Nonlinear Rupture Theory of a Thin Liquid Film With Insoluble Surfactant

1998 ◽  
Vol 120 (3) ◽  
pp. 598-604 ◽  
Author(s):  
Chi-Chuan Hwang ◽  
Chaur-Kie Lin ◽  
Da-Chih Hou ◽  
Wu-Yih Uen ◽  
Jenn-Sen Lin
Keyword(s):  
Liquid Film ◽  
Evolution Equations ◽  
Thin Liquid Film ◽  
Quantitative Difference ◽  
Marangoni Effect ◽  
Nonlinear Evolution Equations ◽  
Rupture Time ◽  
Diffusion Effect ◽  
Dynamic Rupture ◽  
Insoluble Surfactant

Effects of insoluble surfactant on the dynamic rupture of a thin liquid film coated on a flat plate are studied. The strong nonlinear evolution equations derived by the integral method are solved by numerical method. The results show that enhancing (weakening) the Marangoni effect (the surface diffusion effect) will delay the rupture process. Furthermore, the rupture time predicted by the integral theory is shorter than that predicted by the long-wave expansion method. In addition, the quantitative difference in the rupture time predicted by two models enlarges with the increase of Marangoni effect, however, without obvious change as the diffusion effect increases.

The Stability of Evaporating Thin Liquid Film Containing Insoluble Surfactant on Heated Substrate

2012 ◽  
Vol 614-615 ◽  
pp. 191-194
Author(s):  
Chun Xi Li ◽  
Bing Lu ◽  
Xue Min Ye
Keyword(s):  
Liquid Film ◽  
Evolution Equations ◽  
Thin Liquid Film ◽  
Nonlinear Evolution Equations ◽  
Linear Stability Theory ◽  
Film Stability ◽  
Heated Substrate ◽  
Insoluble Surfactant ◽  
The Stability ◽  
Evaporation Number

Flow of evaporating thin liquid film containing insoluble surfactant on a uniformally heated substrate is considered in this paper. Coupled nonlinear evolution equations for the film thickness and surfactant concentration are derived on the base of lubrication theory and reasonable boundary conditions. The flow stability of the thin liquid film has been studied using normal mode method according to the linear stability theory. The results show that the film stability is promoted by increasing the Capillary number and the surfactant Peclet number, while increasing the Marangoni number, the interface resistance number, the vapor recoil number and the evaporation number can reduce the stability of the system.

Nonlinear Rupture of Thin Micropolar Liquid Film Under a Magnetic Field

2016 ◽  
Vol 33 (2) ◽  
pp. 249-256
Author(s):  
P.-J. Cheng ◽  
C.-K. Chen ◽  
Y.-C. Wang ◽  
M.-C. Lin ◽  
C.-K. Yang
Keyword(s):  
Magnetic Field ◽  
Liquid Film ◽  
Evolution Equations ◽  
Film Flow ◽  
Nonlinear Evolution Equations ◽  
Rupture Time ◽  
Initial Disturbance ◽  
Horizontal Plate ◽  
Film Rupture ◽  
Micropolar Liquid

AbstractThis paper investigates the rupture problem of a thin micropolar liquid film under a magnetic field on a horizontal plate, using long-wave perturbation to resolve nonlinear evolution equations with a free film interface. The governing equation is resolved using a finite difference method as part of an initial value problem for spatial periodic boundary conditions. The effect of a micropolar liquid under a magnetic field on the nonlinear rupture mechanism is studied in terms of the micropolar parameter, R, the Hartmann constant, m and the initial disturbance amplitude, H0. Modeling results indicate that the R, m and H0 parameters strongly affect the film flow. Enhancing the micropolar and magnetic effects is found to delay the rupture time. In addition, the results show that the film rupture time increases as the values of initial disturbance magnitude decrease. The micropolar and magnetic parameters indeed play a significant role in the film flow on a horizontal plate. Moreover, the optimum conditions can be found to alter stability of the film flow by controlling the applied magnetic field.

Numerical Analysis on the Dropwise Condensation of a Binary Vapor Mixture

2001 ◽  
Author(s):  
Hirokuni Akiyama ◽  
Takao Nagasaki ◽  
Yutaka Ito
Keyword(s):  
Numerical Simulation ◽  
Liquid Film ◽  
Thin Liquid Film ◽  
Marangoni Effect ◽  
Ethanol Vapor ◽  
Surface Tension Gradient ◽  
Two Dimensional ◽  
Vapor Mixture ◽  
Horizontal Wall ◽  
Phase Equilibrium Condition

