منابع مشابه
Imperfect Hele - Shaw cells
2014 The covering surfaces of a Hele-Shaw cell may be roughened mechanically, or modified by random chemical patches which change the wetting properties. We discuss first the quasi-static injection of a single fluid (with a finite contact angle 03B8e) in an imperfect cell. The shape of the injected region depends critically on a dimensionless number i (ratio of the boundary energy 03C4 over the...
متن کاملSingularity Formation in Hele-Shaw Bubbles
We provide numerical and analytic evidence for the formation of a singu-larity driven only by surface tension in the mathematical model describing a two-dimensional Hele-Shaw cell with no air injection. Constantin and Pugh have proved that no such singularity is possible if the initial shape is close to a circle; thus we show that their result is not true in general. Our evidence takes the form...
متن کاملA kinetic formulation of Hele-Shaw flow
In this note we consider a fourth order degenerate parabolic equation modeling the evolution of the interface of a spreading droplet. The equation is approximated trough a collisional kinetic equation. This permits to derive numerical approximations that preserves positivity of the solution and the main relevant physical properties. A Monte Carlo application is also shown. Formulation cinétique...
متن کاملA Multiphase Hele-shaw Flow with Solidification
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 ...
متن کاملContracting bubbles in Hele-Shaw cells
The problem of bubble contraction in a Hele-Shaw cell is studied for the case in which the surrounding fluid is of power-law type. A small perturbation of the radially symmetric problem is first considered, focussing on the behaviour just before the bubble vanishes, it being found that for shear-thinning fluids the radially symmetric solution is stable, while for shear-thickening fluids the asp...
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ژورنال
عنوان ژورنال: ANNALI DELL'UNIVERSITA' DI FERRARA
سال: 2020
ISSN: 0430-3202,1827-1510
DOI: 10.1007/s11565-020-00339-1