High Rayleigh number (4 x 104-3 × 107) quasi-two-dimensional convection is studied experimentally, numerically, and theoretically. The fluid is contained in an isothermal Hele-Shaw cell, which enforces the two dimensionality, and the convection is driven by an externally imposed vertical concentration gradient. The full two dimensional concentration field is imaged experimentally and is sampled...

The one-phase Hele-Shaw flow has a long history and has been extensively studied from several point of views ranging from the fluid dynamical beginnings to complex analysis and integrable systems, see [5]. We prove existence, using the implicit function theorem, of a solution Wε in the Bochner space L2(0, T ;H1 0 (Ω;Rm)) to a non-local in time semi-linear system of coupled PDEs of second order ...

Existence and uniqueness of classical solutions for the multidimensional expanding Hele–Shaw problem are proved. 1. The problem. We are concerned with a class of moving boundary problems for bounded domains in R n , which comprise in particular the so-called single phase Hele–Shaw problem. In order to describe precisely the involved geometry, let Ω be a bounded domain in R n and assume that its...

Granular materials constitute an intermediate state of matter between fluids and solids[1]. Over the past decade, a large series of experimental assays on granular systems, concentrated in the quantitative studies of compaction, mixing, segregation and patterns formed by vibration, have been done[2-9]. They uncovered numerous mechanisms (percolation, convection, ordered settling, arching, etc.)...

Fundamentals of nonlinear wave-particle interactions are studied in a Hele-Shaw configuration with wave breaking and a dynamic bed. To design this configuration, we determine, mathematically, the gap width which allows inertial flows to survive the viscous damping due to the side walls. Damped wave sloshing experiments compared with simulations confirm that width-averaged potential-flow models ...