Journal articles: 'Cahn effect'

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TEHRANI, ZAHRA ALIAKBAR, ALIREZA FATTAHI, MARJAN JEBELI JAVAN, and MOHAMMAD MAHMOODI HASHEMI. "DFT STUDY ON CONFORMATIONAL BEHAVIOR OF HYDROGEN ION ABSTRACTIONS OF CYTOSINE NUCLEOSIDES: AIM AND NBO ANALYSIS." Journal of Theoretical and Computational Chemistry 10, no. 06 (December 2011): 803–17. http://dx.doi.org/10.1142/s0219633611006797.

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In this paper, we explore theoretically energetic and structural properties of the possible cations formed via hydride ion abstraction at various sites of sugar part of cytosine nucleosides by employing B3LYP exchange-correlation functional with 6-311++G (d,p) orbital basis sets. In general, the hydride ion abstracted sugar cations of cytosine nucleosides have the following stability sequence: caH2′ > caH1′ > caH3′ > caH4′ > caH5′ for cytidine and caH1′ > caH4′ > caH3′ > caH5′ > caH2′ for deoxycytidine. Furthermore, the effect of solvent environment on the stability order of cations integral equation formalism of the polarized model (IEF-PCM) was employed to model aqueous solution. The natural bond orbital method was used for quantitative analysis of the electron delocalization donor–acceptor interaction of various hydride ions abstracted centers of cytosine nucleosides. The role of CH⋯O and HO⋯H intramolecular hydrogen bonds in the stability of cations is investigated based on the results of topological properties of atom in molecule theory. Moreover, variations of significant structural parameters such as puckering amplitudes and phase angles of sugar parts of cytosine nucleosides after cation formation are also found.

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KITAHARA, K., Y. OONO, and DAVID JASNOW. "PHASE SEPARATION DYNAMICS AND EXTERNAL FORCE FIELD." Modern Physics Letters B 02, no. 06 (July 1988): 765–71. http://dx.doi.org/10.1142/s0217984988000461.

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If spinodal decomposition is modeled by the Cahn-Hilliard (-Cook) equation, the effect of a uniform external force such as gravitation does not appear in the bulk phase kinetics. In contrast, in the Kawasaki exchange modeling of the local dynamics of binary alloys, this effect directly modifies the bulk phase kinetics. We resolve this paradox through the cell-dynamical-system modeling of the Kawasaki exchange dynamics. Its continuum version has turned out to be a modified Cahn-Hilliard equation already proposed by Langer et al. about ten years ago. We demonstrate some examples in which the correction to the Cahn-Hilliard equation is significant.

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sci, global. "Effect of Space Dimensions on Equilibrium Solutions of Cahn--Hilliard and Conservative Allen--Cahn Equations." Numerical Mathematics: Theory, Methods and Applications 13, no. 3 (June 2020): 644–64. http://dx.doi.org/10.4208/nmtma.oa-2019-0159.

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Garcke, Harald. "On Cahn—Hilliard systems with elasticity." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 133, no. 2 (April 2003): 307–31. http://dx.doi.org/10.1017/s0308210500002419.

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Elastic effects can have a pronounced effect on the phase-separation process in solids. The classical Ginzburg—Landau energy can be modified to account for such elastic interactions. The evolution of the system is then governed by diffusion equations for the concentrations of the alloy components and by a quasi-static equilibrium for the mechanical part. The resulting system of equations is elliptic-parabolic and can be understood as a generalization of the Cahn—Hilliard equation. In this paper we give a derivation of the system and prove an existence and uniqueness result for it.

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Lee, Dongsun, and Seunggyu Lee. "Image Segmentation Based on Modified Fractional Allen–Cahn Equation." Mathematical Problems in Engineering 2019 (January 30, 2019): 1–6. http://dx.doi.org/10.1155/2019/3980181.

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We present the image segmentation model using the modified Allen–Cahn equation with a fractional Laplacian. The motion of the interface for the classical Allen–Cahn equation is known as the mean curvature flows, whereas its dynamics is changed to the macroscopic limit of Lévy process by replacing the Laplacian operator with the fractional one. To numerical implementation, we prove the unconditionally unique solvability and energy stability of the numerical scheme for the proposed model. The effect of a fractional Laplacian operator in our own and in the Allen–Cahn equation is checked by numerical simulations. Finally, we give some image segmentation results with different fractional order, including the standard Laplacian operator.

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Wu, Shuonan, and Jinchao Xu. "Multiphase Allen–Cahn and Cahn–Hilliard models and their discretizations with the effect of pairwise surface tensions." Journal of Computational Physics 343 (August 2017): 10–32. http://dx.doi.org/10.1016/j.jcp.2017.04.039.

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AKAGI, GORO, and MESSOUD EFENDIEV. "Allen–Cahn equation with strong irreversibility." European Journal of Applied Mathematics 30, no. 04 (July 16, 2018): 707–55. http://dx.doi.org/10.1017/s0956792518000384.

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This paper is concerned with a fully non-linear variant of the Allen–Cahn equation with strong irreversibility, where each solution is constrained to be non-decreasing in time. The main purposes of this paper are to prove the well-posedness, smoothing effect and comparison principle, to provide an equivalent reformulation of the equation as a parabolic obstacle problem and to reveal long-time behaviours of solutions. More precisely, by derivingpartialenergy-dissipation estimates, a global attractor is constructed in a metric setting, and it is also proved that each solutionu(x,t) converges to a solution of an elliptic obstacle problem ast→ +∞.

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L’vov, Pavel, and Renat Sibatov. "Effect of the Particle Size Distribution on the Cahn-Hilliard Dynamics in a Cathode of Lithium-Ion Batteries." Batteries 6, no. 2 (May 15, 2020): 29. http://dx.doi.org/10.3390/batteries6020029.

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The phase-field model based on the Cahn-Hilliard equation is employed to simulate lithium intercalation dynamics in a cathode with particles of distributed size. We start with a simplified phase-field model for a single submicron particle under galvanostatic condition. We observe two stages associated with single-phase and double-phase patterns typical for both charging and discharging processes. The single-phase stage takes approximately 10–15% of the process and plays an important role in the intercalation dynamics. We establish the laws for speed of front propagation and evolution of single-phase concentration valid for different sizes of electrode particles and a wide range of temperatures and C-rates. The universality of these laws allows us to formulate the boundary condition with time-dependent flux density for the Cahn-Hilliard equation and analyze the phase-field intercalation in a heterogeneous cathode characterized by the particle size distribution.

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Yang, Ling Ling, and Yoshiyuki Saito. "Effect of Mo and Ni on Phase Separation in Fe-Cr=Mo-Ni Quaternary Alloys." Advanced Materials Research 409 (November 2011): 449–54. http://dx.doi.org/10.4028/www.scientific.net/amr.409.449.

