Singularities of the Hele-Shaw Flow and Shock Waves in Dispersive Media

Bettelheim, Eldad; Agam, Oded; Zabrodin, A.; Wiegmann, P.

doi:10.1103/physrevlett.95.244504

Cited by 18 publications

(35 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Of particular importance is the limit where the characteristic finger width, set by the mostunstable wavelength, l c , approaches zero. In that case, it was expected that highly ramified fractal structures, similar to diffusion-limited aggregation, would form [15][16][17][18] .…”

mentioning

confidence: 99%

Fingering versus stability in the limit of zero interfacial tension

2014

View full text Add to dashboard Cite

The invasion of one fluid into another of higher viscosity in a quasi-two dimensional geometry typically produces complex fingering patterns. Because interfacial tension suppresses short-wavelength fluctuations, its elimination by using pairs of miscible fluids would suggest an instability producing highly ramified singular structures. Previous studies focused on wavelength selection at the instability onset and overlooked the striking features appearing more globally. Here we investigate the non-linear growth that occurs after the instability has been fully established. We find a rich variety of patterns that are characterized by the viscosity ratio between the inner and the outer fluid, Z in /Z out , as distinct from the mostunstable wavelength, which determines the onset of the instability. As Z in /Z out increases, a regime dominated by long highly-branched fractal fingers gives way to one dominated by blunt stable structures characteristic of proportionate growth. Simultaneously, a central region of complete outer-fluid displacement grows until it encompasses the entire pattern at Z in /Z out E0.3.

show abstract

mentioning

confidence: 99%

Fingering versus stability in the limit of zero interfacial tension

2014

View full text Add to dashboard Cite

show abstract

“…This requires the simultaneous existence of a local cusp structure and a global fractal structure in granular fingering patterns [235]. This was confirmed experimenally for a radial Hele Shaw flow in [236].…”

Section: Pattern Formationmentioning

confidence: 58%

Novel experimentally observed phenomena in soft matter

Bandyopadhyay

2013

Pramana - J Phys

View full text Add to dashboard Cite

Abstract. Soft materials such as colloidal suspensions, polymer solutions and liquid crystals are constituted by mesoscopic entities held together by weak forces. Their mechanical moduli are several orders of magnitude lower than those of atomic solids. The application of small to moderate stresses to these materials results in the disruption of their microstructures. The resulting flow is non-Newtonian and is characterised by features such as shear rate-dependent viscosities and nonzero normal stresses. This article begins with an introduction to some unusual flow properties displayed by soft matter. Experiments that report a spectrum of novel phenomena exhibited by these materials, such as turbulent drag reduction, elastic turbulence, the formation of shear bands and the existence of rheological chaos, flow-induced birefringence and the unusual rheology of soft glassy materials, are reviewed. The focus then shifts to observations of the liquid-like response of granular media that have been subjected to external forces. The article concludes with examples of the patterns that emerge when certain soft materials are vibrated, or when they are displaced with Newtonian fluids of lower viscosities.

show abstract

“…Hence if we assume that (w, v) are even functions of ǫ, then as a consequence of the invariance of (20) under the transformation (16) we deduce that (U, V) are even functions of ǫ too. In this way we have…”

Section: Invariant Solutionsmentioning

confidence: 98%

“…Furthermore, by identifying the coefficient of ǫ 2j in the first equation of the system (20) and by taking into account that (z − u c ) 2 = r c + 4 v c it follows that…”

Section: Invariant Solutionsmentioning

confidence: 99%

The double scaling limit method in the Toda hierarchy

Alonso¹,

Медина²

2008

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

Critical points of semiclassical expansions of solutions to the dispersionful Toda hierarchy are considered and a double scaling limit method of regularization is formulated. The analogues of the critical points characterized by the strong conditions in the Hermitian matrix model are analyzed and the property of doubling of equations is proved. A wide family of sets of critical points is introduced and the corresponding double scaling limit expansions are discussed.

show abstract

Singularities of the Hele-Shaw Flow and Shock Waves in Dispersive Media

Cited by 18 publications

References 16 publications

Fingering versus stability in the limit of zero interfacial tension

Fingering versus stability in the limit of zero interfacial tension

Novel experimentally observed phenomena in soft matter

The double scaling limit method in the Toda hierarchy

Contact Info

Product

Resources

About