Evolution Of Fringes Research Articles

A path-following simulation-based study of elastic instabilities in nearly-incompressible confined cylinders under tension

Recent experiments on hydrogels subjected to large elongations have shown elastic instabilities resulting in the formation of geometrically intricate fringe and fingering deformation patterns. In this paper, we present a robust numerical framework addressing the challenges that emerge in the simulation of this complex material response from the onset of instability to the post-bifurcation behavior. We observe that the numerical difficulties stem from the non-convexity of the strain energy density in the near-incompressible, large-deformation regime, which is responsible for the coexistence of multiple equilibrium paths with vastly-different, sinuous deformation patterns immediately after bifurcation. We show that these numerical challenges can be overcome by using sufficiently-high order of interpolation in the finite element approximation, an arc-length-based nonlinear solution procedure that follows the entire equilibrium path of the system, and an implementation enabling parallel, large-scale simulations. The resulting computational approach provides the ability to conduct highly-resolved, truly quasi-static simulations of complex elastic instabilities. We present numerical results illustrating the ability of the path-following approach to describe the full evolution of fringe and fingering instabilities observed experimentally in recent experiments of confined cylindrical specimens of soft hydrogels subject to tension. Importantly, we observe that the robustness of the static solution procedure enables complete access to the multiplicity of solutions occurring immediately after the onset of bifurcation, as well as to the settled post-bifurcation states.

Colloidal crystal growth monitored by Bragg diffraction interference fringes

We monitored the crystal growth kinetics of crystallization of a shear melted crystalline colloidal array (CCA). The fcc CCA heterogeneously nucleates at the flow cell wall surface. We examined the evolution of the (1 1 1) Bragg diffraction peak, and, for the first time, quantitatively monitored growth by measuring the temporal evolution of the Bragg diffraction interference fringes. Modeling of the evolution of the fringe patterns exposes the time dependence of the increasing crystal thickness. The initial diffusion-driven linear growth is followed by ripening-driven growth. Between 80 and 90 μM NaCl concentrations the fcc crystals first linearly grow at rates between 1.9 and 4.2 μm/s until they contact homogeneously nucleated crystals in the bulk. At lower salt concentrations interference fringes are not visible because the strong electrostatic interactions between particles result in high activation barriers, preventing defect annealing and leading to a lower crystal quality. The fcc crystals melt to a liquid phase at >90 μM NaCl concentrations. Increasing NaCl concentrations slow the fcc CCA growth rate consistent with the expectation of the classical Wilson–Frenkel growth theory. The final thickness of wall-nucleated CCA, that is determined by the competition between growth of heterogeneously and homogenously nucleated CCA, increases with higher NaCl concentrations.

Holographic interferometry as electrochemical emission spectroscopy of carbon steel in seawater with low concentration of RA-41 corrosion inhibitor

In the present investigation, holographic interferometry was utilized for the first time to determine the rate change of the number of the fringe evolutions during the corrosion test of carbon steel in blank seawater and with seawater with different concentrations of a corrosion inhibitor. In other words, the anodic dissolution behaviors (corrosion) of the carbon steel were determined simultaneously by holographic interferometry, an electromagnetic method, and by the electrochemical impedance (EI) spectroscopy, an electronic method. So, the abrupt rate change of the number of the fringe evolutions during corrosion test (EI) spectroscopy, of the carbon steel is called electrochemical emission spectroscopy. The corrosion process of the steel samples was carried out in blank seawater and seawater with different concentrations, 5–20 ppm, of RA-41 corrosion inhibitor using the EI spectroscopy method, at room temperature. The electrochemical emission spectra of the carbon steel in different solutions represent a detailed picture of the rate change of the anodic dissolution of the steel throughout the corrosion processes. Furthermore, the optical interferometry data of the carbon steel were compared to the data, which were obtained from the EI spectroscopy. Consequently, holographic interferometric is found very useful for monitoring the anodic dissolution behaviors of metals, in which the number of the fringe evolutions of the steel samples can be determined in situ.