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Numerical simulation of phase separation in Fe-Cr-Mo and Fe-Cr-Ni ternary alloys and Fe-Cr-Mo-Ni quaternary alloys were performed with use of the Cahn-Hilliard equation for ternary and quaternary alloys. A new numerical model based on the Gauss-Seidel and Newton Raphson methods was utilized to obtain efficient and accurate solution.

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Albosaily, Sahar, Wael W. Mohammed, Amjad E. Hamza, Mahmoud El-Morshedy, and Hijaz Ahmad. "The exact solutions of the stochastic fractional-space Allen–Cahn equation." Open Physics 20, no. 1 (January 1, 2022): 23–29. http://dx.doi.org/10.1515/phys-2022-0002.

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Abstract The fundamental objective of this article is to find exact solutions to the stochastic fractional-space Allen–Cahn equation, which is derived in the Itô sense by multiplicative noise. The exact solutions to this equation are required since it appears in many discipline areas including plasma physics, quantum mechanics and mathematical biology. The tanh–coth method is used to generate new hyperbolic and trigonometric stochastic and fractional solutions. The originality of this study is that the results produced here expand and improve on previously obtained results. Furthermore, we use Matlab package to display 3D surfaces of analytical solutions derived in this study to demonstrate the effect of stochastic term on the solutions of the stochastic-fractional-space Allen–Cahn equation.

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Pandey, Prashant, Sachin Kumar, Hossein Jafari, and Subir Das. "An operational matrix for solving time-fractional order Cahn-Hilliard equation." Thermal Science 23, Suppl. 6 (2019): 2045–52. http://dx.doi.org/10.2298/tsci190725369p.

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In the present scientific work, an operational matrix scheme with Laguerre polynomials is applied to solve a space-time fractional order non-linear Cahn-Hilliard equation, which is used to calculate chemical potential and free energy for a non-homogeneous mixture. Constructing operational matrix for fractional differentiation, the collocation method is applied to convert Cahn-Hilliard equation into an algebraic system of equations, which have been solved using Newton method. The prominent features of the manuscript is to providing the stability analysis of the proposed scheme and the pictorial presentations of numerical solution of the concerned equation for different particular cases and showcasing of the effect of advection and reaction terms on the nature of solute concentration of the considered mathematical model for different particular cases.

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MUKHERJEE, A., and R. KORRAPATI. "TWIST-THREE DISTRIBUTION f⊥(x, k⊥) IN LIGHT-FRONT HAMILTONIAN APPROACH." Modern Physics Letters A 26, no. 35 (November 20, 2011): 2653–62. http://dx.doi.org/10.1142/s0217732311036772.

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We calculate the twist-three distribution f⊥(x, k⊥) contributing to Cahn effect in unpolarized semi-inclusive deep inelastic scattering. We use light-front Hamiltonian technique and take the state to be a dressed quark at one-loop in perturbation theory. The "genuine twist-three" contribution comes from the quark–gluon interaction part in the operator and is explicitly calculated. f⊥(x, k⊥) is compared with f1(x, k⊥).

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Kuznetsov, V. V., P. P. Moskvin, and S. I. Skurativskyi. "Composition modulation in the Ga_xIni-_xPyAs_1-y - InP heterostructure during spinodal decomposition under the conditions of internal energy resonance." Journal of Physics: Conference Series 2103, no. 1 (November 1, 2021): 012117. http://dx.doi.org/10.1088/1742-6596/2103/1/012117.

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Abstract The Cahn-Hilliard concepts are generalized and used to the description of the spinodal decomposition of A3B5 quaternary semiconductor solid solutions, when the mixing of components occurs simultaneously in the metallic and metalloid sublattices of the sphalerite structure. The resulting system of differential equations for material decomposition was used to describe the effect of composition modulation observed in the synthesis of GaxIn1-xPyAs1-y - InP heterostructures. Numerical simulation of the spinodal decomposition of the GaxIm-xPyAsuy solid solution is carried out. The intervals of the thermodynamic parameters of the technological process of the synthesis of structures, in which the effect of modulation of the composition should be manifested, are found.

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Newfeld, Daria J. "The Shemita Effect, How a Jewish agricultural law prompted fear for Evangelical investors: Confirmation Bias and Bandwagoning in Action." Journal of Economics and Behavioral Studies 9, no. 2 (May 18, 2017): 96. http://dx.doi.org/10.22610/jebs.v9i2.1653.

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This paper examines how Shemita, a Jewish agricultural law only applicable in Israel came to be viewed by Evangelical Christian Investors as a signal of a potential stock market crash in September, 2015 purportedly as a consequence of G-d’s displeasure with the United States. In 2014 Johnathan Cahn, a popular Evangelical preacher, published “The Shemita Effect” which claimed that the seven year Shemita cycle mirrored stock market patterns over the last 50 years and suggested an impending crash. This theory was quickly taken up by conservative Christian Evangelical media and at least one man was convinced enough to start an entire investment company based on it despite the fact that it is easily disproven using basic statistical analysis of freely available data. This bizarre incident illustrates confirmation bias and bandwagoning effects in action, amplified with religious fervor.

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Sugathan, Sandeep, and Saswata Bhattacharya. "Phase-Field Modelling of Evolution of Compact Ordered Precipitates in Ternary Alloy Systems." MRS Advances 4, no. 25-26 (2019): 1457–63. http://dx.doi.org/10.1557/adv.2019.104.

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ABSTRACTSeveral technologically important alloys like Al-Li-Zr, Al-Li-Sc, Al-Sc-Zr, Al-Li-Sc-Zr, modified Inconel etc., exhibit compact precipitates in their microstructure. We present a phase-field model in two dimensions to study the morphological evolution of composite precipitates in ternary alloys. The model employs a modified regular solution description of the bulk free energy of the disordered matrix phase and ordered precipitates. Elastic strain energy of the three-phase system is described using Khachaturyan’s microelasticity theory. The temporal evolution of the spatially dependent field variables is determined by numerically solving coupled Cahn-Hilliard and Allen-Cahn equations for composition and order parameter fields, respectively. We systematically vary the misfit strains, alloy chemistry and mobilities of the diffusing species to study their effect on the development of compact precipitates. Compact core-shell morphology destabilizes when the precipitate phases have misfit strains of opposite signs with the matrix phase although the relative interfacial energies between the phases satisfy Cahn’s spontaneous wetting condition. Thus, the stability of “monodisperse” core-shell microstructures is determined by the interplay between the relative interfacial energies and elastic interactions between the phases. Further, our simulations show that low solute mobility within the core leads to sluggish coarsening of the compact particles.

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Afzal, M., M. Khan, and H. Ahmad. "Kinetics of the Sorption of Organic Vapours in Chromatographic Silica Gel." Adsorption Science & Technology 11, no. 2 (June 1994): 113–22. http://dx.doi.org/10.1177/026361749401100205.

