Interfacial Patterns Research Articles

Three techniques of interfacial bond strength estimation from direct observation of crack initiation and propagation in polymer–fibre systems

Three techniques of bond strength determination in micromechanical tests—fibre strain profile analysis by means of Raman spectroscopy, “kink” force determination in a traditional pull-out test, and crack length monitoring in a microbond test—were used for investigation of interfacial debonding in epoxy–glass fibre and epoxy–aramid fibre systems. Crack propagation was characterised by local interfacial parameters—critical energy release rate, Gic, and ultimate interfacial shear strength (IFSS), τult. The comparison of the results showed good agreement both between different techniques and between stress-based and energy-based failure criteria. Sizing of glass fibres caused more pronounced variations in the IFSS than for aramid fibres due to different interfacial failure patterns. The strength of “real” epoxy–glass composites with sized and unsized fibres correlates well with the bond strength determined from the micromechanical tests.

Interferometric observation of the effects of gravity on the horizontal growth of ice crystals in a thin growth cell

The effects of gravity on the horizontal growth of crystals were investigated in a thin growth cell, which is normally assumed to be two-dimensional. Three-dimensional interfacial patterns and the solute concentration distribution during directional growth of ice crystals in a water–KCl solution were obtained using a Mach–Zehnder interferometer. It was found that morphological instability of a straight interface occurs not only in the lateral direction but also in the thickness direction of the growth cell (100 μm in thickness). Side view images of a thin layer were first obtained during horizontal growth and upward growth, where the components of gravitational acceleration in the thickness direction were 1 g and 0 g, respectively. The effects of gravity were clearly observed as follows. In the former case of 1 g, the concentrated solution near the growth interface subsided. Simultaneously, the lower side of the interface retreated due to depression of the freezing temperature. In the latter case of 0 g, the solution remained stationary and distortion of the interfacial pattern was not observed. In addition, top view images of horizontal growth indicated that the mass balance of solute at the interface, which is usually assumed, was lost as soon as instability occurred in the thickness direction. It should be emphasized that three-dimensional analysis that takes into account the effect of gravity is essential for understanding interfacial patterns even in the case of a thin growth cell.

Pattern forming instabilities of the nematic smectic-B interface

Free growth properties of the smectic B liquid crystalline phase into the supercooled nematic have been investigated in quasi-two-dimensional geometry. Different orientation combinations of the two phases have been achieved experimentally and the interfacial patterns have been studied and analysed as a function of undercooling. The angular dependence of the surface tension has been deduced from the shape of the interface in thermal equilibrium. The experimentally determined surface tension anisotropy has been incorporated into computer simulations based on the phase-field model. The simulations have reproduced qualitatively the rich variety of morphologies (extending from the faceted shape to fully developed dendrites) observed in the experiments for a given set of undercoolings in three geometries. Anisotropic heat diffusion on the nematic side, relevant to our experimental system has also been introduced. Both in the experiments and in the simulations we find that the growth is faster in the lower heat diffusion direction.

Polydiacetylene Monolayers as Versatile Photoresists for Interfacial Patterning

Well-defined organic interfaces are central to a broad scope of technological advances ranging from sensor design to molecular electronics applications. Fabricating the desired properties within a single molecular layer has proven to be a significant challenge. In this paper, photopolymerization of an ordered array of diacetylenes is shown to be a versatile means for fabricating spatially controlled interfacial properties within a single molecular layer. The application of a single-layer polymer to this process leads to enhanced ruggedness by covalently linking adjacent molecules within the assembly. In addition to direct chemical-etching applications, these monolayer polymers provide a versatile means for two-dimensional patterning of interfacial chemical properties as well as the localized chromatic phase. Moreover, within these patterned arrays, the vertical position of the polymer backbone within the monolayer structure is successfully controlled. Because the resultant backbone is electronically deloc...

