Academic literature on the topic 'Evolution equation of thin films'

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Journal articles on the topic "Evolution equation of thin films"

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GOTTLIEB, O., and ALEXANDER ORON. "STABILITY AND BIFURCATIONS OF PARAMETRICALLY EXCITED THIN LIQUID FILMS." International Journal of Bifurcation and Chaos 14, no. 12 (2004): 4117–41. http://dx.doi.org/10.1142/s0218127404011958.

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We investigate the stability and bifurcations of parametrically excited thin liquid films. A recently derived nonlinear evolution equation for the two-dimensional spatio-temporal dynamics of falling liquid films on an oscillating vertical wall is expanded to low order Fourier modes. A fourth-order modal dynamical system is validated to yield the primary bifurcation structure of the fundamental falling film dynamics described by the Benney equation, and accurately predicts the quasi-periodic structure of the temporally modulated Benney equation (TMBE). The stability of fundamental steady and pe
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McHugh, J. P., and D. Barkey. "Nonlinear evolution of a thin anodic film." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 473, no. 2202 (2017): 20160930. http://dx.doi.org/10.1098/rspa.2016.0930.

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The formation of pores in anodic aluminium oxide films is treated with a model equation. The model treats the oxide layer as a thin viscous liquid in two dimensions. Surface tension on the top boundary, electrostriction due to the external electric field and mass flow through the bottom boundary due to oxide formation are all included. Viscous flow is treated with the creeping flow assumption. The model equation is solved numerically using a Fourier spectral method in space and Adams–Bashforth/Adams–Moulton methods in time. Initial conditions include sinusoidal shapes as well as random shapes.
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SOPHOCLEOUS, C., and P. G. L. LEACH. "THIN FILMS: INCREASING THE COMPLEXITY OF THE MODEL." International Journal of Bifurcation and Chaos 22, no. 09 (2012): 1250212. http://dx.doi.org/10.1142/s0218127412502124.

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Thin films arise in a variety of contexts. They can be between two solid surfaces in the form of a lubricant or with one surface solid and the other free as in water or oil on a road. When the surface tension is a dominant feature of the physics behind the motion, the governing evolution of partial differential equation is nonlinear and of the fourth order in the spatial derivatives. A particular form proposed by King [2001] invites generalization to create a class of equations of higher order. We examine some of the properties of this class in terms of symmetry and singularity and see that th
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Kirkinis, E., and A. V. Andreev. "Odd-viscosity-induced stabilization of viscous thin liquid films." Journal of Fluid Mechanics 878 (September 4, 2019): 169–89. http://dx.doi.org/10.1017/jfm.2019.644.

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Thin viscous liquid films sitting on a solid substrate support nonlinear capillary waves, driven by surface shear stresses at a liquid–gas interface. When surface tension is spatially dependent other mechanisms, such as the thermocapillary effect, influence the dynamics of thin films. In this article we show that in liquids with broken time-reversal symmetry the character of the aforementioned waves and of the thermocapillary effect are significantly modified due to the presence of odd or Hall viscosity in the liquid. This is because odd viscosity gives rise to new terms in the pressure gradie
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Müller, M., C. L. Azanza Ricardo, R. Di Maggio, and P. Scardi. "Growth kinetics of Cu2ZnSnS4 thin films and powders." Powder Diffraction 28, S2 (2013): S228—S241. http://dx.doi.org/10.1017/s0885715613001012.

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The growth kinetics of Cu2ZnSnS4 thin films and powders was studied using in-situ synchrotron data. Isothermal and isochronal measurements were performed at the MCX beamline of the Elettra synchrotron (Trieste, Italy). Diffraction line profile analysis was used to follow the changes in the domain size distribution during isothermal measurements, and the change in the mean volume of the domains was studied using the Johnson-Mehl-Avrami equation. The growth was found to be diffusion controlled from small dimensions while the nucleation rate is temperature dependent. An activation energy of 210 k
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ARMENDÁRIZ, J., and M. MATALON. "Evaporation and combustion of thin films of liquid fuels." Journal of Fluid Mechanics 435 (May 25, 2001): 351–76. http://dx.doi.org/10.1017/s002211200100413x.

