Surfactant Effects on Fluid-Elastic Instabilities of Liquid-Lined Flexible Tubes: A Model of Airway Closure

1993 ◽  
Vol 115 (3) ◽  
pp. 271-277 ◽  
Author(s):  
D. Halpern ◽  
J. B. Grotberg
Keyword(s):  
Film Thickness ◽  
Surfactant Concentration ◽  
Evolution Equations ◽  
Liquid Films ◽  
Nonlinear Evolution Equations ◽  
Small Airways ◽  
Airway Closure ◽  
Elastic Tubes ◽  
Critical Film Thickness ◽  
The Stability

A theoretical analysis is presented predicting the closure of small airways in the region of the terminal and respiratory bronchioles. The airways are modelled as thin elastic tubes, coated on the inside with a thin viscous liquid lining. This model produces closure by a coupled capillary-elastic instability leading to liquid bridge formation, wall collapse or a combination of both. Nonlinear evolution equations for the film thickness, wall position and surfactant concentration are derived using an extended version of lubrication theory for thin liquid films. The positions of the air-liquid and wall-liquid interfaces and the surfactant concentration are perturbed about uniform states and the stability of these perturbations is examined by solving the governing equations numerically. Solutions show that there is a critical film thickness, dependent on fluid, wall and surfactant properties above which liquid bridges form. The critical film thickness, εc, decreases with increasing mean surface-tension or wall compliance. Surfactant increases εc by as much as 60 percent for physiological conditions, consistent with physiological observations. Airway closure occurs more rapidly with increasing film thickness and wall flexibility. The closure time for a surfactant rich interface can be approximately five times greater than an interface free of surfactant.

scholarly journals Fourth order nonlinear evolution equations for gravity-capillary waves in the presence of a thin thermocline in deep water

2002 ◽  
Vol 43 (4) ◽  
pp. 513-524 ◽  
Author(s):  
Suma Debsarma ◽  
K.P. Das
Keyword(s):  
Fourth Order ◽  
Deep Water ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Capillary Wave ◽  
Capillary Waves ◽  
Nonlinear Evolution Equations ◽  
Marginal Stability ◽  
Stability And Instability ◽  
The Stability

AbstractFor a three-dimensional gravity capillary wave packet in the presence of a thin thermocline in deep water two coupled nonlinear evolution equations correct to fourth order in wave steepness are obtained. Reducing these two equations to a single equation for oblique plane wave perturbation, the stability of a uniform gravity-capillary wave train is investigated. The stability and instability regions are identified. Expressions for the maximum growth rate of instability and the wavenumber at marginal stability are obtained. The results are shown graphically.

Construction of the numerical and analytical wave solutions of the Joseph–Egri dynamical equation for the long waves in nonlinear dispersive systems

2020 ◽  
Vol 34 (30) ◽  
pp. 2050289
Author(s):  
Abdulghani R. Alharbi ◽  
M. B. Almatrafi ◽  
Aly R. Seadawy
Keyword(s):  
Solitary Wave ◽  
Numerical Solution ◽  
Evolution Equations ◽  
Dynamical Equation ◽  
Nonlinear Evolution ◽  
Three Dimensional ◽  
Nonlinear Evolution Equations ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
The Stability

The Kudryashov technique is employed to extract several classes of solitary wave solutions for the Joseph–Egri equation. The stability of the achieved solutions is tested. The numerical solution of this equation is also investigated. We also present the accuracy and the stability of the numerical schemes. Some two- and three-dimensional figures are shown to present the solutions on some specific domains. The used methods are found useful to be applied on other nonlinear evolution equations.

A Molecular Dynamics Study for Stability of Thin Water Films on Nanostructured Surfaces

2015 ◽  
Author(s):  
Liyong Sun ◽  
Jun Zhou
Keyword(s):  
Molecular Dynamics ◽  
Film Thickness ◽  
Molecular Dynamics Simulations ◽  
Van Der Waals Interactions ◽  
Water Molecules ◽  
Nanostructured Surfaces ◽  
Water Films ◽  
Critical Film Thickness ◽  
The Stability ◽  
Dynamics Simulations

The stability of thin water films on a variety of gold nanostructures was simulated by molecular dynamics simulations. The critical film thickness to prevent a film break-up was investigated as a function of the characteristic length of the nanostructures. Layering of water molecules adjacent to the gold substrate was observed as a result of the strong van der Waals interactions between the water molecules and the gold atoms. A model for the critical film thickness in the presence of nanostructures is developed based on the stability analysis. The model prediction is compared with molecular dynamics simulations with good agreement.

