The effects of fluid motion on oscillatory and chaotic fronts

We study oscillatory and chaotic reaction fronts described by the Kuramoto-Sivashinsky equation coupled to different types of fluid motion. We first apply a Poiseuille flow on the fronts inside a two-dimensional slab. We show regions of period doubling transition to chaos for different values of the average speed of Poiseuille flow. We also analyze the effects of a convective flow due to a Rayleigh-Taylor instability. Here the front is a thin interface separating two fluids of different densities inside a two-dimensional vertical slab. Convection is caused by buoyancy forces across the front as the lighter fluid is under a heavier fluid. We first obtain oscillatory and chaotic solutions arising from instabilities intrinsic to the front. Then, we determine the changes on the solutions due to fluid motion.     

Modelling thin-film dewetting on structured substrates and templates: Bifurcation analysis and numerical simulations

We study the dewetting process of a thin liquid film on a chemically patterned solid substrate (template) by means of a thin-film evolution equation incorporating a space-dependent disjoining pressure. Dewetting of a thin film on a homogeneous substrate leads to fluid patterns with a typical length scale, that increases monotonously in time (coarsening). Conditions are identified for the amplitude and periodicity of the heterogeneity that allow to transfer the template pattern onto the liquid structure ("pinning") emerging from the dewetting process. A bifurcation and stability analysis of the possible liquid ridge solutions on a periodically striped substrate reveal parameter ranges where pinning or coarsening ultimately prevail. We obtain an extended parameter range of multistability of the pinning and coarsening morphologies. In this regime, the selected pattern depends sensitively on the initial conditions and potential finite perturbations (noise) in the system as we illustrate with numerical integrations in time. Finally, we discuss the instability to transversal modes leading to a decay of the ridges into rows of drops and show that it may diminish the size of the parameter range where the pinning of the thin film to the template is successful.Received: 29 January 2003, Published online: 15 July 2003PACS: 68.15.+e Liquid thin films - 81.16.Rf Nanoscale pattern formation - 47.20.Ky Nonlinearity (including bifurcation theory)     

MHD Flow and Heat Transfer Characteristics in a Casson Liquid Film Towards an Unsteady Stretching Sheet with Temperature-Dependent Thermal Conductivity

Theoretical and numerical outcomes of the non-Newtonian Casson liquid thin film fluid flow owing to an unsteady stretching sheet which exposed to a magnetic field, Ohmic heating and slip velocity phenomena is reported here. The non-Newtonian thermal conductivity is imposed and treated as it vary with temperature. The nonlinear partial differential equations governing the non-Newtonian Casson thin film fluid are simplified into a group of highly nonlinear ordinary differential equations by using an adequate dimensionless transformations. With this in mind, the numerical solutions for the ordinary conservation equations are found using an accurate shooting iteration technique together with the Runge-Kutta algorithm. The lineaments of the thin film flow and the heat transfer characteristics for the pertinent parameters are discussed through graphs. The results obtained here detect many concern for the local Nusselt number and the local skin-friction coefficient in which they may be beneficial for the material processing industries. Furthermore, in some special conditions, the present problem has an excellent agreement with previously published work.     

Electromagnetic field distribution modelling in microlenses fabrication process

In this article, theoretical modelling of electromagnetic field distribution in the exposed thin film during lithographic process of microlenses array formation is presented. While studying topography of microlenses by means of atomic force microscopy we have found that various diffraction effects are observed due to the small dimensions of microlens patterns comparing to the wavelength. In this article we use finite-difference in time domain (FDTD) method to model electromagnetic field distribution in complex pattern-film geometry. Within FDTD, we solve Maxwell equations numerically, which enables us to model any type of geometry or material properties. Therefore, the effects of different perturbations, like pattern boundary imperfections or thin film roughness can be studied within this method, showing their effect on the electromagnetic field distribution within illuminated chalcogenide thin film.     

Large-Biot-number non-isothermal flow of a thin film on a stationary or rotating cylinder

Using the lubrication approximation we investigate two-dimensional steady flow of a thin film of fluid with temperature-dependent viscosity on a uniformly heated or cooled horizontal cylinder, which may be stationary or rotating about its axis, in the case when the Biot number (a measure of heat transfer at the free surface) is large.We show that the film thickness (but not the fluid velocity) may be obtained from that in the isothermal case by a simple re-scaling.     

Effect of a strong longitudinal magnetic field on capillary disintegration of a magnetic liquid film covering the inner surface of a narrow cylindrical tube

The effect of magnetic forces on the viscous regime of disintegration of a thin cylindrical ferroliquid film magnetized to saturation is studied on the basis of an asymptotic model describing the evolution of small perturbations during capillary disintegration of this film. A formula describing the dependence of the wavelength of the most rapidly increasing mode on the physical parameters characterizing this phenomenon is derived analytically.     