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We consider the evaporation and subsequent burning of thin films of liquid fuels. Previous studies on liquid films, with and without evaporation, have primarily considered the gas phase to be passive. The new element in this study is the introduction of combustion and the examination of both the liquid and gas phases and their effect on the film's behaviour. For the case of a liquid film burning in quiescent air we show that the problem can be simplified to a single nonlinear evolution equation for the film thickness. All remaining variables, which are simply expressed in terms of the function
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Liu, Yunyan, Hongsheng Song, Junshan Xiu, et al. "Surface Dynamics Transition of Vacuum Vapor Deposited CH3NH3PbI3 Perovskite Thin Films." Advances in Condensed Matter Physics 2018 (2018): 1–7. http://dx.doi.org/10.1155/2018/8297918.

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The growth dynamics of CH3NH3PbI3 perovskite thin films on ITO covered glass substrate were investigated. The evolution of the film could be divided into two stages. A mound-like surface was obvious at the first stage. Stable dynamic scaling was observed for thicker films at the second stage. Through analyzing the scaling exponent, growth exponent β, and 2D fast Fourier transform, it is concluded that, at the second stage, the growth mechanism of mound formation does not play a major role, and the film growth mechanism can be described by Mullins diffusion equation.
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Tomlin, R. J., D. T. Papageorgiou, and G. A. Pavliotis. "Three-dimensional wave evolution on electrified falling films." Journal of Fluid Mechanics 822 (June 6, 2017): 54–79. http://dx.doi.org/10.1017/jfm.2017.250.

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We consider the full three-dimensional dynamics of a thin falling liquid film on a flat plate inclined at some non-zero angle to the horizontal. In addition to gravitational effects, the flow is driven by an electric field which is normal to the substrate far from the flow. This extends the work of Tseluiko & Papageorgiou (J. Fluid Mech., vol. 556, 2006b, pp. 361–386) by including transverse dynamics. We study both the cases of overlying and hanging films, where the liquid lies above or below the substrate, respectively. Starting with the Navier–Stokes equations coupled with electrostatics
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Yu, Tony S., Vladimir Bulović, and A. E. Hosoi. "Coarsening and solidification via solvent-annealing in thin liquid films." Journal of Fluid Mechanics 723 (April 16, 2013): 69–90. http://dx.doi.org/10.1017/jfm.2013.115.

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AbstractWe examine solidification in thin liquid films produced by annealing amorphous ${\mathrm{Alq} }_{3} $ (tris-(8-hydroxyquinoline) aluminium) in methanol vapour. Micrographs acquired during annealing capture the evolution of the film: the initially-uniform film breaks up into drops that coarsen, and single crystals of ${\mathrm{Alq} }_{3} $ nucleate randomly on the substrate and grow as slender ‘needles’. The growth of these needles appears to follow power-law behaviour, where the growth exponent, $\gamma $, depends on the thickness of the deposited ${\mathrm{Alq} }_{3} $ film. The evolu
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Frenkel, Alexander L. "On evolution equations for thin films flowing down solid surfaces." Physics of Fluids A: Fluid Dynamics 5, no. 10 (1993): 2342–47. http://dx.doi.org/10.1063/1.858895.

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Dissertations / Theses on the topic "Evolution equation of thin films"

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Goodnight, Randall James Truett. "Derivation of an Evolution Equation for Two-Dimensional Waves on Thin Films." Thesis, Virginia Tech, 2013. http://hdl.handle.net/10919/23125.

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We examine wave propagation on thin liquid films subjected to gravity, fluid friction, surface tension, and Marangoni effects. The physical configuration is a thin liquid layer on a planar incline. Following previous studies, the Marangoni effect is incorporated by a constant surface tension gradient and yields a non-convex flux function in our thin film equation. We extend previous studies by deriving the thin film equation governing two-dimensional waves on the liquid layer. We then derive a simplified evolution equation governing weakly nonlinear, quasi-planar, and weakly dissipative waves
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Ulusoy, Suleyman. "The Mathematical Theory of Thin Film Evolution." Diss., Georgia Institute of Technology, 2007. http://hdl.handle.net/1853/16213.