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Organic vapours such as ethyl methyl ketone, methyl acetate, methyl alcohol, diethyl ether, acetone and acetaldehyde were adsorbed on to the chromatographic silica gel between 273 K and 297 K under a vacuum of 10–4 to 10–5 Torr. A Cahn 1000 electrobalance and an X–Y Beckman chart recorder were used for recording the data. Kinetic parameters such as rate constant, Knudsen diffusivities, bulk diffusivities and effective diffusivities have been calculated employing the Fick-type equation. The effect of temperature on the sorption of these organic vapours has also been discussed.

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Newfeld, Daria J. "The Shemita Effect, How a Jewish agricultural law prompted fear for Evangelical investors: Confirmation Bias and Bandwagoning in Action." Journal of Economics and Behavioral Studies 9, no. 2(J) (May 18, 2017): 96–103. http://dx.doi.org/10.22610/jebs.v9i2(j).1653.

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This paper examines how Shemita, a Jewish agricultural law only applicable in Israel came to be viewed by Evangelical Christian Investors as a signal of a potential stock market crash in September, 2015 purportedly as a consequence of G-dâ€™s displeasure with the United States. In 2014 Johnathan Cahn, a popular Evangelical preacher, published â€œThe Shemita Effectâ€ which claimed that the seven year Shemita cycle mirrored stock market patterns over the last 50 years and suggested an impending crash. This theory was quickly taken up by conservative Christian Evangelical media and at least one man was convinced enough to start an entire investment company based on it despite the fact that it is easily disproven using basic statistical analysis of freely available data. This bizarre incident illustrates confirmation bias and bandwagoning effects in action, amplified with religious fervor.

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Shen, Mingguang, and Ben Q. Li. "A Phase Field Approach to Modeling Heavy Metal Impact in Plasma Spraying." Coatings 12, no. 10 (September 22, 2022): 1383. http://dx.doi.org/10.3390/coatings12101383.

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A phase field model enhanced with the shared memory parallelism OpenMP was proposed, capable of modeling the impact of a heavy metal droplet under practical plasma spraying conditions. The finite difference solution of the Navier-Stokes equations, coupled with the Cahn-Hilliard equation, tracks the gas-liquid interface. The liquid fraction, defined over the computational domain, distinguishes fluid from solid. The model is employed for Ni and YSZ drop impacts after ruling out the effect of mesh size. The model exhibits a reasonable parallel-computing efficiency, and the predicted maximum spread factors agree well with analytical models.

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Jornet, Marc. "Modeling of Allee effect in biofilm formation via the stochastic bistable Allen–Cahn partial differential equation." Stochastic Analysis and Applications 39, no. 1 (June 16, 2020): 22–32. http://dx.doi.org/10.1080/07362994.2020.1777163.

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Chen, Jie, Shuyu Sun, and Zhangxin Chen. "Coupling Two-Phase Fluid Flow with Two-Phase Darcy Flow in Anisotropic Porous Media." Advances in Mechanical Engineering 6 (January 1, 2014): 871021. http://dx.doi.org/10.1155/2014/871021.

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This paper reports a numerical study of coupling two-phase fluid flow in a free fluid region with two-phase Darcy flow in a homogeneous and anisotropic porous medium region. The model consists of coupled Cahn-Hilliard and Navier-Stokes equations in the free fluid region and the two-phase Darcy law in the anisotropic porous medium region. A Robin-Robin domain decomposition method is used for the coupled Navier-Stokes and Darcy system with the generalized Beavers-Joseph-Saffman condition on the interface between the free flow and the porous media regions. Obtained results have shown the anisotropic properties effect on the velocity and pressure of the two-phase flow.

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Lee, Hyun Geun, Jintae Park, Sungha Yoon, Chaeyoung Lee, and Junseok Kim. "Mathematical Model and Numerical Simulation for Tissue Growth on Bioscaffolds." Applied Sciences 9, no. 19 (September 28, 2019): 4058. http://dx.doi.org/10.3390/app9194058.

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Tissue growth on bioscaffolds can be controlled using substrate geometry such as substrate curvature. In this study, we present a mathematical model and numerical simulation method for tissue growth on a bioscaffold to investigate the effect of local curvature on tissue growth. The mathematical model is based on the Allen–Cahn (AC) equation, which has been extensively used to model many problems involving motion by mean curvature. By solving the AC equation using the explicit Euler method, the proposed method is simple and fast. Numerical simulations on various geometries are presented to demonstrate the applicability of the proposed framework on tissue growth on a bioscaffold.

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Mendelev, M. I., D. J. Srolovitz, G. J. Ackland, and S. Han. "Effect of Fe Segregation on the Migration of a Non-Symmetric Σ5 Tilt Grain Boundary in Al." Journal of Materials Research 20, no. 1 (January 2005): 208–18. http://dx.doi.org/10.1557/jmr.2005.0024.

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We present an analysis, based upon atomistic simulation data, of the effect of Fe impurities on grain boundary migration in Al. The first step is the development of a new interatomic potential for Fe in Al. This potential provides an accurate description of Al–Fe liquid diffraction data and the bulk diffusivity of Fe in Al. We use this potential to determine the physical parameters in the Cahn–Lücke–Stüwe (CLS) model for the effect of impurities on grain boundary mobility. These include the heat of segregation of Fe to grain boundaries in Al and the diffusivity of Fe in Al. Using the simulation-parameterized CLS model, we predict the grain boundary mobility in Al in the presence of Fe as a function of temperature and Fe concentration. The order of magnitude and the trends in the mobility from the simulations are in agreement with existing experimental results.

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Moskvin, Pavel, Sergii Skurativskyi, Wojciech Sadowski, Barbara Koscielska, Petro Melnychuk, and Oleksandr Prylypko. "Resonance of mixing energy and energy of elastic deformations during spinodal decomposition and the composition modulation effect in ZnхCd1-ХTe solid solutions." Metallurgical and Materials Engineering 27, no. 3 (September 9, 2021): 385–96. http://dx.doi.org/10.30544/614.

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The Cahn-Hilliard equation is adapted to consider the spinodal decomposition of A2B6 semiconductor solid solutions. This approach is used to analyze the process of spinodal decomposition of ZnхCd1-хTe solid solution, which is accompanied by the appearance of the composition modulation effect during its low-temperature synthesis. Numerical simulations of the spinodal decomposition of the ZnхCd1-хTe solid solution are performed. It is shown that micro-variations of the material composition are related by the resonance phenomenon between the excess mixing energy and the energy of elastic strains arising in the inclusions of the new phase, which are coherently conjugated with the initial crystal lattice. It is revealed that such resonance phenomena are most intense when the conditions for the material synthesis are located in close proximity to the spinodal curves on the phase state diagram of the system.

