Interfacial Patterns Research Articles

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.

Double Rosensweig instability in a ferrofluid sandwich structure.

We consider a horizontal ferrofluid layer sandwiched between two layers of immiscible nonmagnetic fluids. In a sufficiently strong vertical magnetic field the flat interfaces between magnetic and nonmagnetic fluids become unstable to the formation of peaks. We theoretically investigate the interplay between these two instabilities for different combinations of the parameters of the fluids and analyze the evolving interfacial patterns. We also estimate the critical magnetic field strength at which thin layers disintegrate into an ordered array of individual drops.

Direct energy transfer at electrified liquid–liquid interfaces: a way to study interface morphology on mesoscopic scales

Direct energy transfer (DET) technique is widely used to study the morphology of heterogeneous media in which the chromophores capable to energy exchange are imbedded. Here, we present a theory of DET at corrugated interfaces, with a special attention to electrified interfaces, particularly the interfaces between two immiscible electrolyte solutions. We show that the dependence of DET-signal on the potential drop across the interface can give valuable information about the interfacial dynamic corrugations and pattern formation on the length scales between 1 and 10 nm.

Asymptotic theory for disc-like crystal growth (II): interfacial instability and pattern formation at early stage of growth

This paper is a continuation of the paper ([1] ), which is called paper (I) afterward. In the present paper, which we shall call paper (II), we study the interfacial instability property of the side interface of a growing disc-like crystal at the early stage of growth by using the approach developed in the interfacial wave (IFW) theory of dendritic growth. Our analysis show that the system allows two types of unstable modes over the side-interface: (1). The axi-symmetric $(m=0)$ modes. The most dangerous axi-symmetric mode is the base mode $A_0$, which is responsible for formation of the axi-symmetric pattern over the side-interface, anti-symmetric about the central plane of the disc; (2). The non-axi-symmetric modes, which are responsible for non-axi-symmetric pattern formation around the edge of the disc. The growth rates of these non-axi-symmetric modes are much smaller than the growth rate of the base mode $A_0$. During the course of disc growth, the unstable $A_0$-mode merges first. It leads to the formation of anti-symmetric pattern about the central plane over the side-interface. Following the onset of unstable base mode $A_0$, a set of non-axi-symmetric growing modes also appear. However, due to the smallness of growth rate of these unstable modes, the non-axi-symmetric pattern around the edge of the disc becomes observable, only after a sufficiently long time. Our theoretical predictions are in good agreement with the available experimental data.

Crystallization of Antimony Nanoparticles: Pattern Formation and Fractal Growth

The spontaneous formation of complex interfacial patterns from thermally deposited Sb4 clusters on HOPG is controlled by the deposition conditions (i.e., coverage and deposition rate) at constant t...

Elastic properties of a cellular dissipative structure

Transition towards spatio-temporal chaos in one-dimensional interfacial patterns often involves two degrees of freedom: drift and out-of-phase oscillations of cells, respectively associated to parity breaking and vacillating-breathing secondary bifurcations. In this paper, the interaction between these two modes is investigated in the case of a single domain propagating along a circular array of liquid jets. As observed by Michalland and Rabaud for the printer’s instability [1], the velocity V g of a constant width domain is linked to the angular frequency $\omega$ of oscillations and to the spacing between columns $\lambda_0$ by the relationship $V_g = \alpha \lambda_0 \omega$ . We show by a simple geometrical argument that $\alpha$ should be close to $1/ \pi$ instead of the initial value $\alpha = 1/2$ deduced from their analogy with phonons. This fact is in quantitative agreement with our data, with a slight deviation increasing with flow rate.

Global Instability, Limiting-State Selection and Nonlinear Pattern Formation

Interfacial pattern formation in phase transition and crystal growth and material science is one of the most important subjects in the broad field of nonlinear science. This subject involves the concepts and issues, include the basic states, global stability, limiting-state selection, quantization conditions of eigenvalues, scaling law and free boundary problems of dynamic system far away from the equilibrium state. This talk attempts to explore these issues through the two prototype problems: (1). dendritic growth from melt; (2). disc-like crystal growth from melt. These problems are highly challenging fundamental problems in condensed matter physics and material science, which have preoccupied many investigators from various areas of science, including applied mathematics for a long period of time. We shall summarize the major results achieved in terms of a unified systematic asymptotic approach during the last decade. For the case of dendritic growth, these results described the wave-characteristics of interface evolution and led to the so-called interfacial wave (IFW) theory.