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We try to explain the mathematical theory of thin liquid film evolution. We start with introducing physical processes in which thin film evolution plays an important role. Derivation of the classical thin film equation and existing mathematical theory in the literature are also introduced. To explain the thin film evolution we derive a new family of degenerate parabolic equations. We prove results on existence, uniqueness, long time behavior, regularity and support properties of solutions for this equation. At the end of the thesis we consider the classical thin film Cauchy problem on t
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Alriyabi, Ali. "Analyse de quelques équations différentielles à retard et EDP modélisant les instabilités de surfaces." Thesis, Poitiers, 2013. http://www.theses.fr/2013POIT2255/document.

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Cette thèse est divisée en deux parties principales : La première partie concerne la déformation plastique d'un matériau contraint. Nous commençons cette partie par une introduction physique sur la dislocation et son rôle dans l'étude de la déformation plastique. Nous exposons ensuite deux types de modélisation de la déformation plastique ce qui nous conduit à deux équations différentielles à retard de Mecking-Lüke-Grilhé. Nous présentons une analyse mathématique complète des deux modèles linéaire et non linéaire. Nous terminons cette partie par des tests numériques et une comparaison des deux
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Groh, Christian Michael. "Asymptotic and numerical studies of nonlinear evolution equations of viscous thin-film flows." Thesis, University of Leeds, 2010. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.534751.

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Masson, Jean-Loup Didier. "Pattern formation and evolution in thin polymer films." Access restricted to users with UT Austin EID Full text (PDF) from UMI/Dissertation Abstracts International, 2001. http://wwwlib.umi.com/cr/utexas/fullcit?p3034981.

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Duffy, Hugh. "Microstructural evolution in calcium phosphate thin films." Thesis, Ulster University, 2011. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.550567.

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Hydroxyapatite (HA) is an important class of biomaterial which has been extensively researched as a coating on metallic implant devices and/or as a model for the study of cells on bioactive surfaces. The composition of such coatings, when compared with the raw HA target powder, has led to them being termed as calcium phosphate (CaP) thin films with varying "HA-like" properties. The ability of the coating to deliver some or all of the properties of the sources material is limited by the unit cell composition that originates from the crystallinity of the coating during its growth. Although struc
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Carel, Roland. "Grain growth and texture evolution in thin films." Thesis, Massachusetts Institute of Technology, 1995. http://hdl.handle.net/1721.1/31064.

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Walker, Tanya L. M. "Symmetry-enhancing for a thin film equation." View thesis, 2008. http://handle.uws.edu.au:8081/1959.7/43978.

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Thesis (Ph.D.)--University of Western Sydney, 2008.<br>A thesis presented to the University of Western Sydney, College of Health and Science, School of Computing and Mathematics, in fulfilment of the requirements for the degree of Doctor of Philosophy - Science. Includes bibliographies.
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Yoon, Chang-Kyu. "Evolution of annealing twins in sputtered Cu thin films." Pullman, Wash. : Washington State University, 2009. http://www.dissertations.wsu.edu/Thesis/Summer2009/C_Yoon_070609.pdf.

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Thesis (M.S. in materials science and engineering)--Washington State University, August 2009.<br>Title from PDF title page (viewed on Aug. 7, 2009). "School of Mechanical and Materials Engineering." Includes bibliographical references (p. 44-46).
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Borglum, Joshua Christopher. "Numerical Simulations of Electrohydrodynamic Evolution of Thin Polymer Films." Thesis, North Dakota State University, 2015. https://hdl.handle.net/10365/27736.

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Recently developed needleless electrospinning and electrolithography are two successful techniques that have been utilized extensively for low-cost, scalable, and continuous nano-fabrication. Rational understanding of the electrohydrodynamic principles underneath these nano-manufacturing methods is crucial to fabrication of continuous nanofibers and patterned thin films. This research project is to formulate robust, high-efficiency finite-difference Fourier spectral methods to simulate the electrohydrodynamic evolution of thin polymer films. Two thin-film models were considered and refined. Th
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Books on the topic "Evolution equation of thin films"

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Brown, James L. The thin oil film equation. National Aeronautics and Space Administration, Ames Research Center, 1999.

