Molecular visualization of conformation-triggered flow instability

A new type of flow fingering instability was observed in monolayer-thick polymer films as they spread on a solid substrate. Tracing the movement of individual molecules by atomic force microscopy enabled us to follow the development of the flow instability on the molecular level and to understand the underlying physical mechanism. The fingering instability was observed to be triggered by conformational changes of brushlike macromolecules in response to the pressure gradient driving the flow.     

Fingering instability in forward smolder combustion

We use numerical strategies to examine the linear and nonlinear stability of forward smolder waves in the framework of a simplified thermal–diffusive model, with the hydrodynamic effects completely filtered out. The configuration consists of a horizontal thin solid fuel, over which air blows in the same direction as the smolder front propagation. It is found that, in the absence of convective heat losses, the whole one-dimensional adiabatic solution branch is linearly stable; in contrast, when the convective heat loss effect is taken into account, fingering instability emerges provided the incoming air flow rate is within a narrow range near the one-dimensional extinction limit, a manifestation that is reminiscent of the familiar cellular instability occurring in the context of low-Lewis-number diffusion flames. Accordingly, the fingering instability herein identified in forward smolder combustion is purely thermal–diffusive in nature. Furthermore, a heuristic analysis by drawing an analogy with premixed flame suggests that the occurrence of such fingering instability is the joint consequence of the Lewis number effects and convective heat losses. It is proposed that a Hele–Shaw-type combustion channel may be adopted to experimentally reveal the fingering patterns predicted by current numerical simulations.     

Fingering instability in combustion: an extended view

We detail the experimental situation concerning the fingering instability that occurs when a solid fuel is forced to burn against a horizontal oxidizing wind. The instability appears when the Rayleigh number for convection is below criticality. The focus is on the developed fingering state. We present direct measurements of the depletion of oxygen by the front as well as new results that connect heat losses to the characteristic scale of the instability. In addition, we detail the experimental system, elaborate (qualitatively and quantitatively) on the results that were previously presented, and discuss new observations. We also show that the same phenomenological model applies to electrochemical deposition.     

Influence of double diffusive effects on miscible viscous fingering

Miscible viscous fingering classically occurs when a less viscous fluid displaces a miscible more viscous one in a porous medium. We analyze here how double diffusive effects between a slow diffusing S and a fast diffusing F component, both influencing the viscosity of the fluids at hand, affect such fingering, and, most importantly, can destabilize the classically stable situation of a more viscous fluid displacing a less viscous one. Various instability scenarios are classified in a parameter space spanned by the log-mobility ratios R(s) and R(f) of the slow and fast component, respectively, and parametrized by the ratio of diffusion coefficients δ. Numerical simulations of the full nonlinear problem confirm the existence of the predicted instability scenarios and highlight the influence of differential diffusion effects on the nonlinear fingering dynamics.     

Fingering of chemical fronts in porous media

The influence of chemical reactions on the hydrodynamical fingering instability is analyzed for miscible systems in porous media. Using a realistic reaction scheme, it is shown that the stability of chemical fronts towards density fingering crucially depends on the width and the speed of the front which are functions of chemical parameters. The major difference between the pure and chemically driven fingering is that, in the presence of chemical reactions, the dispersion curves do not vary in time which has important practical experimental consequences. Good agreement with recent experimental data is found.     

Viscous Fingering Patterns in Ferrofluids

Viscous fingering occurs in the flow of two immiscible, viscous fluids between the plates of a Hele–Shaw cell. Due to pressure gradients or gravity, the initially planar interface separating the two fluids undergoes a Saffman–Taylor instability and develops fingerlike structures. When one of the fluids is a ferrofluid and a perpendicular magnetic field is applied, the labyrinthine instability supplements the usual viscous fingering instability, resulting in visually striking, complex patterns. We consider this problem in a rectangular flow geometry using a perturbative mode-coupling analysis. We deduce two general results: viscosity contrast between the fluids drives interface asymmetry, with no contribution from magnetic forces; magnetic repulsion within the ferrofluid generates finger tip-splitting, which is absent in the rectangular geometry for ordinary fluids.     