The singular perturbation of surface tension in Hele-Shaw flows

Morphological instabilities are common to pattern formation problems such as the non-equilibrium growth of crystals and directional solidification. Very small perturbations caused by noise originate convoluted interfacial patterns when surface tension is small. The generic mechanisms in the formation of these complex patterns are present in the simpler problem of a Hele-Shaw interface. Amid this extreme noise sensitivity, what is then the role played by small surface tension in the dynamic formation and selection of these patterns? What is the asymptotic behaviour of the interface in the limit as surface tension tends to zero? The ill-posedness of the zero-surface-tension problem and the singular nature of surface tension pose challenging difficulties in the investigation of these questions. Here, we design a novel numerical method that greatly reduces the impact of noise, and allows us to accurately capture and identify the singular contributions of extremely small surface tensions. The numerical method combines the use of a compact interface parametrization, a rescaling of the governing equations, and very high precision. Our numerical results demonstrate clearly that the zero-surface-tension limit is indeed singular. The impact of a surface-tension-induced complex singularity is revealed in detail. The singular effects of surface tension are first felt at the tip of the interface and subsequently spread around it. The numerical simulations also indicate that surface tension defines a length scale in the fingers developing in a later stage of the interface evolution.

Multiscale random-walk algorithm for simulating interfacial pattern formation.

We present a novel computational method to simulate accurately a wide range of interfacial patterns whose growth is limited by a large-scale diffusion field. To illustrate the computational power of this method, we demonstrate that it can be used to simulate three-dimensional dendritic growth in a previously unreachable range of low undercoolings that is of direct experimental relevance.

Interface dynamics in liquid crystals

We have experimentally observed the pattern instabilities of an Ising wall formed in a nematic or cholesteric liquid crystal layer. We have deduced an envelope equation, relevant close to the Freedericksz transition, from which we derived an equation for the dynamics of the interface in the vicinity of its bifurcation. In the case of the zig-zag instability, this model is characterized by a conservative and variational order parameter whose gradient satisfies a Cahn-Hilliard equation. We have also investigated the influence of slightly broken symmetries on the dynamical behaviour of the system. The disappearance of the interface translational invariance or of the reflection symmetry along the wall axis may induce new interfacial patterns which have been both experimentally and theoretically pointed out.

Pattern Formation at the Nematic Smectic-B Interface

Free growth properties of the smectic B liquid crystalline phase into the supercooled nematic have been investigated in quasi-twodimensional geometry. Different orientation combinations of the two phases have been achieved experimentally and the interfacial patterns have been studied and analysed as a function of undercooling. The angular dependence of the surface tension has been deduced from the shape of the interface in thermal equilibrium. The experimentally determined surface tension anisotropy has been incorporated into computer simulations based on the phase-field model. The simulations have reproduced qualitatively the rich variety of morphologies observed in the experiments for a given set of undercoolings in three geometries. Anisotropic heat diffusion on the nematic side, relevant to our experimental system has also been introduced. Both in the experiments and in the simulations we find that the growth is faster in the lower heat diffusion direction.

Numerical studies of two-dimensional Faraday oscillations of inviscid fluids

The dynamics of two-dimensional standing periodic waves at the interface between two inviscid fluids with different densities, subject to monochromatic oscillations normal to the unperturbed interface, is studied under normal- and low-gravity conditions. The motion is simulated over an extended period of time, or up to the point where the interface intersects itself or the curvature becomes very large, using two numerical methods: a boundary-integral method that is applicable when the density of one fluid is negligible compared to that of the other, and a vortex-sheet method that is applicable to the more general case of arbitrary densities. The numerical procedure for the boundary-integral formulation uses a global isoparametric parametrization based on cubic splines, whereas the numerical method for the vortex-sheet formulation uses a local boundary-element parametrization based on circular arcs. Viscous dissipation is simulated by means of a phenomenological damping coefficient added to the Bernoulli equation or to the evolution equation for the strength of the vortex sheet. A comparative study reveals that the boundary-integral method is generally more accurate for simulating the motion over an extended period of time, but the vortex-sheet formulation is significantly more efficient. In the limit of small deformations, the numerical results are in excellent agreement with those predicted by the linear model expressed by Mathieu's equation, and are consistent with the predictions of the Floquet stability analysis. Nonlinear effects for non-infinitesimal amplitudes are manifested in several ways: deviation from the predictions of Mathieu's equation, especially at the extremes of the interfacial oscillation; growth of harmonic waves with wavenumbers in the unstable regimes of the Mathieu stability diagram; formation of complex interfacial structures including paired travelling waves; entrainment and mixing by ejection of droplets from one fluid into the other; and the temporal period tripling observed recently by Jiang et al. (1998). Case studies show that the surface tension, density ratio, and magnitude of forcing play a significant role in determining the dynamics of the developing interfacial patterns.