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Antonopoulou, Dimitra, Ĺubomír Baňas, Robert Nürnberg, and Andreas Prohl. "Numerical approximation of the stochastic Cahn–Hilliard equation near the sharp interface limit." Numerische Mathematik 147, no. 3 (February 17, 2021): 505–51. http://dx.doi.org/10.1007/s00211-021-01179-7.

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AbstractWe consider the stochastic Cahn–Hilliard equation with additive noise term $$\varepsilon ^\gamma g\, {\dot{W}}$$ ε γ g W ˙ ($$\gamma >0$$ γ > 0 ) that scales with the interfacial width parameter $$\varepsilon $$ ε . We verify strong error estimates for a gradient flow structure-inheriting time-implicit discretization, where $$\varepsilon ^{-1}$$ ε - 1 only enters polynomially; the proof is based on higher-moment estimates for iterates, and a (discrete) spectral estimate for its deterministic counterpart. For $$\gamma $$ γ sufficiently large, convergence in probability of iterates towards the deterministic Hele–Shaw/Mullins–Sekerka problem in the sharp-interface limit $$\varepsilon \rightarrow 0$$ ε → 0 is shown. These convergence results are partly generalized to a fully discrete finite element based discretization. We complement the theoretical results by computational studies to provide practical evidence concerning the effect of noise (depending on its ’strength’ $$\gamma $$ γ ) on the geometric evolution in the sharp-interface limit. For this purpose we compare the simulations with those from a fully discrete finite element numerical scheme for the (stochastic) Mullins–Sekerka problem. The computational results indicate that the limit for $$\gamma \ge 1$$ γ ≥ 1 is the deterministic problem, and for $$\gamma =0$$ γ = 0 we obtain agreement with a (new) stochastic version of the Mullins–Sekerka problem.

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Ahmadlouydarab, Majid, and James J. Feng. "Motion and coalescence of sessile drops driven by substrate wetting gradient and external flow." Journal of Fluid Mechanics 746 (April 1, 2014): 214–35. http://dx.doi.org/10.1017/jfm.2014.133.

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AbstractWe report two-dimensional simulations of drop dynamics on a substrate subject to a wetting gradient and an external pressure gradient along the substrate. A phase-field formulation is used to represent the drop interface, and the moving contact line is modelled by Cahn–Hilliard diffusion. The Navier–Stokes–Cahn–Hilliard equations are solved by finite elements on an adaptively refined unstructured grid. For a single drop and a pair of drops, we consider three scenarios of drop motion driven by the wetting gradient only, by the external flow only, and by a combination of the two. Both the capillary force and the hydrodynamic drag depend strongly on the shape of the drop. Since the drop adapts its shape to the local wetting angles and to the external flow on a finite time scale, hysteresis is a prominent feature of the drop dynamics under opposing forces. For each wetting gradient, there is a narrow range of the magnitude of the external flow within which a single drop can achieve a stationary state. The equilibrium drop shape and position depend on its initial shape and the history of forcing. For a pair of drops, the wetting gradient or external flow alone tends to produce catch-up and coalescence. The flow-driven coalescence arises from a viscous shielding effect that relies on the asymmetric shape of the trailing drop once it is deformed by flow. This mechanism operates at zero Reynolds number, but is much enhanced by inertia. With the two forces opposing each other, the external flow favours separation while the wetting gradient favours coalescence. The outcome depends on their competition.

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Giardino, Luciano, Flaviana Bombarda de Andrade, and Riccardo Beltrami. "Antimicrobial Effect and Surface Tension of Some Chelating Solutions with Added Surfactants." Brazilian Dental Journal 27, no. 5 (October 2016): 584–88. http://dx.doi.org/10.1590/0103-6440201600985.

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Abstract This study assessed the antimicrobial efficacy and surface tension of established irrigating solutions with a new experimental chelating solution in infected dentin tubes. Twenty-five specimens were randomly assigned to each of the irrigating solutions. Twenty specimens were used as negative and positive controls. After 21 days of contamination with E. faecalis, the irrigating solutions MTAD, QMiX and Tetraclean NA were delivered into each infected root canal. The solutions were removed and dentin samples were withdrawn from the root canals with sterile low-speed round burs with increasing ISO diameters. The dentin powder samples obtained with each bur were immediately collected in separate test tubes containing 3 mL of BHI broth. After that, 100 μL from each test tube was cultured on blood agar. The grown colonies were counted and recorded as colony-forming units (CFU). The surface tension of the irrigants was measured using a Cahn DCA-322 Dynamic Contact Angle Analyzer. A Kruskal Wallis nonparametric ANOVA and a Friedman test were used (p<0.05). Tetraclean NA showed lower surface tension and CFU values than MTAD and QMiX. Better antibacterial action and low surface tension were observed for Tetraclean NA, probably due to the improved penetration into the root canal and dentinal tubes

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Long, Yong Qiang, Ping Liu, Yong Liu, Shu Guo Jiao, and Bao Hong Tian. "Numerical Simulation of Spinodal Deposition in Cu–6at.%Ni–3at.%Si Ternary Alloy Using of Phase Field Method." Materials Science Forum 704-705 (December 2011): 1410–15. http://dx.doi.org/10.4028/www.scientific.net/msf.704-705.1410.

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Based on Cahn-Hilliard nonlinear diffusion equation, the phase field model has been established for ternary alloy spinodal decomposition, which directly couples with Calphad thermodynamics and dynamics calculation and takes into account the effect of the coherent elastic energy. The simulated microstructures of spinodal decomposition were carried out in the isothermally-aged of Cu-6at.%Ni-3at.%Si alloy. The results indicate that the spinodal decomposition takes place at the early stage of Cu-6at.%Ni-3at.%Si alloy aging at temperatures of 723K, forming two-phases mixture of Cu-rich and Ni/Si-rich, and the decomposition microstructures are distributed in a semi-interconnected labyrinth-like form. Under the effect of the coherent elastic energy, the decomposition microstructures demonstrate the obvious anisotropic characteristics, and present interconnected rectangular stripes aligned along [10] and [01] directions. The growth of the decomposition microstructures is in accordance with the growth law of growth exponentn≈0.29, slightly less than the LSW’s prediction.

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Defu, Li, and Wang Jinqu. "The Adsorption and Separation of Ethylene, Oxygen and Carbon Dioxide Gases on Molecular Sieves." Adsorption Science & Technology 20, no. 1 (February 2002): 83–90. http://dx.doi.org/10.1260/026361702760120944.