Abstract A numerical simulation was performed on the condensation of water and ethanol vapor mixture on a horizontal wall in a plane two-dimensional field. The analysis solves unsteady flow and heat-and-mass transfer both for liquid and vapor with the phase equilibrium condition at the interface, using FDM and boundary-fitted coordinates to track the deformation of interface. The calculation was started from a very thin smooth liquid film, and it was found that instability occurs when the film thickness reaches a certain value resulting in the formation of relatively small droplets. With the growth of the droplets, they coalesce into larger ones. Between the droplets an extremely thin liquid film exists, and the surface tension gradient sustains the droplets. With the increase of the wall subcooling the maximum droplet becomes large due to the increase of the Marangoni effect.

scholarly journals Surfactant and gravity dependent instability of two-layer Couette flows and its nonlinear saturation

2017 ◽  
Vol 826 ◽  
pp. 158-204 ◽  
Author(s):  
Alexander L. Frenkel ◽  
David Halpern
Keyword(s):  
Evolution Equations ◽  
Normal Modes ◽  
Gravitational Effect ◽  
Bond Number ◽  
Nonlinear Evolution Equations ◽  
Immiscible Fluid ◽  
Base Shear ◽  
Diffusion Term ◽  
Insoluble Surfactant ◽  
Infinite Case

A horizontal channel flow of two immiscible fluid layers with different densities, viscosities and thicknesses, subject to vertical gravitational forces and with an insoluble surfactant monolayer present at the interface, is investigated. The base Couette flow is driven by the uniform horizontal motion of the channel walls. Linear and nonlinear stages of the (inertialess) surfactant and gravity dependent long-wave instability are studied using the lubrication approximation, which leads to a system of coupled nonlinear evolution equations for the interface and surfactant disturbances. The (inertialess) instability is a combined result of the surfactant action characterized by the Marangoni number $Ma$ and the gravitational effect corresponding to the Bond number $Bo$ that ranges from $-\infty$ to $\infty$. The other parameters are the top-to-bottom thickness ratio $n$, which is restricted to $n\geqslant 1$ by a reference frame choice, the top-to-bottom viscosity ratio $m$ and the base shear rate $s$. The linear stability is determined by an eigenvalue problem for the normal modes, where the complex eigenvalues (determining growth rates and phase velocities) and eigenfunctions (the amplitudes of disturbances of the interface, surfactant, velocities and pressures) are found analytically by using the smallness of the wavenumber. For each wavenumber, there are two active normal modes, called the surfactant and the robust modes. The robust mode is unstable when $Bo/Ma$ falls below a certain value dependent on $m$ and $n$. The surfactant branch has instability for $m<1$, and any $Bo$, although the range of unstable wavenumbers decreases as the stabilizing effect of gravity represented by $Bo$ increases. Thus, for certain parametric ranges, even arbitrarily strong gravity cannot completely stabilize the flow. The correlations of vorticity-thickness phase differences with instability, present when gravitational effects are neglected, are found to break down when gravity is important. The physical mechanisms of instability for the two modes are explained with vorticity playing no role in them. This is in marked contrast to the dynamical role of vorticity in the mechanism of the well-known Yih instability due to effects of inertia, and is contrary to some earlier literature. Unlike the semi-infinite case that we previously studied, a small-amplitude saturation of the surfactant instability is possible in the absence of gravity. For certain $(m,n)$-ranges, the interface deflection is governed by a decoupled Kuramoto–Sivashinsky equation, which provides a source term for a linear convection–diffusion equation governing the surfactant concentration. When the diffusion term is negligible, this surfactant equation has an analytic solution which is consistent with the full numerics. Just like the interface, the surfactant wave is chaotic, but the ratio of the two waves turns out to be constant.

scholarly journals The spreading and stability of a surfactant-laden drop on an inclined prewetted substrate

2015 ◽  
Vol 772 ◽  
pp. 535-568 ◽  
Author(s):  
J. V. Goddard ◽  
S. Naire
Keyword(s):  
Numerical Simulations ◽  
Evolution Equations ◽  
Leading Edge ◽  
Equation Model ◽  
Nonlinear Evolution Equations ◽  
Late Time ◽  
Differential Algebraic Equation ◽  
Scaling Properties ◽  
Insoluble Surfactant ◽  
Free Liquid Film

We consider a viscous drop, loaded with an insoluble surfactant, spreading over an inclined plane that is covered initially with a thin surfactant-free liquid film. Lubrication theory is employed to model the flow using coupled nonlinear evolution equations for the film thickness and surfactant concentration. Exploiting high-resolution numerical simulations, we describe the late-time multi-region asymptotic structure of the spatially one-dimensional spreading flow. A simplified differential–algebraic equation model is derived for key variables characterising the spreading process, using which the late-time spreading and thinning rates are determined. Focusing on the neighbourhood of the drop’s leading-edge effective contact line, we then examine the stability of this region to small-amplitude disturbances with transverse variation. A dispersion relationship is described using long-wavelength asymptotics and numerical simulations, which reveals physical mechanisms and new scaling properties of the instability.

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