Time development of a solute diffusion field and morphological instability on a planar interface in the directional growth of ice crystals

The solute distribution in front of directionally growing ice crystals in a water–KCl solution was observed in situ as well as the three-dimensional interfacial patterns, using a Mach–Zehnder interferometer. We give a direct evidence for the constitutional supercooling and discuss the wavelength selection of perturbation. The morphological instability occurred much earlier than the establishment of the steady-state condition of diffusion field. The steady-state analysis using Mullins–Sekerka theory could not predict the wavelength of perturbation. However, when the measured values of solute distribution and growth rate at the time of instability are substituted for the parameters assuming the quasi-steady state, it is found that the analysis precisely predicts the experiments.

Adsorption of Antifreeze Glico Protein (AFGP) at the Ice/water Interface and its Effect for Interfacial Pattern Formation

Adsorption of Antifreeze Glico Protein (AFGP) at the Ice/water Interface and its Effect for Interfacial Pattern Formation

Dose mapping of inhomogeneities positioned in radiosensitive polymer gels

A gel matrix (gelatin), infused with acrylamide monomer and a crosslinking agent has been used as a three-dimensional dosimeter of X- and γ-rays are used in radiotherapy. Magnetic resonance imaging is used to create a parameter map of transverse relaxation time ( T 2) from which a map of absorbed dose is calculated. We are using the technique to investigate the interfacial radiation patterns resulting from the presence of implanted inhomogeneities in the gel phantom being irradiated, a concept which is as yet underdeveloped. The inhomogeneities, which may be either low or high density with respect to the surrounding medium, are designed to simulate the effects of air cavities or bone in the body and their effects on the absorbed dose during radiotherapy. This paper explores ways of introducing inhomogeneities into the gel and presents results of dose maps obtained post irradiation. An inherent problem of the dosimeter is the inhibition of polymerisation due to dissolved oxygen. Free radicals produced by the incident radiation are key to the polymerisation and crosslinking effects but are consumed by the dissolved oxygen. This paper describes the observed effects of oxygen contamination within a gel and suggests steps to be taken to minimise the problem.

Gravity-driven creeping flow of two adjacent layers through a channel and down a plane wall

