Dynamical regimes of directional viscous fingering: Spatiotemporal chaos and wave propagation

Rabaud, Marc; Michalland, S.; Couder, Y.

doi:10.1103/physrevlett.64.184

Cited by 179 publications

(108 citation statements)

References 23 publications

Supporting

Mentioning

103

Contrasting

Order By: Relevance

“…Many studies have been devoted to this problem in the case of stationary spatial patterns and more recently in the case of oscillatory instabilities and non-linear traveling-waves patterns. For example, Rayleigh-Bénard convection [2] and directional viscous fingering [3] in quasi one-dimensional experiments have revealed a transition to spatio-temporal chaos via spatio-temporal intermittency. On the other hand, non-linear traveling-waves have exhibited a fascinating variety of behaviors and patterns.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear dynamics of waves and modulated waves in 1D thermocapillary flows. II. Convective/absolute transitions

Garnier¹,

Chiffaudel²,

Daviaud³

2003

Physica D: Nonlinear Phenomena

View full text Add to dashboard Cite

We present experimental results on hydrothermal traveling-waves dynamics in long and narrow 1D channels. The onset of primary traveling-wave patterns is briefly presented for different fluid heights and for annular or bounded channels, i.e., within periodic or non-periodic boundary conditions. For periodic boundary conditions, by increasing the control parameter or changing the discrete mean-wavenumber of the waves, we produce modulated waves patterns. These patterns range from stable periodic phase-solutions, due to supercritical Eckhaus instability, to spatio-temporal defect-chaos involving traveling holes and/or counter-propagating-waves competition, i.e., traveling sources and sinks. The transition from non-linearly saturated Eckhaus modulations to transient pattern-breaks by traveling holes and spatiotemporal defects is documented. Our observations are presented in the framework of coupled complex Ginzburg-Landau equations with additional fourth and fifth order terms which account for the reflection symmetry breaking at high wave-amplitude far from onset. The second part of this paper [1] extends this study to spatially non-periodic patterns observed in both annular and bounded channel.

show abstract

Section: Introductionmentioning

confidence: 99%

Nonlinear dynamics of waves and modulated waves in 1D thermocapillary flows. II. Convective/absolute transitions

Garnier¹,

Chiffaudel²,

Daviaud³

2003

Physica D: Nonlinear Phenomena

View full text Add to dashboard Cite

show abstract

“…There are a lot of experiments with a very rich phenomenology for which a whole description is not available. Experimental systems with such dynamics are Taylor-Couette [10], laterally heated fluid layers (for high fluid depths) [2], directional solidification [11][12][13][14][15], directed fingering (printer instability) [16][17][18], laser spectra [19], Rayleigh-Bénard [20][21][22][23] and Rayleigh-Taylor [24][25][26][27][28] instabilities.…”

Section: Introductionmentioning

confidence: 99%

One-dimensional dynamics in locally heated liquid layers

Burguete

Maza

Mancini

2003

Physica D: Nonlinear Phenomena

View full text Add to dashboard Cite

Recent results on one-dimensional patterns in locally heated experiments are presented. A fluid layer is heated locally by a nearly one-dimensional heater, and subjected to both horizontal and vertical temperature gradients. Depending on the fluid depth and on the temperature difference established across the layer different convective regimes appear. When a very small temperature gradient is applied a basic convective state appears. It consists of two big rolls parallel to the heater and filling the convective cell. A primary instability in the homogeneous basic flow gives rise to a one-dimensional cellular stationary pattern. For higher values of the control parameters, time-dependent patterns appear through a secondary instability. Various regimes are analyzed: oscillations, traveling waves and alternating patterns. The hydrodynamic characteristics of these patterns are provided. Local temperature measurements allows to describe the physical mechanisms responsible for the instabilities. The similarities and discrepancies of the experimental data with some theoretical models are provided.

show abstract

“…Despite the complexity of the underlying flow, the authors determined that the finger length l is inversely proportional to the tangent of the elastic wall's inclination angle; this remarkably simple relationship suggests that, for a given fluid layer thickness, the fingers extend to a constant reopening height. Interestingly, these properties appear analogous to those observed in the viscous adhesive problem as well as the so-called printer's instability (Rabaud et al 1990). Such short, flattipped, viscous fingers are very different to those normally observed in a Hele-Shaw flow, and in fact look more like molar teeth than fingers!…”

Section: Short Flat-tipped Viscous Fingersmentioning

confidence: 57%

Short, flat-tipped, viscous fingers: novel interfacial patterns in a Hele-Shaw channel with an elastic boundary

McCue

2017

J. Fluid Mech.

View full text Add to dashboard Cite

Injecting a less viscous fluid into a more viscous fluid in a Hele-Shaw cell triggers two-dimensional viscous fingering patterns which are characterised by increasingly long fingers undergoing tip splitting and branching events. These complex structures are considered to be a paradigm for interfacial pattern formation in porous media flow and other related phenomena. Over the past five years, there has been a flurry of interest in manipulating these interfacial fingering patterns by altering the physical components of the Hele-Shaw apparatus. In this Focus on Fluids article, we summarise some of this work, concentrating on a very recent study in which the alterations include replacing one of the two bounding plates with an elastic membrane (Ducloué et al., J. Fluid Mech., vol. 826, 2017, R2). The resulting experimental set-up gives rise to a wide variety of novel interfacial patterns including periodic sideways fingers, dendritic-like patterns and short, flat-tipped viscous fingers that appear to resemble molar teeth. These latter fingers are similar to those observed in the printer's instability and when peeling off a layer of adhesive tape. This delightful work brings together a number of well-studied themes in interfacial fluid mechanics, including how viscous and surface tension forces compete to drive fingering patterns, how interfaces are affected by fluid-solid interactions and, finally, how novel strategies can be implemented to control interfacial instabilities.

show abstract

Dynamical regimes of directional viscous fingering: Spatiotemporal chaos and wave propagation

Cited by 179 publications

References 23 publications

Nonlinear dynamics of waves and modulated waves in 1D thermocapillary flows. II. Convective/absolute transitions

Nonlinear dynamics of waves and modulated waves in 1D thermocapillary flows. II. Convective/absolute transitions

One-dimensional dynamics in locally heated liquid layers

Short, flat-tipped, viscous fingers: novel interfacial patterns in a Hele-Shaw channel with an elastic boundary

Contact Info

Product

Resources

About