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The equilibrium adsorption and diffusion properties of ethylene, oxygen and carbon dioxide gases on two kinds of molecular sieve at 25°C were measured by gravimetric methods using a Cahn-2000 electrobalance. On both molecular sieves, the equilibrium adsorption capacity of ethylene was larger than that of oxygen and close to that of carbon dioxide, indicating that it would not be possible to remove oxygen and carbon dioxide gases from their mixture with ethylene in order to effect recovery of the latter via equilibrium separation methods. However, during the early stages of adsorption, the adsorption rates of carbon dioxide and oxygen were faster than that of ethylene thereby suggesting recovery of the latter from the gaseous mixture via kinetic separation based on the difference in adsorption diffusivity. Such separation was conducted using a two-bed column pressure swing adsorption arrangement with the effects of the experimental conditions on the separation being investigated. Oxygen and carbon dioxide may be adsorbed and removed from the gaseous mixture, leaving the output gases rich in ethylene.

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ABELS, H., and J. KAMPMANN. "On a model for phase separation on biological membranes and its relation to the Ohta–Kawasaki equation." European Journal of Applied Mathematics 31, no. 2 (March 11, 2019): 297–338. http://dx.doi.org/10.1017/s0956792519000056.

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We provide a detailed mathematical analysis of a model for phase separation on biological membranes which was recently proposed by Garcke, Rätz, Röger and the second author. The model is an extended Cahn–Hilliard equation which contains additional terms to account for the active transport processes. We prove results on the existence and regularity of solutions, their long-time behaviour, and on the existence of stationary solutions. Moreover, we investigate two different asymptotic regimes. We study the case of large cytosolic diffusion and investigate the effect of an infinitely large affinity between membrane components. The first case leads to the reduction of coupled bulk-surface equations in the model to a system of surface equations with non-local contributions. Subsequently, we recover a variant of the well-known Ohta–Kawasaki equation as the limit for infinitely large affinity between membrane components.

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Ghaedi, Mohammad Sadegh, and Mahdi Javanbakht. "Effect of a thermodynamically consistent interface stress on thermal-induced nanovoid evolution in NiAl." Mathematics and Mechanics of Solids 26, no. 9 (January 18, 2021): 1320–36. http://dx.doi.org/10.1177/1081286520986603.

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In the present work, the effect of a thermodynamically consistent inelastic interface stress on nanovoid evolution in NiAl is studied. Such interface stress is introduced for the solid–gas interface of nanovoids within the concept of the phase field approach. The Cahn–Hilliard (CH) equation using the Helmholtz free energy describes the evolution of nanovoid concentration. The interface stress changes the total stress distribution and affects the elastic stress field. Thus, due to the significant effect of the elastic energy on nanovoid dynamics, it can indirectly affect nanovoid nucleation and growth. The highly nonlinear coupled CH and elasticity equations are solved using the finite element method and the COMSOL code. The coupling appears due to the presence of the nonlinear nanovoid inelastic strain in the total strain, the presence of the nonlinear inelastic interface stress in the stress tensor and the presence of elastic energy in the Helmholtz free energy. Several examples of thermal-induced nanovoid evolutions are presented to investigate the effect of the solid–gas interface stress. The obtained results show the significant effect of the interface stress on the total stress distribution, and consequently a different distribution of thermodynamic driving force which can affect the nanostructure evolution and the deformation. Mainly, the interface stress represents a promotive effect on nanovoid growth which results in a faster nanovoid growth and a larger nanovoid concentration and region.

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Takemoto, Norihisa, and Yoshiyuki Saito. "Effects of Minor Elements X(X=Mo, Ni, Ti) on Aympotic Behavior along Peak Top of the Major Elenet in Fe-Cr Type Alloys." Advanced Materials Research 409 (November 2011): 423–30. http://dx.doi.org/10.4028/www.scientific.net/amr.409.423.

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Numerical simulations of phase separation in Fe-Cr-Mo and Fe-Cr-Ti ternary alloys and Fe-Cr-Mo-Ti quaternary alloys were performed with use of the Cahn-Hilliard equation for ternary alloys and quaternary alloys. We obtained that the asymptotic behaviours of minor element X(Mo, Ti) in Fe-Cr-X ternary alloys and Fe-Cr-Mo-Ti quaternary alloys along a trajectory of a peak top of the major element Cr was classified into three groups according to the sign of the second derivative of the chemical free energy with respect to the compositions of Cr and X(Mo, Ti). Theoretical analysis for the symptotic behavior Mo in Fe-Cr-Mo ternary has been formed in order to discuss the simulation results. Effect of the other elements, such as Ti on separation behaviours of Cr in Fe-Cr-Ti ternary alloys were also investigated. A simple theory for describing the effect of subsutitutonal element in Fe-Cr-X ternary alloys on the basis of simulations and theoretical analyses was proposed.

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Jiang, Yongyue, Ping Lin, Zhenlin Guo, and Shuangling Dong. "Numerical Simulation for Moving Contact Line with Continuous Finite Element Schemes." Communications in Computational Physics 18, no. 1 (July 2015): 180–202. http://dx.doi.org/10.4208/cicp.170314.160115a.

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AbstractIn this paper, we compute a phase field (diffuse interface) model of Cahn-Hilliard type for moving contact line problems governing the motion of isothermal multiphase incompressible fluids. The generalized Navier boundary condition proposed by Qian et al. [1] is adopted here. We discretize model equations using a continuous finite element method in space and a modified midpoint scheme in time. We apply a penalty formulation to the continuity equation which may increase the stability in the pressure variable. Two kinds of immiscible fluids in a pipe and droplet displacement with a moving contact line under the effect of pressure driven shear flow are studied using a relatively coarse grid. We also derive the discrete energy law for the droplet displacement case, which is slightly different due to the boundary conditions. The accuracy and stability of the scheme are validated by examples, results and estimate order.

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Wu, Ping Ping, Guan Wang, and Shu Min Pang. "A Phase-Field Model for Multilayered Heterostructure Morphology." Materials Science Forum 944 (January 2019): 788–94. http://dx.doi.org/10.4028/www.scientific.net/msf.944.788.

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Heteroepitaxially grown multilayered thin film structures have been attracted of great interest due to its potential applications in photovoltaic/light emitting/electronics devices. The thin film morphology plays an important role in enhancing its related physical properties. It is not easy to simulate the multi-layered thin film structures due to the influence of the interface/surface fluctuation. However, the phase field method, based on thermodynamics and Cahn-Hilliard diffusion model, can predict the thin film morphologies without tracking the interfaces. In this paper, a new phase field model was developed for predicting multi-layer structures with multi-order parameters. The morphologies with strain distributions of the quantum wells, quantum dots and buffer layers structures were investigated in the current study. We found that the strain distribution has a strong effect on the suface/interface morphologies in the multilayered structures. Some simulation results are consistent with experimental observations.

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Gondyul, Е. А., and V. V. Lisitsa. "Modeling of unsteady flows of multiphase viscous fluid in a pore space." Interexpo GEO-Siberia 2, no. 2 (May 18, 2022): 32–37. http://dx.doi.org/10.33764/2618-981x-2022-2-2-32-37.