We study the stability of the interface between (a) two adjacent viscous layers flowing due to gravity through an inclined or vertical channel that is confined between two parallel plane walls, and (b) two superimposed liquid films flowing down an inclined or vertical plane wall, in the limit of Stokes flow. In the case of channel flow, linear stability analysis predicts that, when the fluids are stably stratified, the flow is neutrally stable when the surface tension vanishes and the channel is vertical, and stable otherwise. This behaviour contrasts with that of the gravity-driven flow of two superimposed films flowing down an inclined plane, where an instability has been identified when the viscosity of the fluid next to the plane is less than that of the top fluid, even in the absence of fluid inertia. We investigate the nonlinear stages of the motion subject to finite-amplitude two-dimensional perturbations by numerical simulations based on boundary-integral methods. In both cases of channel and film flow, the mathematical formulation results in integral equations for the unknown interface and free-surface velocity. The properties of the integral equation for multi-film flow are investigated with reference to the feasibility of computing a solution by the method of successive substitutions, and a deflation strategy that allows an iterative procedure is developed. In the case of channel flow, the numerical simulations show that disturbances of sufficiently large amplitude may cause permanent deformation in which the interface folds or develops elongated fingers. The ratio of the viscosities and densities of the two fluids plays an important role in determining the morphology of the emerging interfacial patterns. Comparing the numerical results with the predictions of a model based on the lubrication approximation shows that the simplified approach can only describe a limited range of motions. In the case of film flow down an inclined plane, we develop a method for extracting the properties of the normal modes, including the ratio of the amplitudes of the free-surface and interfacial waves and their relative phase lag, from the results of a numerical simulation for small deformations. The numerical procedure employs an adaptation of Prony's method for fitting a signal described by a time series to a sum of complex exponentials; in the present case, the signal is identified with the cosine or sine Fourier coefficients of the interface and free-surface waves. Numerical simulations of the nonlinear motion confirm that the deformability of the free surface is necessary for the growth of small-amplitude perturbations, and show that the morphology of the interfacial patterns developing subject to finite-amplitude perturbations is qualitatively similar to that for channel flow.

The influence of interfacial growth patterns on the transmission of electrons through nonabrupt GaAs/AlxGa1−xAs double-barriers

It is investigated how the interfacial growth pattern changes the transmission properties of graded GaAs/AlxGa1−xAs double-barriers. Five interfacial growth patterns are studied, all of them representative of interfacial alloy variations that can be the result of different growth techniques and growth conditions of the interfaces. It is shown that the transmission resonances are shifted toward low energies in comparison to those of an abrupt GaAs/AlxGa1−xAs double-barriers. The shift increases with the interface width and with the order of the resonance, and depends on the type of growth pattern.

Three basic issues concerning interface dynamics in nonequilibrium pattern formation

In these lecture notes, we discuss at an elementary level three themes concerning interface dynamics that play a role in pattern forming systems: (i) We briefly review three examples of systems in which the normal growth velocity is proportional to the gradient of a bulk field which itself obeys a Laplace or diffusion type of equation (solidification, viscous fingers and streamers), and then discuss why the Mullins–Sekerka instability is common to all such gradient systems. (ii) Secondly, we discuss how underlying an effective interface or moving boundary description of systems with smooth fronts or transition zones, is the assumption that the relaxation time of the appropriate order parameter field(s) in the front region is much smaller than the time scale of the evolution of interfacial patterns. Using standard arguments we illustrate that this is generally so for fronts that separate two (meta)stable phases: in such cases, the relaxation is typically exponential, and the relaxation time in the usual models goes to zero in the limit in which the front width vanishes. (iii) We finally summarize recent results that show that so-called “pulled” or “linear marginal stability” fronts which propagate into unstable states have a very slow universal power-law relaxation. This slow relaxation makes the usual “moving boundary” or “effective interface” approximation for problems with thin fronts, like streamers, impossible.

Non-Newtonian Hele-Shaw Flow and the Saffman-Taylor Instability

We explore the Saffman-Taylor instability of a gas bubble expanding into a shear thinning liquid in a radial Hele-Shaw cell. Using Darcy{close_quote}s law generalized for non-Newtonian fluids, we perform simulations of the full dynamical problem. The simulations show that shear thinning significantly influences the developing interfacial patterns. Shear thinning can suppress tip splitting, and produce fingers which oscillate during growth and shed side branches. Emergent length scales show reasonable agreement with a general linear stability analysis. {copyright} {ital 1998} {ital The American Physical Society}