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1943-, Lu T. M., ed. Evolution of thin film morphology: Modeling and simulations. Springer, 2008.

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Freund, L. B. Thin film materials: Stress, defect formation, and surface evolution. Cambridge University Press, 2009.

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Freund, L. B. Thin film materials: Stress, defect formation, and surface evolution. Cambridge University Press, 2009.

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S, Suresh, ed. Thin film materials: Stress, defect formation and surface evolution. Cambridge University Press, 2003.

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Krishnamoorthy, S. Full-scale direct numerical simulation of two- and three-dimensional instabilities and rivulet formation in heated falling films. National Aeronautics and Space Administration, 1995.

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Krishnamoorthy, S. Full-scale direct numerical simulation of two- and three-dimensional instabilities and rivulet formation in heated falling films. National Aeronautics and Space Administration, 1995.

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United States. National Aeronautics and Space Administration., ed. Fast methods to numerically integrate the Reynolds equation for gas fluid films. National Aeronautics and Space Administration, 1992.

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Structural and Morphological Evolution in Metal-Organic Films and Multilayers. Taylor & Francis Group, 2015.

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G, Demczyk B., and Materials Research Society, eds. Evolution of thin film structure and morphology: Symposium held November 28-December 2, 1994, Boston, Massachusetts, USA. Materials Research Society, 1995.

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Book chapters on the topic "Evolution equation of thin films"

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Hoppe, Ronald H. W., and Eva Nash. "Numerical Solution of a Nonlinear Evolution Equation Describing Amorphous Surface Growth of Thin Films." In Numerical Mathematics and Advanced Applications. Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-642-18775-9_41.

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Suwas, Satyam, and Ranjit Kumar Ray. "Texture Evolution in Thin Films." In Engineering Materials and Processes. Springer London, 2014. http://dx.doi.org/10.1007/978-1-4471-6314-5_7.

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Mwema, Fredrick Madaraka, Esther Titilayo Akinlabi, and Oluseyi Philip Oladijo. "Multifractal Characterization of Structure Evolution with Sputtering Parameters of Thin Films." In Sputtered Thin Films. CRC Press, 2021. http://dx.doi.org/10.1201/9781003053507-8.

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Ruan, Jeng, and Kao-Shuo Chang. "Mutually Influenced Stacking and Evolution of Inorganic/Organic Crystals for Piezo-Related Applications." In Functional Thin Films Technology. CRC Press, 2021. http://dx.doi.org/10.1201/9781003088080-5.

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Bediako, D. Kwabena, Andrew M. Ullman, and Daniel G. Nocera. "Catalytic Oxygen Evolution by Cobalt Oxido Thin Films." In Topics in Current Chemistry. Springer International Publishing, 2015. http://dx.doi.org/10.1007/128_2015_649.

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Field, David P., John E. Sanchez, No Jin Park, and Paul R. Besser. "Texture Evolution in Thin Cu Films and Lines." In Materials Science Forum. Trans Tech Publications Ltd., 2005. http://dx.doi.org/10.4028/0-87849-975-x.1323.

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Welzel, U., and Eric J. Mittemeijer. "Stress Evolution in Thin Films; Diffusion and Reactions." In Defect and Diffusion Forum. Trans Tech Publications Ltd., 2007. http://dx.doi.org/10.4028/3-908451-41-8.71.

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Broekmann, P., M. Wilms, A. Spaenig, and K. Wandelt. "Highly Ordered Adsorbate Structures on Cu(111) in the Potential Regime of Hydrogen Evolution-An In-Situ STM Study." In Thin Films: Preparation, Characterization, Applications. Springer US, 2002. http://dx.doi.org/10.1007/978-1-4615-0775-8_1.

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Hofmeister, H. "The Structural Evolution of Nanocrystalline Thin Films of Germanium." In Nanophase Materials. Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-011-1076-1_26.

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Hoefnagels, J. P. M., L. I. J. C. Bergers, and M. G. D. Geers. "Anelasticity in Al-Alloy Thin Films: A Micro-mechanical Analysis." In Fracture, Fatigue, Failure, and Damage Evolution, Volume 5. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-06977-7_14.