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The authors have developed and implemented a numerical algorithm to model unsteady flows of a viscous multiphase isothermal fluid by finite difference method using the projection method for the numerical solution of the Navier-Stokes equation. The projection method implies splitting the initial system of equations by physical processes, in which convective transport and the effect of the pressure gradient are separately taken into account. As a result, at each step, it is necessary to solve the Poisson equation to find the pressure field. The solution of SLAE is performed by a parallel direct solver based on LU decomposition. An explicit scheme is used to solve the Cahn-Hilliard equation to update the phase field, the parameter of which is taken into account when adding surface forces to the Navier-Stokes equation. Computational experiments showing qualitative and quantitative agreement with experimental and numerical data from the literature are presented.

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Fukuzawa, Hideya, Sarami Ishida, and Shigetoh Miyachi. "cDNA cloning and gene expression of carbonic anhydrase in Chlamydomonas reinhardtii." Canadian Journal of Botany 69, no. 5 (May 1, 1991): 1088–96. http://dx.doi.org/10.1139/b91-139.

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cDNA and genes encoding periplasmic carbonic anhydrase (CA) polypeptides of Chlamydomonas reinhardtii have been isolated and characterized. Nucleotide sequence analysis of cDNA clones revealed that the large subunit (35 kDa or 36.5 kDa) and the small subunit (4 kDa) are cotranslated as a precursor polypeptide (41 626 Da) with a NH2-terminal hydrophobic signal peptide of 20 amino acids. The amino acid sequence of Chlamydomonas CA showed 20–22% identity with animal CA isozymes (CAI, CAII, CAIII, and CAVII). Three zinc-liganded histidine residues and those forming the hydrogen-bond network to zinc-bound solvent molecules were highly conserved. No significant sequence similarity was observed between Chlamydomonas CA and chloroplast CAs of spinach and pea. Two copies of structurally related CA genes (CAH1 and CAH2) were tandemly clustered in Chlamydomonas nuclear genome and regulated by external CO2 concentration in a reverse manner. The 5′ upstream gene CAH1 encodes the major periplasmic CA whose mRNA level is induced under low CO2 condition in light. Photosynthesis is absolutely required for the accumulation of the CAH1 mRNA. The 3′ downstream gene CAH2 is possibly a gene for another periplasmic CA isozyme, which is induced under high CO2 conditions. Light has an inhibitory effect on the accumulation of the CAH2 mRNA. Key words: photosynthesis, light regulation, zinc, CO2-concentrating mechanism, intracellular processing.

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Cooper, L. J., K. R. Daly, P. D. Hallett, M. Naveed, N. Koebernick, A. G. Bengough, T. S. George, and T. Roose. "Fluid flow in porous media using image-based modelling to parametrize Richards' equation." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 473, no. 2207 (November 2017): 20170178. http://dx.doi.org/10.1098/rspa.2017.0178.

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The parameters in Richards' equation are usually calculated from experimentally measured values of the soil–water characteristic curve and saturated hydraulic conductivity. The complex pore structures that often occur in porous media complicate such parametrization due to hysteresis between wetting and drying and the effects of tortuosity. Rather than estimate the parameters in Richards' equation from these indirect measurements, image-based modelling is used to investigate the relationship between the pore structure and the parameters. A three-dimensional, X-ray computed tomography image stack of a soil sample with voxel resolution of 6 μm has been used to create a computational mesh. The Cahn–Hilliard–Stokes equations for two-fluid flow, in this case water and air, were applied to this mesh and solved using the finite-element method in COMSOL Multiphysics. The upscaled parameters in Richards' equation are then obtained via homogenization. The effect on the soil–water retention curve due to three different contact angles, 0°, 20° and 60°, was also investigated. The results show that the pore structure affects the properties of the flow on the large scale, and different contact angles can change the parameters for Richards' equation.

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Zhou, Jingjing, Lijun Zhang, and Li Chen. "Effect of Cr on metastable phase equilibria and spinodal decomposition in c-TiAlN coatings: A CALPHAD and Cahn-Hilliard study." Surface and Coatings Technology 311 (February 2017): 231–37. http://dx.doi.org/10.1016/j.surfcoat.2017.01.007.

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Tian, Ben, Bing Zhang, Junkai Deng, Dong Wang, Houjun Gong, Yang Li, Kerong Guo, Sen Yang, and Xiaoqin Ke. "Morphological evolution during liquid-liquid phase separation governed by composition change pathways." Journal of Applied Physics 132, no. 6 (August 14, 2022): 064702. http://dx.doi.org/10.1063/5.0089516.

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Liquid-liquid phase separation (LLPS) phenomenon are widely recognized to be of vital importance for physics, materials science, and biology. It is highly desired to develop powerful tools to study the LLPS behavior and related physical mechanisms. For this purpose, a phase-field method was developed here which combines the Cahn-Hilliard diffusion equation and the Navier-Stokes equation. The morphological evolution of LLPS behavior with the change in composition was comprehensively investigated under a prototypical ternary theoretical phase diagram. The phase-field simulation results indicated that the microstructural evolution was controlled by the phase diagram and driven by the coupling of diffusion and gravity effect. Moreover, the intermediate morphological microstructures and corresponding interfacial properties during LLPS could be tuned by selecting different composition change pathways. Furthermore, gravity-dependent density overturning and consequent Rayleigh-Taylor instability were observed in a unique LLPS process, demonstrating that the proposed model can capture the critical features of LLPS phenomenon.

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He, Zhennan, Fachun Liang, and Jia Meng. "Pore-scale study of the effect of bifurcated fracture on spontaneous imbibition in heterogeneous porous media." Physics of Fluids 34, no. 7 (July 2022): 072003. http://dx.doi.org/10.1063/5.0095553.

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Fracturing is an important technique to improve the remediation of low permeability soils and heterogeneous soils, which produce a fracture system with obvious bifurcation characteristics. Understanding the interaction mechanism between bifurcated fractures and matrix can help further enhance the beneficial effect of fracturing on soil remediation. In this study, the coupled Cahn–Hilliard phase field method and Navier–Stokes equations were solved using the finite element solver COMSOL Multiphysics to capture the oil–water interface evolution during the dynamic imbibition process in a 2D realistic pore geometry with different bifurcation fracture morphologies. The results show that the spontaneous imbibition process of the single fracture model is divided into the blocking regime and the discharging regime, while an additional connecting regime exists in the bifurcated fracture model. The growing pressure near the inlet under the blocking regime and the connecting regime is responsible for the higher remediation efficiency in the left part of the matrix. Due to the snap-off phenomenon of the oil plug expelled by the bifurcated fracture, the remediation efficiency curve shows a periodic fluctuation trend. Compared with the single fracture model, the ultimate remediation efficiency in the model with a secondary fracture and that with a tertiary fracture is improved by 30% and 33%, respectively. These results shed light upon the imbibition mechanism in a heterogeneous porous media with bifurcated fracture, which can provide guidance for the development of enhancement strategies in soil remediation.