Growth patterns of yeast colonies depending on nutrient supply

AbstractCommon theories of microbial growth and physiology are formulated exclusively in terms of the isolated microorganisms – especially bacteria. This is, however, an inadmissible simplification because it is obvious that the organization of microbial populations and colonies follows certain general rules.Bacterial colonies are able to generate complex interfacial growth patterns similar to those observed during diffusion‐limited growth processes in non‐living systems. One reason for these patterns is assumed to be the ability of many bacteria to swarm in an active manner on a substrate surface. Therefore the models of bacterial colony growth incorporate “random walkers”, which move actively in response to a gradient in the concentration of nutrients and communicate with each other by means of a chemotactic feedback.A selected number of yeasts were tested with regard to their colony growth patterns depending on the medium parameters such as nutrient concentration. Growth patterns similar to those which were described in literature for bacteria were also found in these experiments. It concerns in particular growth types like compact growth, fractal growth and dense‐branching growth.This result allows a hypothesis to be formulated, that – especially in the case of fractal growth patterns – wandering of cells on a substrate surface may be induced by uncontrolled “swimming” on a thin water film caused by the metabolic activity (e.g. respiration) of the cells on the surface of the agar.Furthermore it was found that an interplay between changes in the individual morphology of yeast cells and the morphology transitions takes place. Such growth patterns are known for Candida sp. which are able to form pseudomycel and blastospores.

Interfacial pattern formation in nonlinear dynamic systems: Dendrites, fingers and interfacial waves by

Interfacial pattern formation in nonlinear dynamic systems: Dendrites, fingers and interfacial waves by

Instability of two-layer creeping flow in a channel with parallel-sided walls

The evolution of the interface between two viscous fluid layers in a two-dimensional horizontal channel confined between two parallel walls is considered in the limit of Stokes flow. The motion is generated either by the translation of the walls, in a shear-driven or plane-Couette mode, or by an axial pressure gradient, in a plane-Poiseuille mode. Linear stability analysis for infinitesimal perturbations and fluids with matched densities shows that when the viscosities of the fluids are different and the Reynolds number is sufficiently high, the flow is unstable. At vanishing Reynolds number, the flow is stable when the surface tension has a non-zero value, and neutrally stable when the surface tension vanishes. We investigate the behaviour of the interface subject to finite-amplitude two-dimensional perturbations by solving the equations of Stokes flow using a boundary-integral method. Integral equations for the interfacial velocity are formulated for the three modular cases of shear-driven, pressure-driven, and gravity-driven flow, and numerical computations are performed for the first two modes. The results show that disturbances of sufficiently large amplitude may cause permanent interfacial deformation in which the interface folds, develops elongated fingers, or supports slowly evolving travelling waves. Smaller amplitude disturbances decay, sometimes after a transient period of interfacial folding. The ratio of the viscosities of the two fluids plays an important role in determining the morphology of the emerging interfacial patterns, but the parabolicity of the unperturbed velocity profile does not affect the character of the motion. Increasing the contrast in the viscosities of the two fluids, while keeping the channel capillary number fixed, destabilizes the interfaces; re-examining the flow in terms of an alternative capillary number that is defined with respect to the velocity drop across the more-viscous layer shows that this is a reasonable behaviour. Comparing the numerical results with the predictions of a lubrication-flow model shows that, in the absence of inertia, the simplified approach can only describe a limited range of motions, and that the physical relevance of the steadily travelling waves predicted by long-wave theories must be accepted with a certain degree of reservation.

Solute Distribution in front of an Ice/Water Interface during Directional Growth of Ice Crystals and Its Relationship to Interfacial Patterns

Directional growth experiments in a water−KCl solution were carried out using a new experimental apparatus combined with an optical system of a Mach−Zehnder interferometer, and the solute distribution in the solution in front of the ice/water interface, as well as the interfacial patterns, was observed in situ. This is the first study in which the solute diffusion field was obtained by analyzing the interference fringes. It was found that the solute distribution is strongly affected by the pattern of interface (i.e., the diffusion field of solute varies greatly with the development of interfacial patterns). On the other hand, observations of interference fringes inside the ice crystal showed that the crystal shape develops in three dimensions even in a thin growth cell. Interaction between the diffusion field and the interfacial pattern is closely related to the three-dimensional structure of the ice/water interface.