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Conference papers on the topic "Evolution equation of thin films"

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Narendranath, Aneet D., Jeramy Kimball, James C. Hermanson, Robert W. Kolkka, and Jeffrey S. Allen. "Stability of Liquid Films." In ASME 2010 International Mechanical Engineering Congress and Exposition. ASMEDC, 2010. http://dx.doi.org/10.1115/imece2010-40090.

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Macroscopic thin liquid films are entities that are important in biophysics, physics, and engineering, as well as in natural settings. They can be composed of common liquids such as water or oil, rheologically complex materials such as polymers solutions or melts, or complex mixtures of phases or components. When the films are subjected to the action of various mechanical, thermal, or structural factors, they display interesting dynamic phenomena such as wave propagation, wave steepening, and development of chaotic responses. Such films can display rupture phenomena creating holes, spreading o
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Gurrum, Siva P., William P. King, Yogendra K. Joshi, and Koneru Ramakrishna. "Joule Heating and Thermal Conductivity Determination of Nanoscale Metallic Thin Films and Interconnects." In ASME 2005 International Mechanical Engineering Congress and Exposition. ASMEDC, 2005. http://dx.doi.org/10.1115/imece2005-82909.

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Evolution of high performance microprocessors has resulted in a steady decrease in on-chip feature sizes. Increasing requirements on maximum current density are expected to increase interconnect temperature drastically due to Joule heating. As interconnect dimensions approach the electron mean free path range, effective conductivity reduces due to size effects. Thermal characterization of sub-micron interconnects and thin films is thus highly important. This work investigates current crowding and the associated Joule heating near a constriction in a thin metallic film and proposes a novel tech
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Fukui, Shigehisa, Kazuya Yorino, Kiyomi Yamane, and Hiroshige Matsuoka. "Deformation and Stability Analysis of Ultra-Thin Lubricant Films by the Long Wave Equation: Analysis Considering the van der Waals Force and Gas Pressure at the Liquid Surface." In World Tribology Congress III. ASMEDC, 2005. http://dx.doi.org/10.1115/wtc2005-63629.

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To examine deformations of ultra-thin but continuum liquid film, the long wave theory was employed, which is the time-evolution equation for the shape and deformation of the thin liquid film and includes the surface tension and surface forces such as the van der Waals (vdW) force. By solving the linearized long wave equation considering the vdW pressure and gas pressures at the lubricant surface, deformations of the ultra-thin lubricant film caused by air pressure were obtained. Stability/instability of the liquid surface was analyzed as the growth and decay problem of the infinitesimal deform
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Nazaripoor, Hadi, Charles R. Koch, and Subir Bhattacharjee. "Dynamics of Thin Liquid Bilayers Subjected to an External Electric Field." In ASME 2014 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/imece2014-37302.

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Spatiotemporal evolution of liquid-liquid interface leading to dewetting and pattern formation is investigated for thin liquid bilayeres subjected to the long range electrostatic force and the short range van der Waals forces. Based on the 2D weakly non-linear thin film equation three dimensional structure evolution is numerically simulated. A combined finite difference for the spatial dimensions and an adaptive time step ODE solver is used to solve the governing equation. For initially non-wetting surfaces, the stabilizing effects of viscosity and interfacial tension and the destabilizing eff
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Fukui, Shigehisa, Soichi Shimizu, Kiyomi Yamane, and Hiroshige Matsuoka. "Deformation Characteristics of the Ultrathin Liquid Film Surface Considering the Effects of Polar Endgroups." In ASME/STLE 2007 International Joint Tribology Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/ijtc2007-44502.

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To examine deformations of ultra-thin but continuum liquid film, the long wave theory was employed. The long wave theory uses the time-evolution equation for the shape and deformation of the thin liquid film and includes the surface tensions and surface forces such as the van der Waals (vdW) force. By numerically solving the time-dependent long wave equation, deformations of the ultra-thin lubricant film considering the vdW pressure with initial/boundary configurations of the liquid surfaces were obtained.
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Messier, Russell F., Paul D. Sunal, and Vijayakumar C. Venugopal. "Evolution of sculptured thin films." In SPIE's International Symposium on Optical Science, Engineering, and Instrumentation, edited by Akhlesh Lakhtakia and Russell F. Messier. SPIE, 1999. http://dx.doi.org/10.1117/12.351244.

