We propose to combine image registration and volumetric reconstruction from a monocular video of a draining off Hele-Shaw cell filled with water. A Hele-Shaw cell is a tank whose depth is small (e.g. 1 mm) compared to the other dimensions (e.g. 400 × 800 mm2). We use a technique known as molecular tagging which consists in marking by photobleaching a pattern in the fluid and then tracking its d...

Several mathematical models of tumor growth are now commonly used to explain medical observations and predict cancer evolution based on images. These models incorporate mechanical laws for tissue compression combined with rules for nutrients availability which can differ depending on the situation under consideration, in vivo or in vitro. Numerical solutions exhibit, as expected from medical ob...

Submitted for the DFD11 Meeting of The American Physical Society Hydrodynamic instability induced by a precipitation reaction in a Hele-Shaw cell YUKI ISHII, YUICHIRO NAGATSU, Nagoya Institute of Technology, 466-8555, Japan, ANNE DE WIT, Nonlinear Physical Chemistry Unit, CP 231, Université Libre de Bruxelles (ULB), 1050 Brussels, Belgium — We experimentally demonstrate hydrodynamic fingering d...

We report the results of three dimensional molecular dynamic simulations on the angle of repose of a sandpile formed by pouring mono-sized cohesionless spherical grains into a granular Hele-Shaw cell. In particular, we are interested to investigate the effects of those variables which may impact significantly on pattern formation of granular mixtures in Hele-Shaw cells. The results indicate tha...

In this paper, we give a precise description of the rescaling behaviors of global strong polynomial solutions to the reformulation of zero surface tension Hele-Shaw problem driven by injection, the PolubarinovaGalin equation, in terms of Richardson complex moments. From past results, we know that this set of solutions is large. This method can also be applied to zero surface tension Stokes flow...

A family of two-dimensional Faraday waves in extremely shallow depth (1 mm to 2 mm) of absolute ethanol are observed experimentally using a Hele-Shaw cell that vibrates vertically. The same phenomena are not observed by means of water, ethanol solution, and silicone oil. These Faraday waves are quite different from the traditional ones. These phenomena are helpful to deepen and enrich our under...

For the free boundary dynamics of the two-phase Hele-Shaw and Muskat problems, and also for the irrotational incompressible Euler equation, we prove existence locally in time when the Rayleigh-Taylor condition is initially satisfied for a 2D interface. The result for water waves was first obtained by Wu in a slightly different scenario (vanishing at infinity), but our approach is different beca...

Fractal viscous fingering patterns are observed in an infinite Hele-Shaw cell at long times when the capillary forces become negligible. On the contrary, growth of monocrystals from a punctual seed shows dendrites growing independently in 4 or 6 directions, according to the crystal symmetry. A close comparison of numerical and experimental data explains first the origin of the tip-splitting ins...

This paper is concerned with the motion of an incompressible, viscous fluid in a Hele–Shaw cell. The free surface is moving under the influence of gravity and the fluid is modelled using a modified Darcy law for Stokesian fluids. We combine results from the theory of quasilinear elliptic equations, analytic semigroups and Fourier multipliers to prove existence of a unique classical solution to ...

Hele-Shaw flow describes the slow flow of a viscous liquid between two parallel plates separated by a small gap. In some configurations such a flow generates instabilities known as Saffman-Taylor fingers, which form intricate visual patterns. While these patterns have been an inspiration for artists, as well as thoroughly analyzed by mathematicians, efficiently simulating them remains challengi...