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Suwa, Yoshihiro, and Yoshiyuki Saito. "Effect of Mo on Phase Separation in Fe-40 at% Cr Alloys Based on Numerical Solutions of the Cahn Hilliard Equation." MATERIALS TRANSACTIONS 48, no. 7 (2007): 1891–95. http://dx.doi.org/10.2320/matertrans.mra2006335.

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Javanbakht, Mahdi, Mohammad Sadegh Ghaedi, Emilio Barchiesi, and Alessandro Ciallella. "The effect of a pre-existing nanovoid on martensite formation and interface propagation: a phase field study." Mathematics and Mechanics of Solids 26, no. 1 (August 6, 2020): 90–109. http://dx.doi.org/10.1177/1081286520948118.

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In the present work, the effect of a pre-existing nanovoid on martensitic phase transformation (PT) is investigated using the phase field approach. The nanovoid is created as a solution of the coupled Cahn–Hilliard and elasticity equations. The coupled Ginzburg–Landau and elasticity equations are solved to capture the martensitic nanostructure. The above systems of equations are solved using the finite element method and COMSOL code. The austenite ( A)–martensite ( M) interface propagation is investigated without the nanovoid and with it for different nanovoid misfit strains and different temperatures. With the nanovoid, the evolution of the moving interface is changed even before it reaches the nanovoid surface due to the nanovoid stress concentration. It is also found that for small misfit strains, pre-transformation occurs near the nanovoid. For larger misfit strains, martensite nucleates and grows near the nanovoid surface and coalesces with the moving interface. The nanovoid shows a promotive effect on the PT with an increase in the rate of transformation, which is discussed based on the transformation work distribution. The effect of the nanovoid is more pronounced on a curved interface. The nanovoid-induced martensitic growth is mainly dependent on the transformation strain tensor. Examples for different transformation strains are presented where a stable non-complete transformed sample with no void becomes unstable in the presence of the nanovoid. The presented model and results will help to develop an interaction model between nanovoids and multiphase structures at the nanoscale.

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Munk, Lukas, Silvia Reschka, Hans Jürgen Maier, Peter Wriggers, and Stefan Löhnert. "A Sharp-Interface Model of the Diffusive Phase Transformation in a Nickel-Based Superalloy." Metals 12, no. 8 (July 27, 2022): 1261. http://dx.doi.org/10.3390/met12081261.

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A sharp-interface model employing the extended finite element method is presented. It is designed to capture the prominent γ-γ′ phase transformation in nickel-based superalloys. The novel combination of crystal plasticity and sharp-interface theory outlines a good modeling alternative to approaches based on the Cahn–Hilliard equation. The transformation is driven by diffusion of solute γ′-forming elements in the γ-phase. Boundary conditions for the diffusion problem are computed by the stress-modified Gibbs–Thomson equation. The normal mass balance of solute atoms at the interface yields the normal interface velocity, which is integrated in time by a level set procedure. In order to capture the influence of dislocation glide and climb on interface motion, a crystal plasticity model is assumed to describe the constitutive behaviour of the γ-phase. Cuboidal equilibrium shapes and Ostwald ripening can be reproduced. According to the model, in low γ′ volume-fraction alloys with separated γ′-precipitates, interface movement does not have a significant effect on tensile creep behaviour at various lattice orientations.

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Shah, Abdullah, Sadia Saeed, and L. Yuan. "An Artificial Compressibility Method for 3D Phase-Field Model and its Application to Two-Phase Flows." International Journal of Computational Methods 14, no. 05 (January 6, 2017): 1750059. http://dx.doi.org/10.1142/s0219876217500591.

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In this work, a numerical scheme based on artificial compressibility formulation of a phase-field model is developed for simulating two-phase incompressible flow problems. The coupled nonlinear systems composed of the incompressible Navier–Stokes equations and volume preserving Allen–Cahn-type phase-field equation are recast into conservative form with source terms, which are suited to implement high-resolution schemes originally developed for hyperbolic conservation laws. The Boussinesq approximation is used to account for the buoyancy effect in flow with small density difference. The fifth-order weighted essentially nonoscillatory (WENO) scheme is used for discretizing the convective terms while dual-time stepping (DTS) technique is used for obtaining time accuracy at each physical time step. Beam–Warming approximate factorization scheme is utilized to obtain block tridiagonal system of equations in each spatial direction. The alternating direction implicit (ADI) algorithm is used to solve the resulting system of equations. The performance of the method is demonstrated by its application to some 2D and 3D benchmark viscous two-phase flow problems.

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44

Boettinger, W. J., J. E. Guyer, C. E. Campbell, and G. B. McFadden. "Computation of the Kirkendall velocity and displacement fields in a one-dimensional binary diffusion couple with a moving interface." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 463, no. 2088 (October 9, 2007): 3347–73. http://dx.doi.org/10.1098/rspa.2007.1904.

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The moving interface problem in a one-dimensional binary α/β diffusion couple is studied using sharp and diffuse interface (Cahn–Hilliard) approaches. With both methods, we calculate the solute field and the Kirkendall marker velocity and displacement fields. In the sharp interface treatment, the velocity field is generally discontinuous at the interphase boundary, but can be integrated to obtain a displacement field that is continuous everywhere. The diffuse interface approach avoids this discontinuity, simplifies the integration and yet gives the same qualitative behaviour. Special features observed experimentally and reported in the literature are also studied with the two methods: (i) multiple Kirkendall planes, where markers placed on the initial compositional discontinuity of the diffusion couple bifurcate into two locations, and (ii) a Kirkendall plane that coincides with the interphase interface. These situations occur with special values of the interdiffusion coefficients and starting couple compositions. The details of the deformation in these special situations are given using both methods and are discussed in terms of the stress-free strain rate associated with the Kirkendall effect.

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Shen, Mingguang, and Ben Q. Li. "Phase Field Modeling of Air Entrapment in Binary Droplet Impact with Solidification Microstructure Formation." Coatings 12, no. 12 (December 19, 2022): 1990. http://dx.doi.org/10.3390/coatings12121990.