Segregation induced instabilities of granular fronts

Experimental investigation of granular flows containing particles of several sizes and moving down slopes shows that segregation of coarse-grained, irregularly shaped particles induces a fingering instability at the propagating front. The size-segregation mechanism involves percolation of small particles downward and a corresponding migration of large ones toward the flow surface. Large particles at the flow surface experience velocities that are greater than average so that they migrate forward and begin to collect at the flow front. In the case of dry cohesionless flows, the instability depends upon these large particles at the flow perimeter being more angular and thus more resistant to flow than the smaller rounder ones in the interior. A simple analytical model predicts the fingering instability when friction of the flow front is greater than that of the following flow. The presence of viscous liquid inhibits both size-segregation and the development of the instability. Fluidization of dry flows permits segregation of large particles to flow perimeters, thus increasing permeability and permitting a similar instability that owes its development to the dry frictional perimeter that surrounds a partly fluidized interior. (c) 1999 American Institute of Physics.     

Pattern formation during deformation of a confined viscoelastic layer: from a viscous liquid to a soft elastic solid

We study pattern formation during tensile deformation of confined viscoelastic layers. The use of a model system [poly(dimethylsiloxane) with different degrees of cross-linking] allows us to go continuously from a viscous liquid to an elastic solid. We observe two distinct regimes of fingering instabilities: a regime called "elastic" with interfacial crack propagation, where the fingering wavelength scales only with the film thickness, and a bulk regime called "viscoelastic," where the fingering instability shows a Saffman-Taylor-like behavior. We find good quantitative agreement with theory in both cases and present a reduced parameter describing the transition between the two regimes and allowing us to predict the observed patterns over the whole range of viscoelastic properties.     

Fingering instabilities in dewetting nanofluids

The growth of fingering patterns in dewetting nanofluids (colloidal solutions of thiol-passivated gold nanoparticles) has been followed in real time using contrast-enhanced video microscopy. The fingering instability on which we focus here arises from evaporatively driven nucleation and growth in a nanoscopically thin precursor solvent film behind the macroscopic contact line. We find that well-developed isotropic fingering structures only form for a narrow range of experimental parameters. Numerical simulations, based on a modification of the Monte Carlo approach introduced by Rabani et al. [Nature (London) 426, 271 (2003)10.1038/nature02087], reproduce the patterns we observe experimentally.     

Anomalous Richtmyer-Meshkov fingering in dissipative particle systems

We study the fingering instability induced by a shock that propagates across a perturbed interface that separates two types of discrete particles. If collisions between particles conserve energy, then the relative sizes and growth rates of the fingers are similar to those in the analogous shock-induced fingering instability in fluids. However, we show that energy loss during particle collisions, even when very small, causes the qualitative features of the finger growth to be completely opposite to the fluid case. The fingers formed by light particles grow faster and become longer and narrower than the fingers formed by heavy particles. In addition, the finger composed of light particles collapses into an extremely compact, tortuous filament, and diffusive mixing between particle types at the particle scale is heavily suppressed.     

Undulation instability of epithelial tissues

Treating the epithelium as an incompressible fluid adjacent to a viscoelastic stroma, we find a novel hydrodynamic instability that leads to the formation of protrusions of the epithelium into the stroma. This instability is a candidate for epithelial fingering observed in vivo. It occurs for sufficiently large viscosity, cell-division rate and thickness of the dividing region in the epithelium. Our work provides physical insight into a potential mechanism by which interfaces between epithelia and stromas undulate and potentially by which tissue dysplasia leads to cancerous invasion.     

Spot deformation and replication in the two-dimensional Belousov-Zhabotinski reaction in a water-in-oil microemulsion

In the limit of a large duffusivity ratio, spotlike solutions in the two-dimensional Belousov-Zhabotinski reaction in water-in-oil microemulsion are studied. It is shown analytically that such spots undergo an instability as the diffusivity ratio is decreased. An instability threshold is derived. For spots of small radius, it is shown that this instability leads to a spot splitting into precisely two spots. For larger spots, it leads to deformation, fingering patterns, and space-filling curves. Numerical simulations are shown to be in close agreement with the analytical predictions.     

Suppression of complex fingerlike patterns at the interface between air and a viscous fluid by elastic membranes

Growth of complex dendritic fingers at the interface of air and a viscous fluid in the narrow gap between two parallel plates is an archetypical problem of pattern formation. We find a surprisingly effective means of suppressing this instability by replacing one of the plates with an elastic membrane. The resulting fluid-structure interaction fundamentally alters the interfacial patterns that develop and considerably delays the onset of fingering. We analyze the dependence of the instability on the parameters of the system and present scaling arguments to explain the experimentally observed behavior.     

