Analysis of a one-dimensional free boundary flow problem

Caboussat, Alexandre; Rappaz, Jacques

doi:10.1007/s00211-005-0619-0

Cited by 6 publications

(7 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The free surface of this compressed droplet is a surface of mean curvature R; this is not a circular arc of constant radius as R 1 varies with height. To obtain R i,1 and R i,2 of the droplet, we fit the surface using the the method of Caboussat and Glowinski 44 (an algorithm to generate the surface of a droplet compressed between two boundaries). In Fig.…”

Section: A1 Measurable Variablesmentioning

confidence: 99%

Experimental study of forces between quasi-two-dimensional emulsion droplets near jamming

et al. 2013

View full text Add to dashboard Cite

We experimentally study the jamming of quasi-two-dimensional emulsions. Our experiments consist of oil-in-water emulsion droplets confined between two parallel plates. From the droplet outlines, we can determine the forces between every droplet pair to within 8% over a wide range of area fractions φ . We study three bidisperse samples that jam at area fractions φ c ≈ 0.86. Our data show that for φ > φ c , the contact numbers and pressure have power-law dependence on φ − φ c in agreement with the critical scaling found in numerical simulations. Furthermore, we see a link between the interparticle force law and the exponent for the pressure scaling, supporting prior computational observations. We also observe linear-like force chains (chains of large interdroplet forces) that extend over 10 particle lengths, and examine the origin of their linearity. We find that the relative orientation of large force segments are random and that the tendency for force chains to be linear is not due to correlations in the direction of neighboring large forces, but instead occurs because the directions are biased towards being linear to balance the forces on each droplet.

show abstract

Section: A1 Measurable Variablesmentioning

confidence: 99%

Experimental study of forces between quasi-two-dimensional emulsion droplets near jamming

et al. 2013

View full text Add to dashboard Cite

show abstract

“…The existence of a semi-discrete approximation (u h , s h ) is ensured, see [22], and there exists 0 <T ≤ T (T independent of h > 0) and a constant C independent of h such that ||u h || H 1 (0,T ,V h ) ≤ C f L 2 (QT ) + |u 0 | V . A priori error estimates are obtained in the following theorem, whose proof is based on [72]: Theorem A.3 (A priori error estimate).…”

Section: Analysis Of a One-dimensional Problemmentioning

confidence: 99%

“…All the proofs that have been disregarded here can be found in [22] for details concerning the one-dimensional problem and in [19] for details about the two-dimensional problem. Observe that the solvability of the corresponding problems with given moving boundary has also been obtained.…”

Section: Extension To the Two-dimensional Problemmentioning

confidence: 99%

“…Results about this one-dimensional free surface problem are summarized here and extracted from [22]. The well-posedness of the problem is proved and error estimates for the semi-discretization in space are obtained, following [24,72] for the a priori error analysis and [160] for a posteriori error estimates.…”

Section: Introductionmentioning

confidence: 99%

“…The well-posedness of the problem is proved and error estimates for the semi-discretization in space are obtained, following [24,72] for the a priori error analysis and [160] for a posteriori error estimates. We refer to [19,22] for details and demonstrations.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Numerical simulation of two-phase free surface flows

Caboussat

2005

Arch. Comput. Meth. Engng.

Self Cite

View full text Add to dashboard Cite

Free surface flows are of most interest in many engineering or mathematical problems and many methods have been developed for their numerical resolution in various fields of the physics or the engineering. In this work, the volume-of-fluid method is used for the numerical simulation of two-phase free surface flows involving an incompressible liquid and a compressible gas and taking into account the surface tension effects. The incompressible Navier-Stokes equations are assumed to hold in the liquid domain, while the dynamical effects in the ideal gas are disregarded. A time splitting scheme is used together with a two-grids method for the space discretization. An original algorithm is introduced to track the bubbles of gas trapped in the liquid. Numerical results are presented in the frame of mold filling and bubbles and droplets flows. Some theoretical results concerning free boundary problems are also summarized.

show abstract