Radial fingering in a Hele-Shaw cell: a weakly nonlinear analysis

The Saffman-Taylor viscous fingering instability occurs when a less viscous fluid displaces a more viscous one between narrowly spaced parallel plates in a Hele-Shaw cell. Experiments in radial flow geometry form fan-like patterns, in which fingers of different lengths compete, spread and split. Our weakly nonlinear analysis of the instability predicts these phenomena, which are beyond the scope of linear stability theory. Finger competition arises through enhanced growth of sub-harmonic perturbations, while spreading and splitting occur through the growth of harmonic modes. Nonlinear mode-coupling enhances the growth of these specific perturbations with appropriate relative phases, as we demonstrate through a symmetry analysis of the mode coupling equations. We contrast mode coupling in radial flow with rectangular flow geometry.     

Linear stability of particle-laden thin films

Recent experiments [Zhou, Dupuy, Bertozzi, and Hosoi, Phys. Rev. Lett., 94 (2005)] of particle-laden film flow on an incline demonstrate new behavior distinct from the well-known clear fluid case, including the formation of a particle-rich ridge which can stabilize the advancing contact line with respect to “fingering" perturbations. We consider a model similar to that of Zhou et al. with the additional regularizing effect of shear-induced diffusion. A linear stability analysis demonstrates that particle settling moderately reduces the growth rate of unstable modes, while increasing the most unstable wavelength.     

Hall Effects on Unsteady Magnetohydrodynamic Flow of a Third Grade Fluid

The unsteady magnetohydrodynamic flow of an electrically conducting viscous incompressible third grade fluid bounded by an infinite porous plate is studied with the Hall effect. An external uniform magnetic field is applied perpendicular to the plate and the fluid motion is subjected to a uniform suction and injection. Similarity transformations are employed to reduce the non-linear equations governing the flow under discussion to two ordinary differential equations （with and without dispersion terms）. Using the finite difference scheme, numerical solutions represented by graphs with reference to the various involved parameters of interest are discussed and appropriate conclusions are drawn.     

Two-dimensional microrheology of freely suspended liquid crystal films

Smectic liquid crystals form freely-suspended, fluid films of highly uniform structure and thickness, making them ideal systems for studies of hydrodynamics in two dimensions. We have measured particle mobility and shear viscosity by direct observation of the gravitational drift of silica spheres and smectic islands included in these fluid membranes. In thick films, we observe a hydrodynamic regime dominated by lateral confinement effects, with the mobility of the inclusion determined predominantly by coupling of the fluid flow to the fixed boundaries of the film. In thin films, the mobility of inclusions is governed primarily by coupling of the fluid to the surrounding air, as predicted by Saffman-Delbrück theory.     

一种简单的光纤光栅电调谐方法

采用较简单的双点源真空蒸发法在光栅外表面上蒸镀一层均匀铝膜,利用电流流过铝膜时产生的电阻热改变光栅的温度而使光栅的中心波长向长波方向发生改变.光栅中心波长的变化与所加电流的平方成正比.实验中用较小的电流(约43mA)获得了较大的波长调谐范围(约4nm),其调谐精度达到2.15×10^-3nm/(mA)².     

On the influence of a magnetic field with circular field lines on the gravity flow of a magnetic fluid film down a thin cylinder

The gravity-induced flow of a magnetic fluid film down a vertical thin current-carrying cylindrical conductor is considered. The relative thickness of the film is small. A nonlinear equation is derived from a system of ferrohydrodynamic equations that describes the time evolution of the axisymmetric shape of the free film surface, which is set at the zero time. Using this equation, the development of disturbances of the hydrodynamic field is studied in the linear statement. The hydrodynamic field corresponds to the steady flow of the magnetic fluid in the form of a cylindrical film. It is found that such a flow is stable if the current passing through the conductor is sufficiently high.     