Interfacial turbulence in evaporating liquids: Theory and preliminary results of the ITEL-master 9 sounding rocket experiment

Evaporation of a pure liquid into a inert gas is studied theoretically and experimentally. In contrast with the case where the gas phase is made of pure vapor, the thermocapillary (Marangoni) effect strongly destabilizes the system, and results in intensive and often chaotic forms of interfacial convection. Theoretically, a generalized one-sided model is proposed, which allows the solution of the thermo-hydrodynamic equations in the liquid phase only, still taking into account relevant effects in the gas phase. The equivalent heat transfer coefficient (Biot number) to be incorporated in this one-sided model appears to be high, which results in an acceleration of transitions to polygonal chaotic patterns. Chaotic interfacial patterns driven by the Marangoni effect have indeed been observed during the ITEL-Maser 9 sounding rocket experiment flown in March 2002, in preparation of the CIMEX (Convection and Interfacial Mass Exchange) experiment foreseen for the International Space Station.

Mode-coupling approach to non-Newtonian Hele-Shaw flow.

The Saffman-Taylor viscous fingering problem is investigated for the displacement of a non-Newtonian fluid by a Newtonian one in a radial Hele-Shaw cell. We execute a mode-coupling approach to the problem and examine the morphology of the fluid-fluid interface in the weak shear limit. A differential equation describing the early nonlinear evolution of the interface modes is derived in detail. Owing to vorticity arising from our modified Darcy's law, we introduce a vector potential for the velocity in contrast to the conventional scalar potential. Our analytical results address how mode-coupling dynamics relates to tip splitting and sidebranching in both shear-thinning and shear-thickening cases. The development of non-Newtonian interfacial patterns in rectangular Hele-Shaw cells is also analyzed.

Shear bond strength of self-etching adhesives to dentin and sem analysis

The purpose of this study was to compare shear bond strength and interfacial pattern of composite bond-ed to dentin using self-etching adhesive systems. Sixty extracted human molars with exposed occlusal dentin were divided into four groups and bonded with four adhesives and composites. Single Bond/Filtek Z 350(SB), Tyrian SPE-One-Step Plus/Aelitefil(TY), Prompt L-Pop/Filtek Z 250(LP), and One-Up Bond F/palfique Toughwell(OU). The results of this study were as follows; 1 Shear bond strength for OU was significantly lower than that of other groups(p＜0.05). No significant difference was founded among SB, TY, and LP. 2. Failure modes to dentin showed adhesive and mixed for SB TY and LP, but them for OU showed adhesive in all spceimens. 3. Dentin-resin interface showed close adaptation for SB, TY, and LP, but it showed gap for OU. 4. The hybrid layers for TY, LP OU were thinner than that of SB. Adhesive layers were observed between composite and hybrid layer, which were 5 thick for TY and 10 thick for OU.

Dynamical systems approach to Saffman-Taylor fingering: dynamical solvability scenario.

A dynamical systems approach to competition of Saffman-Taylor fingers in a Hele-Shaw channel is developed. This is based on global analysis of the phase space flow of the low-dimensional ordinary-differential-equation sets associated with the classes of exact solutions of the problem without surface tension. Some simple examples are studied in detail. A general proof of the existence of finite-time singularities for broad classes of solutions is given. Solutions leading to finite-time interface pinchoff are also identified. The existence of a continuum of multifinger fixed points and its dynamical implications are discussed. We conclude that exact zero-surface tension solutions taken in a global sense as families of trajectories in phase space are unphysical because the multifinger fixed points are nonhyperbolic, and an unfolding does not exist within the same class of solutions. Hyperbolicity (saddle-point structure) of the multifinger fixed points is argued to be essential to the physically correct qualitative description of finger competition. The restoring of hyperbolicity by surface tension is proposed as the key point to formulate a generic dynamical solvability scenario for interfacial pattern selection.

A biperiodic interfacial pattern of misfit dislocation interacting with both free surfaces of a thin bicrystalline sandwich

The elastic field, of a thin bicrystalline sandwich with parallel faces when the interface between the two anisotropic crystal components is parallel to the faces and is composed of a biperiodic pattern of defects is numerically computed, using a double Fourier series method, an explicit formulation of each harmonic term of series is derived that depends explicitly on the anisotropic elasticity coefficients and thickness of each crystal. Application is made to the particular case of intrinsic dislocation meshes using a InAs/( 1 1 1 )GaAs related system by a regular array of MDS at the interface, cf. J.G. Belk et al., Phys. Rev. Lett. 77 (1997) 475 and H. Yamaguchi et al., Phys. Rev. B 55 (1997) 1337, to determine free surface deformations through different thickness of the bicrystal. Graphic

Advanced Fluid Information. Growth-Morphologies in Solidification and Hydrodynamics.