Confined ferrofluid droplet in crossed magnetic fields

When a ferrofluid drop is trapped in a horizontal Hele-Shaw cell and subjected to a vertical magnetic field, a fingering instability results in the droplet evolving into a complex branched structure. This fingering instability depends on the magnetic field ramp rate but also depends critically on the initial state of the droplet. Small perturbations in the initial droplet can have a large influence on the resulting final pattern. By simultaneously applying a stabilizing (horizontal) azimuthal magnetic field, we gain more control over the mode selection mechanism. We perform a linear stability analysis that shows that any single mode can be selected by appropriately adjusting the strengths of the applied fields. This offers a unique and accurate mode selection mechanism for this confined magnetic fluid system. We present the results of numerical simulations that demonstrate that this mode selection mechanism is quite robust and “overpowers” any initial perturbations on the droplet. This provides a predictable way to obtain patterns with any desired number of fingers.     

Viscous-fingering-like instability of cell fragments

We present a novel flow instability that can arise in thin films of cytoskeletal fluids if the friction with the substrate on which the film lies is sufficiently strong. We consider a two-dimensional, membrane-bound fragment containing actin filaments that polymerize at the edge and depolymerize in the fragment. Performing a linear stability analysis of the initial state due to perturbations of the fragment boundary, we find, in the limit of large friction, that the perturbed actin velocity and pressure fields obey the same laws governing the viscous fingering instability of an interface between immiscible fluids in a Hele-Shaw cell. A remarkable feature of this instability is that it is independent of the strength of the interaction between actin filaments and myosin motors.     

Viscous fingering as a paradigm of interfacial pattern formation: recent results and new challenges

We review recent results on dynamical aspects of viscous fingering. The Saffman-Taylor instability is studied beyond linear stability analysis by means of a weakly nonlinear analysis and the exact determination of the subcritical branch. A series of contributions pursuing the idea of a dynamical solvability scenario associated to surface tension in analogy with the traditional selection theory is put in perspective and discussed in the light of the asymptotic theory of Tanveer and co-workers. The inherently dynamical singular effects of surface tension are clarified. The dynamical role of viscosity contrast is explored numerically. We find that the basin of attraction of the Saffman-Taylor finger depends on viscosity contrast, and that the sensitivity to this parameter is maximal in the usual limit of high viscosity contrast. The competing attractors are identified as closed bubble solutions. We briefly report on recent results and work in progress concerning rotating Hele-Shaw flows, topological singularities and wetting effects, and also discuss future directions in the context of viscous fingering.     

Realizing microgravity flame spread characteristics at 1 g over a bed of nano-aluminum powder

Nanoscale aluminum (nAl) powders demonstrate relatively fast counter-flow flame spread rates compared to typical fuels such as Poly(methyl methacrylate) or cellulose at similar conditions. This allows for the dominant forward heat transfer mechanism to be through the solid fuel at higher applied oxidizer velocities, and flame structure characteristics typically observed in microgravity to be realized at 1 g conditions. Because of the porosity of the nAl powder, the gaseous oxidizer can diffuse into the bed and reactions within the solid phase become important. Using an energy balance applied to only the solid phase, an analytical model is developed which predicts the experiments for flame spread over a nAl bed. Moreover, an explanation for fingering phenomenon is established based on the effective Lewis and Damköhler numbers. This allows for an explanation of why flame spread over a bed of nAl will demonstrate this fingering instability in a quiescent, 1 g environment without a top plate to hinder buoyant flows.     

Spontaneous branching of anode-directed streamers between planar electrodes

Nonionized media subject to strong fields can become locally ionized by penetration of finger-shaped streamers. We study negative streamers between planar electrodes in a simple deterministic continuum approximation. We observe that, for sufficiently large fields, the streamer tip can split. This happens close to the limit of "ideal conductivity." Qualitatively, the tip splitting is due to a Laplacian instability quite like that in viscous fingering. For future quantitative analytical progress, our stability analysis of planar fronts identifies the screening length as a regularization mechanism.     

Stokes instability in inhomogeneous membranes: application to lipoprotein suction of cholesterol-enriched domains

We examine the time-dependent distortion of a nearly circular viscous domain in an infinite viscous sheet when suction occurs. Suction, the driving force of the instability, can occur everywhere in the two phases separated by an interface. The model assumes a two-dimensional Stokes flow; the selection of the wavelength at short times is determined by a variational procedure. Contrary to the viscous fingering instability, undulations of the boundary may be observed for enough pumping, whatever the sign of the viscosity contrast between the two fluids involved. We apply our model to the suction by lipoproteins of cholesterol-enriched domains in giant unilamellar vesicles. Comparison of the number of undulations given by the model and by the experiments gives reasonable values of physical quantities such as the viscosities of the domains.