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A novel numerical model was developed to investigate air entrapment in binary droplet impact with solidification microstructure formation under practical plasma spraying conditions. The evolving liquid–gas interface was tracked by the explicit finite difference solution to the Cahn–Hilliard equation, coupled with the Navier–Stokes equations. Another diffuse interface model was invoked to trace solid–liquid and grain–grain boundaries. The model was discretized using an explicit finite difference method on a half-staggered grid. The velocity pressure coupling was decoupled with the projection method. The in-house code was written in Fortran and was run with the aid of the shared memory parallelism, OpenMP. The time duration over which gas compressibility matters was estimated. Typical cases with air entrapment were studied with the model. The effect of droplet porosity on air entrapment was probed into as well: the larger the porosity of a droplet, the bigger the trapped air bubble. The grain growth near the air bubble is skewed. Moreover, a case without air entrapment was also shown herein to stress that air bubbles could be suppressed or even eliminated in plasma spraying by adjusting the landing positions of successive droplets.

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Santoki, Jay, Simon Daubner, Daniel Schneider, Marc Kamlah, and Britta Nestler. "Effect of tortuosity, porosity, and particle size on phase-separation dynamics of ellipsoid-like particles of porous electrodes: Cahn–Hilliard-type phase-field simulations." Modelling and Simulation in Materials Science and Engineering 29, no. 6 (July 20, 2021): 065010. http://dx.doi.org/10.1088/1361-651x/ac11bc.

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Ranjbarrad, Samira, and Philip K. Chan. "The Effect of Conductive Heat Transfer on the Morphology Formation in Polymer Solutions Undergoing Thermally Induced Phase Separation." Polymers 14, no. 20 (October 15, 2022): 4345. http://dx.doi.org/10.3390/polym14204345.

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Owing to the fact that heat transfer during the thermally induced phase separation process is limited, a quench rate is inevitably entailed, which leads to the existence of temporal and spatial variations in temperature. Hence, it is of great importance to take into account the nonisothermality during the phase separation process, especially in high viscosity polymer solutions. In this study, the influence of conductive heat transfer on the morphology formation during the thermally induced phase separation process was investigated theoretically in terms of quench depth, boundary conditions, and enthalpy of demixing to elucidate the interaction between temperature and concentration through incorporating the nonlinear Cahn-Hilliard equation and the Fourier heat transfer equation in two dimensions. The Flory-Huggins free energy theory for the thermodynamics of phase separation, slow mode theory, and Rouse law for polymer diffusion without entanglements were taken into account in the model development. The simulation results indicated a strong interaction between heat transfer and phase separation, which impacted the morphology formation significantly. Results confirmed that quench depth had an indispensable impact on phase separation in terms of higher characteristic frequency by increasing the driving force for heat transfer. Applying quench from various boundaries led to a difference in the quench rate due to the high viscosity of the polymer solution. This led to a gradation in pore size and anisotropic morphology formation. The degree and direction of anisotropy depended on quench depth and rate, quench time, heat conduction rate inside the solution, solution viscosity, temperature evolution, and the enthalpy of demixing. It was also verified that the influence of enthalpy of demixing on phase separation could not be neglected as it increased the solution temperature and led to phase separation being accomplished at a higher temperature than the initial quench temperature.

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BISTAGNINO, A., G. BOFFETTA, A. CELANI, A. MAZZINO, A. PULIAFITO, and M. VERGASSOLA. "Nonlinear dynamics of the viscoelastic Kolmogorov flow." Journal of Fluid Mechanics 590 (October 15, 2007): 61–80. http://dx.doi.org/10.1017/s0022112007007859.

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The weakly nonlinear dynamics of large-scale perturbations in a viscoelastic flow is investigated both analytically, via asymptotic methods, and numerically. For sufficiently small elasticities, dynamics is ruled by a Cahn–Hilliard equation with a quartic potential. Physically, this amounts to saying that, for small elasticities, polymers do not alter the purely hydrodynamical mechanisms responsible for the nonlinear dynamics in the Newtonian case (i.e. without polymers). The approach to the steady state is quantitatively similar to the Newtonian case as well, the dynamics being ruled by the same kink–antikink interactions as in the Newtonian limit. The above scenario does not extend to large elasticities. We found a critical value above which polymers drastically affect the dynamics of large-scale perturbations. In this latter case, a new dynamics not observed in the Newtonian case emerges. The most evident fingerprint of the new dynamics is the slowing down of the annihilation processes which lead to the steady states via weaker kink–antikink interactions. In conclusion, polymers strongly affect the large-scale dynamics. This takes place via a reduction of drag forces we were able to quantify from the asymptotic analysis. This suggests a possible relation of this phenomenon with the dramatic drag-reduction effect taking place in the far turbulent regime.

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Shao, Sihong, and Tiezheng Qian. "A Variational Model for Two-Phase Immiscible Electroosmotic Flow at Solid Surfaces." Communications in Computational Physics 11, no. 3 (March 2012): 831–62. http://dx.doi.org/10.4208/cicp.071210.040511a.

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AbstractWe develop a continuum hydrodynamic model for two-phase immiscible flows that involve electroosmotic effect in an electrolyte and moving contact line at solid surfaces. The model is derived through a variational approach based on the On-sager principle of minimum energy dissipation. This approach was first presented in the derivation of a continuum hydrodynamic model for moving contact line in neutral two-phase immiscible flows (Qian, Wang, and Sheng, J. Fluid Mech. 564, 333-360 (2006)). Physically, the electroosmotic effect can be formulated by the Onsager principle as well in the linear response regime. Therefore, the same variational approach is applied here to the derivation of the continuum hydrodynamic model for charged two-phase immiscible flows where one fluid component is an electrolyte exhibiting electroosmotic effect on a charged surface. A phase field is employed to model the diffuse interface between two immiscible fluid components, one being the electrolyte and the other a nonconductive fluid, both allowed to slip at solid surfaces. Our model consists of the incompressible Navier-Stokes equation for momentum transport, the Nernst-Planck equation for ion transport, the Cahn-Hilliard phase-field equation for interface motion, and the Poisson equation for electric potential, along with all the necessary boundary conditions. In particular, all the dynamic boundary conditions at solid surfaces, including the generalized Navier boundary condition for slip, are derived together with the equations of motion in the bulk region. Numerical examples in two-dimensional space, which involve overlapped electric double layer fields, have been presented to demonstrate the validity and applicability of the model, and a few salient features of the two-phase immiscible electroosmotic flows at solid surface. The wall slip in the vicinity ofmoving contact line and the Smoluchowski slip in the electric double layer are both investigated.

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Cherfils, Laurence, Alain Miranville, and Shuiran Peng. "Higher-order anisotropic models in phase separation." Advances in Nonlinear Analysis 8, no. 1 (March 16, 2017): 278–302. http://dx.doi.org/10.1515/anona-2016-0137.

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Abstract Our aim in this paper is to study higher-order (in space) Allen–Cahn and Cahn–Hilliard models. In particular, we obtain well-posedness results, as well as the existence of the global attractor. We also give, for the Allen–Cahn models, numerical simulations which illustrate the effects of the higher-order terms and the anisotropy.

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Journal articles on the topic 'Cahn effect'

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