Fractal growth viscous fingers: quantitative characterization of a fluid instability phenomenon

Nittmann, J.; Daccord, G.; Stanley, H. Eugene

doi:10.1038/314141a0

Cited by 592 publications

(187 citation statements)

References 14 publications

Supporting

Mentioning

170

Contrasting

Unclassified

Order By: Relevance

“…The &point local slopes were calculated as the slope of a least-squares line fit to every 8 successive points. This protocol has been successfully applied to a wide range of fractal objects (Nittmann et al, 1985;Daccord et al, 1986;Daccord, 1987;Daccord and Lenormand, 1987). To extend these methods to 3 dimensions, we counted all the mass (pixels) inside spheres of various radii instead of disks.…”

Section: Methodology For Fractal Analysismentioning

confidence: 99%

Determination of fractal dimension of physiologically characterized neurons in two and three dimensions

Caserta

Eldred

Fernández

et al. 1995

Journal of Neuroscience Methods

158

126

View full text Add to dashboard Cite

Although there is a growing interest in the application of fractal analysis in neurobiology, questions about the methodology have restricted its wider application. In this report we discuss some of the underlying principles for fractal analysis. we propose the cumulative-mass method as a standard method and we extend the applicability of fractal analysis to both 2 and 3 dimensions. We have examined the relationship between the method of log-log Sholl analysis and fractal analysis and have found that they correlate well. Measurements of physiologically characterized retinal ganglion cells indicate that different cell types can have significantly different fractal dimensions. Such differences may allow the correlation of the physiological type of a neuron with its morphological fractal dimension.

show abstract

Section: Methodology For Fractal Analysismentioning

confidence: 99%

Determination of fractal dimension of physiologically characterized neurons in two and three dimensions

Caserta

Eldred

Fernández

et al. 1995

Journal of Neuroscience Methods

158

126

View full text Add to dashboard Cite

show abstract

“…[32]. Simulations [33] and experiments [34,35] probing the Saffman-Taylor instability led to the conclusions that no interfacial tension exists between miscible fluids; in particular, the observation of a fractal-like interface between two miscible fluids was attributed to a vanishing interfacial energy cost, i.e., to Γ e ¼ 0 [34,35]. This has to be contrasted with experiments and simulations on miscible fluids probing capillary waves [14,15,36], the shape of drops and menisci [13,16,17,37,38], and that of patterns in hydrodynamic instabilities [18,[27][28][29][39][40][41], which all claimed the existence of an effective interfacial tension.…”

Section: Introductionmentioning

confidence: 99%

Nonequilibrium Interfacial Tension in Simple and Complex Fluids

et al. 2016

View full text Add to dashboard Cite

Interfacial tension between immiscible phases is a well-known phenomenon, which manifests itself in everyday life, from the shape of droplets and foam bubbles to the capillary rise of sap in plants or the locomotion of insects on a water surface. More than a century ago, Korteweg generalized this notion by arguing that stresses at the interface between two miscible fluids act transiently as an effective, nonequilibrium interfacial tension, before homogenization is eventually reached. In spite of its relevance in fields as diverse as geosciences, polymer physics, multiphase flows, and fluid removal, experiments and theoretical works on the interfacial tension of miscible systems are still scarce, and mostly restricted to molecular fluids. This leaves crucial questions unanswered, concerning the very existence of the effective interfacial tension, its stabilizing or destabilizing character, and its dependence on the fluid's composition and concentration gradients. We present an extensive set of measurements on miscible complex fluids that demonstrate the existence and the stabilizing character of the effective interfacial tension, unveil new regimes beyond Korteweg's predictions, and quantify its dependence on the nature of the fluids and the composition gradient at the interface. We introduce a simple yet general model that rationalizes nonequilibrium interfacial stresses to arbitrary mixtures, beyond Korteweg's small gradient regime, and show that the model captures remarkably well both our new measurements and literature data on molecular and polymer fluids. Finally, we briefly discuss the relevance of our model to a variety of interface-driven problems, from phase separation to fracture, which are not adequately captured by current approaches based on the assumption of small gradients.

show abstract

“…Quite non-intuitively, a thin film is observed to be drawn out from the drop in a direction that opposes that of the SAW propagation due to the dominant Rayleigh streaming in the film. Fresnel diffraction of the acoustic wave as a consequence of the finite aperture of the electrodes used to generate the SAW, however, leads to transverse variations in the speed at which the film front advances, in turn driving a front instability reminiscent of, but distinct from, viscous and granular fingering instabilities [19][20][21][22][23] . Finally, rather unique 'soliton-like' wave train pulses were observed to grow above these fingers; these are subsequently transported away along the propagation direction of the SAW under the influence of long-range Eckart streaming that dominates when the wave pulses grow beyond a critical height commensurate with the SAW wavelength.…”

mentioning

confidence: 99%

Unique fingering instabilities and soliton-like wave propagation in thin acoustowetting films

et al. 2012

View full text Add to dashboard Cite

Acoustic-fluid interactions not only has had a long history but has recently experienced renewed scrutiny because of their vast potential for microscale fluid and particle manipulation. Here we unravel a fascinating and anomalous ensemble of dynamic 'acoustowetting' phenomena in which a thin film drawn from a sessile drop first spreads in opposition to the acoustic wave propagation direction. The advancing film front then exhibits fingering instabilities akin to classical viscous fingering, but arising through a different and novel mechanism: transverse Fresnel diffraction of the underlying acoustic wave. Peculiar 'solitonlike' wave pulses are observed to grow above these fingers, which, on reaching a critical size, translate away along the wave propagation direction. By elucidating the complex hydrodynamics underpinning the spreading, and associated flow reversal and instability phenomena, we offer insight into the possibility of acoustically controlling fast and uniform film spreading, constituting a flexible and powerful alternative for microfluidic transport.

show abstract

Fractal growth viscous fingers: quantitative characterization of a fluid instability phenomenon

Cited by 592 publications

References 14 publications

Determination of fractal dimension of physiologically characterized neurons in two and three dimensions

Determination of fractal dimension of physiologically characterized neurons in two and three dimensions

Nonequilibrium Interfacial Tension in Simple and Complex Fluids

Unique fingering instabilities and soliton-like wave propagation in thin acoustowetting films

Contact Info

Product

Resources

About