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Joo, Sang W., Shizhi Qian, Yingtao Jiang, and Marcos A. Cheney. "Electro-Osmotic Flow With Free Surface in Nanochannels." In 2008 Second International Conference on Integration and Commercialization of Micro and Nanosystems. ASMEDC, 2008. http://dx.doi.org/10.1115/micronano2008-70302.

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A thin-film flow induced by the electro-osmosis is studied. In contrast to the single-phase electro-osmosis flow through micro- and nanochannels, the flow considered has a free surface, which may deform with the flow developments. A new type of interfacial instability is identified via a linear stability analysis, and subsequent nonlinear flow behavior, including that for the film surface corrugations, is examined by deriving an evolution equation.
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Usha, R., and I. Mohammed Rizwan Sadiq. "Weakly Nonlinear Stability Analysis of a Non-Uniformly Heated Non-Newtonian Falling Film." In ASME/JSME 2007 5th Joint Fluids Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/fedsm2007-37201.

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A thin liquid layer of a non-Newtonian film falling down an inclined plane that is subjected to non-uniform heating has been considered. The temperature of the inclined plane is assumed to be linearly distributed and the case when the temperature gradient is positive or negative is investigated. The film flow is influenced by gravity, mean surface-tension and thermocapillary force acting along the free surface. The coupling of thermocapillary instability and surface-wave instabilities is studied for two-dimensional disturbances. A non-linear evolution equation is derived by applying the long-w
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Narendranath, Aneet D., James C. Hermanson, Allan A. Struthers, Robert W. Kolkka, and Jeffrey S. Allen. "Stability of an Evaporating Liquid Film Under Nonequilibrium Conditions With Variable Gravity." In ASME 2012 Fluids Engineering Division Summer Meeting collocated with the ASME 2012 Heat Transfer Summer Conference and the ASME 2012 10th International Conference on Nanochannels, Microchannels, and Minichannels. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/fedsm2012-72283.

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An evolution equation describing the dynamics of an evaporating liquid film has previously been developed from the governing equations of fluid dynamics after the application of the lubrication approximation and the choice of a viscous time scale. The authors have solved the evaporating liquid film evolution equation with a validated numeric program. Different mechanical boundary conditions were successfully applied and their effect on the film dynamics was examined. The evolution equation has also been modified to include buoyancy driven instabilities. This paper outlines a linear stability a
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Cazzoli, Giulio, Claudio Forte, Cristiano Vitali, Piero Pelloni, and Gian Marco Bianchi. "Modeling of Wall Film Formed by Impinging Spray Using a Fully Explicit Integration Method." In ASME 2005 Internal Combustion Engine Division Spring Technical Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/ices2005-1063.

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A wall film model has been implemented in a customized version of KIVA-3 code developed at University of Bologna. The model simulates the dynamics of a liquid wall film generated by impinging sprays by solving the mass, momentum and energy equations of a two-dimensional liquid flow over a three-dimensional surface under the basic hypothesis of a ‘thin laminar flow’. The major phenomena taken into account in the present model are: wall film formation by impinging spray; body forces, such as gravity or acceleration of the wall; shear stress at the interface with the gas and no slip condition on
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Reports on the topic "Evolution equation of thin films"

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Abdeljawad, Fadi F. Microstructural evolution of thin polycrystalline metallic films under extreme conditions. Office of Scientific and Technical Information (OSTI), 2016. http://dx.doi.org/10.2172/1562840.

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ADAMS, DAVID P., LAURENCE E. BROWN, RONALD S. GOEKE, JUAN A. ROMERO, and ANDREW D. SILVA. Evolution of Stress in ScD{sub 2}/Cr Thin Films Fabricated by Evaporation and High Temperature Reaction. Office of Scientific and Technical Information (OSTI), 2001. http://dx.doi.org/10.2172/783088.

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Jiang, Hua. Evolution of Surface Morphology and Chemistry in ZnO Thin Films and Steel Surfaces studied by Synchrotron X-ray Spectroscopy and Imaging. Office of Scientific and Technical Information (OSTI), 2016. http://dx.doi.org/10.2172/1484758.

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