非晶态Se薄膜的自发晶化研究

利用真空热蒸镀的方法制备了非晶Se薄膜,测试了稳定的非晶Se薄膜,不稳定的非晶Se薄膜和初始自发晶化的非晶Se薄膜的透射率光谱和拉曼光谱,对透射率光谱曲线进行了拟合,计算了薄膜的厚度和折射率随波长的变化关系。在自我晶化过程中,Se薄膜折射率逐渐增大;随波长增大,折射率则减小,初始自发晶体的Se薄膜中,出现标志Se8环和链的结构,不完整的环和链结构在自发晶化过程中得到了增强。     

Nonlinear evolution of perturbations in a thin fluid layer during wave formation

A mathematical model is presented for the state of a free surface of a thin fluid layer (a fluid film) in heat-mass-exchange processes of condensation and evaporation. The wave motion of a fluid film is studied under inhomogeneous surface tension. Nonlinear development of perturbations belonging to a continuous band of wave numbers on the surface of a thin fluid layer is investigated within the framework of a non-linear parabolic equation. It is shown that wave packets with carrier wave lying near the harmonic of maximum increment become self-ordered; as a result, a monochromatic wave is generated on the surface of the fluid film. When a wave packet is generated in the neighborhood of the neutral stability curve, one can observe a phenomenon of directed energy transfer to the waves in the neighborhood of the harmonic of maximum increment.     

The influence of heat transfer in an MHD second grade fluid film over an unsteady stretching sheet

The flow and heat transfer problem of a second grade fluid film over an unsteady stretching sheet is considered. The fluid is incompressible and electrically conducting in the presence of a uniform applied magnetic field. The series solutions of the governing boundary value problems are obtained by employing homotopy analysis method (HAM). The convergence of the developed solutions is discussed explicitly. The dependence of velocity and temperature profiles on various parameters is shown and discussed through graphs. The values of skin-friction coefficient, Nusselt number and free surface temperature are given in tabular form for various emerging parameters.     

MHD equations in the atmosphere of the stars

In this paper, we find the perturbations depending on the magnetohydrodynamics time in a static and homogeneous plasma, with the help of the set of nonlinear equations. However, we only focus on low-amplitude perturbations, and therefore we can find a set of linear differential equations with the corresponding wave form solutions. We should also mention that if the non-perturbed velocity is non-zero but uniform, one can always translate the plasma to a framework where it is stationary there. Hence, we suppose that the plasma is in equilibrium state and its initial velocity is zero. This static equilibrium is changed to the small perturbations in the magnetic field, in the pressure fluid, and in the mass density.     

Contact line instabilities of thin liquid films

We present results of fully nonlinear time-dependent simulations of a thin liquid film flowing down an inclined plane. Within the lubrication approximation, and assuming complete wetting, we find that varying the inclination angle considerably modifies the shape of the emerging patterns (fingers versus sawtooth). Our results strongly suggest that the shape of the patterns is not necessarily related to either partial or complete coverage of the substrate, a technologically important feature of the flow. We find quantitative agreement with reported experiments and suggest new ones.     

Transient thin film flow of nonlinear radiative Maxwell nanofluid over a rotating disk

In this letter, a mathematical model for transient nature thin film flow of Maxwell nanofluid over a rotating disk is studied in the presence of a uniform magnetic field and non-linear thermal radiation. The Brownian motion and thermophoresis features due to nanofluid are captured by adopting the Buongiorno model. The prime emphasize is to explore the temperature field and nanoparticles volume fraction in nanofluid thin film flow. The reduced system of differential equations is solved numerically by finite difference based method namely bvp4c. The numerical outcomes regarding film thickness, Nusselt number, Sherwood number, velocity, temperature, and concentration are revealed for varying estimation of involved physical parameters. It is shown that the film thickness decreases with increasing values of the magnetic number. Further, the impact of thermophoresis and thermal radiation parameters is worthwhile in enhancing the fluid temperature. The Solute concentration is found to decrease with Brownian motion and Schmidt number.     

Competition between anisotropic viscous fingers

We consider viscous fingers created by injection of low viscosity fluid into the network of capillaries initially filled with a more viscous fluid (motor oil). Due to the anisotropy of the system and its geometry, such a setup promotes the formation of long-and-thin fingers which then grow and compete for the available flow, interacting through the pressure field. The interaction between the fingers is analyzed using the branched growth formalism of Halsey and Leibig (Phys. Rev. A 46, 7723, 1992) using a number of simple, analytically tractable models. It is shown that as soon as the fingers are allowed to capture the flow from one another, the fixed point appears in the phase space, corresponding to the asymptotic state in which the growth of one of the fingers in hindered by the other. The properties of phase space flows in such systems are shown to be remarkably insensitive to the details of the dynamics.     

The wind instability and the resonant interaction of the elastic vibration of a thin plate with a supersonic gas stream

In a supersonic flow, the longwave perturbations running along the stream are stable, whereas the most rapidly growing waves propagate at an angle to the flow velocity. It has been shown that the wind instability of a nonuniform compressible gas flow having a velocity profile can give rise to elastic vibrations of a thin plate at a characteristic wavelength. The dispersion equation and the instability increment showing a maximum in the longwave band have been obtained.