Optical interferometry as electrochemical emission spectroscopy of copper alloys in seawater

In the present investigation, holographic interferometry was utilized for the fast time to determine the rate change of the number of the fringe evolutions during the corrosion test of a pure copper, 99% Cu, and an aluminium brass, 76% Cu +22% Ni +2%Al, in natural seawater. In other words, the anodic dissolution behaviours (corrosion) of the pure copper and the aluminium brass were determined by holographic interferometry, an electromagnetic method. Thus, the abrupt rate change of the number of the fringe evolutions during corrosion tests of both the copper alloys is called electrochemical emission spectroscopy. The corrosion process of both copper alloys was carried out in the seawater at room temperature. The electrochemical emission spectra of both copper alloys in seawater represent a detailed picture of the rate change of the anodic dissolution of both copper alloys throughout the corrosion processes. Furthermore, the optical interferometry data of the both copper alloys were compared to data obtained from the common methods of electrochemical techniques of corrosion measurements, namely, the linear polarization method and electrochemical impedance spectroscopy. The comparison indicates that there is good agreement between the data ofthe electrochemical emission spectra of both copper alloys with data of the electrochemical techniques in seawater. In both techniques of electrochemical emission spectroscopy and electrochemical techniques, the corrosion behaviour of the pure copper was observed to be higher than that of aluminium brass. Consequently, holographic interferometry was found very useful for monitoring the anodic dissolution behaviours ofmetals, in which the number ofthe fringe evolutions ofboth copper alloys can be determined in situ.

Holographic interferometry as electrochemical emission spectroscopy of a carbon steel in 5–20 ppm TROS C-70 inhibited seawater

In the present investigation, holographic interferometry was utilized for the first time to determine the rate change of the number of the fringe evolutions during the corrosion test of a carbon steel in blank seawater and seawater with different concentrations of a corrosion inhibitor. In other words, the anodic dissolution behaviors (corrosion) of the carbon steel were determined simultaneously by holographic interferometry, as an electromagnetic method, and by the electrochemical impedance (EI) spectroscopy, as an electronic method. So, the abrupt rate change of the number of the fringe evolutions during corrosion tests, EI spectroscopy, of the carbon steel is called electrochemical emission spectroscopy. The corrosion process of the steel samples was carried out in blank seawater and seawater with different concentrations, 5–20 ppm, of TROS C-70 corrosion inhibitor using the EI spectroscopy method, at room temperature. The electrochemical-emission spectra of the carbon steel in different solutions represent a detailed picture of the rate change of the anodic dissolution of the steel throughout the corrosion processes. Furthermore, the optical interferometry data of the carbon steel were compared to the data, which was obtained from the EI. spectroscopy. Consequently, holographic interferometry is found very useful for monitoring the anodic dissolution behaviors of metals, in which the number of the fringe evolutions of the steel samples can be determined in situ.

Electrochemical interferometry of a carbon steel in 5–20 ppm KGR-134 inhibited seawater

In the present investigation, holographic interferometry was utilized for the first time to determine the rate change of the number of the fringe evolutions during the corrosion test of a carbon steel in blank seawater and with seawater with different concentrations of a corrosion inhibitor. In other words, the anodic dissolution behaviors (corrosion) of the carbon steel were determined simultaneously by holographic interferometry, an electromagnetic method, and by the electrochemical impedance spectroscopy (EIS), an electronic method. So, the abrupt rate change in the number of the fringe evolutions during corrosion test, EIS, of the carbon steel is called electrochemical interferometry. The corrosion process of the steel samples was carried out in blank seawater and seawater with different concentrations, 5–20 ppm, of KGR-134 corrosion inhibitor using the EIS method, at room temperature. The electrochemical interferograms of the carbon steel in different solutions represent a detail picture of the rate change of the anodic dissolution of the steel throughout the corrosion processes. Furthermore, the optical interferometry data of the carbon steel were compared to the data which were obtained from the EIS tests. Consequently, holographic interferometry is found to be very useful as an electrochemical interferometer for monitoring the anodic dissolution behaviors of metals in aqueous solutions, in which the number of the fringe evolutions of the steel samples can be determined in situ.

Recording the behaviour of an avian embryo using holography

A novel application of holographic interferometry to study the development of behaviour of an avian embryo in an intact incubating egg is reported. A holographic system is implanted astribe both the interior and exterior of the incubator. The observation of the movements of the embryo is obtained in the form of the evolution of fringes in real-time by means of a vidicon camera placed behind the holographic plate. Besides being useful in the study of the pre-natal motility cycle, the method allows one to follow the development of specific behaviour patterns, their onset, duration and frequency of repetition. The steady development of the intense movements leading to the first cracking of the shell is vividly displayed. Preliminary results confirming the experimental viability of the proposed application are presented.

Holographic interferometric study of liquid diffusion

The technique of holographic interferometry is applied to the study of diffusion in transparent liquid mixtures. A simple method is derived for determining the diffusion coefficient from measurements of the location and the time evolution of fringes on a double exposed hologram. Results on sucrose solution are presented and compared with other methods.