The evolution of interfacial patterns during growth processes is shortly summarized. The analogy between hydrodynamic dewetting patterns and diffusion controlled growth patterns is demonstrated. A phase-field method for the treatment of hydrodynamic flow with free interfaces is presented and illustrated with some examples.

Effects of gravity on pattern formation in directional growth of ice crystals

Side-view images of interfacial patterns and solute concentration distribution during directional growth of ice crystals in a water-KCl solution were obtained by Moire phase shift interferometry. It was shown that the vertical distribution of solute concentration changed drastically due to the effect of gravity depending on the growth cell thickness h. In the case of h=900 μm, the concentrated solution near the growth interface subsided and flowed ahead much further than the diffusion length of solute. In thinner cells, the subsided dense solution extended the brine channel under the lower side of the interface instead of flowing ahead, and caused the formation of an asymmetrical wedged pattern. In the thinnest cell of h=135 μm, although the turbulence in the solution was quite small, the symmetry of the interfacial pattern was still broken. The results indicate that the three-dimensional analysis considering the effect of gravity is essential for the interfacial patterns even in the thin growth cell.

Spatio-temporal interfacial potential patterns during the electrocatalyzed oxidation of formic acid on Bi-modified Pt

We report experimental observations of the spatio-temporal dynamics in the electro-oxidation of formic acid on a Pt ring electrode modified by bismuth adatoms. Bismuth modification significantly enhanced the current density and it was found to considerably increase the existence range of oscillations and spatio-temporal self-organization. Hidden negative differential resistance and the existence of a Hopf bifurcation were deduced from the electrochemical impedance spectra and the occurrence of galvanostatic oscillations. The pattern formation resulted from hybrid effects of the nonlinear chemistry during formic acid oxidation and the long-range coupling of the interfacial potential induced by the chosen geometry (ring type) of the working electrode. Reversible transitions between traveling pulses and oscillating standing waves were observed when the outer potential or the formic acid concentration near the electrode were used as control parameters. Experimental results were compared with computer simulations of a reaction-migration system. The role of electrode inhomogeneities in pattern formation and the transform between patterns were discussed.

Phase-field model of mode III dynamic fracture.

We introduce a phenomenological continuum model for the mode III dynamic fracture that is based on the phase-field methodology used extensively to model interfacial pattern formation. We couple a scalar field, which distinguishes between "broken" and "unbroken" states of the system, to the displacement field in a way that consistently includes both macroscopic elasticity and a simple rotationally invariant short-scale description of breaking. We report two-dimensional simulations that yield steady-state crack motion in a strip geometry above the Griffith threshold.

Interfacial molecular assembly and surface patterning

Based on a brief review of the traditional surface patterning research, this article introduces the recent progress in the research on surface patterning via molecular self-assembly. Because the size scale of molecular self-assemblies is in the range of 1–100 nm, the method of molecular self-assembly can easily lead to the construction of ordered structures in nanometer scale, and thus break through the size limit of traditional lithography. Some novel ways of molecular self-assembly for surface patterning are particularly introduced in this review, including supramolecular architecture at interface, chemisorption of dendron thoils, and surface aggregation of bolaform amphiphiles. Provided that we know more and more about the basic principles governing the surface morphology, it is believed that interfacial molecular assembly would be a very competitive supramolecular technique, and a potential application in many fields such as surface property adjustment, organic patterned devices, surface molecular recognition, and combinatorial chemistry is greatly anticipated.

Interfacial Pattern Formation in the Pt-Ni-O System, Studied by Energy-Filtering Transmission Electron Microscopy

Interfacial Pattern Formation in the Pt-Ni-O System, Studied by Energy-Filtering Transmission Electron Microscopy

Saffman-Taylor problem on a sphere

The Saffman-Taylor problem addresses the morphological instability of an interface separating two immiscible, viscous fluids when they move in a narrow gap between two flat parallel plates (Hele-Shaw cell). In this work, we extend the classic Saffman-Taylor situation, by considering the flow between two curved, closely spaced, concentric spheres (spherical Hele-Shaw cell). We derive the mode-coupling differential equation for the interface perturbation amplitudes and study both linear and nonlinear flow regimes. The effect of the spherical cell (positive) spatial curvature on the shape of the interfacial patterns is investigated. We show that stability properties of the fluid-fluid interface are sensitive to the curvature of the surface. In particular, it is found that positive spatial curvature inhibits finger tip-splitting. Hele-Shaw flow on weakly negative, curved surfaces is briefly discussed.

Viscous beads on vertical fibre

The dynamics of a thick layer of viscous liquid flowing down a thin vertical fibre is investigated. Three qualitatively different regimes of the interfacial patterns in the form of beads were observed experimentally. Two typical regimes at relatively small flow rate are described reasonably well by the creeping-flow model equation proposed here.