidal grains in a simple or a complex fluid. Typical examples are the coating, gluing or sealing mortars used in building applications. We study the rupture of a thick layer of mortar paste in a simple pulling test where the paste is confined between two flat surfaces. It is shown that, depending on the rheological properties of the paste and the plate separation velocity, two main failure modes are obtained. The first mode is the inwards shear flow of the paste with viscous fingering instabilities, similarly to what has been observed with Newtonian fluids and with non-Newtonian colloidal suspensions or polymer solutions. The second failure mode is stemming from the expansion of bubbles, similarly to what has been observed in soft adhesive polymer layers and, more recently, in highly viscous fluids. It is shown that the crossover between the two failure modes is determined by the conditions required to generate a pressure drop able to trigger the growth of pre-existing micro-bubbles smaller than the inter-granular distance.     

Lineshapes in quasi-elastic scattering from species hopping between non-equivalent surface sites

We present an analytic model applied to quasi-elastic scattering from an adsorbed surface species undergoing jump diffusion between adsorption sites described by a Bravais lattice combined with a basis of multiple points. The model allows for hops between adsorption sites which are both symmetrically and energetically inequivalent. We give results for 1-D hopping, which are applicable to a species jumping between the top and bridge sites along the [11?0] direction on an fcc-(110) surface or for jumps along a step edge. In 2-D, results for hopping between fcc and hcp hollow sites and between the bridge sites of an fcc-(111) surface are presented. These examples give characteristic signatures which will allow these forms of motion to be recognized in experimental data and will enable the underlying physical parameters to be extracted by comparison with the analytical forms derived here.