The shock peakon wave solutions of the general Degasperis–Procesi equation

2019 ◽  
Vol 33 (29) ◽  
pp. 1950351 ◽  
Author(s):  
Lijuan Qian ◽  
Raghda A. M. Attia ◽  
Yuyang Qiu ◽  
Dianchen Lu ◽  
Mostafa M. A. Khater
Keyword(s):  
Stability Property ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Dynamical Behavior ◽  
Nonlinear Evolution Equations ◽  
Wave Solutions ◽  
Generalized Kudryashov Method ◽  
Kudryashov Method ◽  
Different Types ◽  
The Stability

This research paper applies the modified Khater method and the generalized Kudryashov method to the general Degasperis–Procesi (DP) equation, which is used to describe the dynamical behavior of the shallow water outflows. Some shock peakon wave solutions are obtained by using these methods. Moreover, some figures are sketched for these solutions to explain more physical properties of the general DP equation and to figure out the coincidence between different types of obtained solutions. The stability property by using the features of the Hamiltonian system is tested to some obtained solutions to show their ability for applying in the model’s applications. The obtained solutions were verified with Maple 16 & Mathematica 12 by placing them back into the original equations. The performance of these methods shows their power and effectiveness for applying to many different forms of the nonlinear evolution equations with an integer and fractional order.

scholarly journals Electrohydrodynamic Instability of Two Thin Viscous Leaky Dielectric Fluid Films in a Porous Medium

2011 ◽  
Vol 2011 ◽  
pp. 1-35 ◽  
Author(s):  
M. F. El-Sayed ◽  
M. H. M. Moussa ◽  
A. A. A. Hassan ◽  
N. M. Hafez
Keyword(s):  
Porous Medium ◽  
Evolution Equations ◽  
Nonlinear Evolution Equations ◽  
Dielectric Fluid ◽  
Physical Parameters ◽  
Fluid Films ◽  
Linearized Stability ◽  
Leaky Dielectric ◽  
The Stability ◽  
Wave Limit

The effect of an applied electric field on the stability of the interface between two thin viscous leaky dielectric fluid films in porous medium is analyzed in the long-wave limit. A systematic asymptotic expansion is employed to derive coupled nonlinear evolution equations of the interface and interfacial free charge distribution. The linearized stability of these equations is determined and the effects of various parameters are examined in detail. For perfect-perfect dielectrics, the various parameters affect only for small wavenumber values. For dielectrics, the various parameters affect only for small wavenumber values. For effect for small wavenumbers, and a stabilizing effect afterwards, and for high wavenumber values for the other physical parameters, new regions of stability or instability appear. For leaky-leaky dielectrics, the conductivity of upper fluid has a destabilizing effect for small or high wavenumbers, while it has a dual role on the stability of the system in a wavenumber range between them. The effects of all other physical parameters behave in the same manner as in the case of perfect-leaky dielectrics, except that in the later case, the stability or instability regions occur more faster than the corresponding case of leaky-leaky dielectrics.

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.

Traveling wave solutions for the Couple Boiti-Leon-Pempinelli System by using extended Jacobian elliptic function expansion method

2015 ◽  
Vol 11 (3) ◽  
pp. 3134-3138 ◽  
Author(s):  
Mostafa Khater ◽  
Mahmoud A.E. Abdelrahman
Keyword(s):  
Elliptic Function ◽  
Traveling Wave ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Mathematical Physics ◽  
Nonlinear Evolution Equations ◽  
Jacobian Elliptic Function ◽  
Function Expansion

In this work, an extended Jacobian elliptic function expansion method is pro-posed for constructing the exact solutions of nonlinear evolution equations. The validity and reliability of the method are tested by its applications to the Couple Boiti-Leon-Pempinelli System which plays an important role in mathematical physics.

scholarly journals Approximate Analytical Solution of Nonlinear Evolution Equations

2020 ◽  
Author(s):  
Laxmikanta Mandi ◽  
Kaushik Roy ◽  
Prasanta Chatterjee
Keyword(s):  
Acoustic Waves ◽  
Evolution Equations ◽  
Solitary Wave Solution ◽  
Perturbation Technique ◽  
Nonlinear Evolution Equations ◽  
Charged Dust ◽  
De Vries ◽  
Frame Work ◽  
Dust Grain ◽  
Charged Ions

Analytical solitary wave solution of the dust ion acoustic waves (DIAWs) is studied in the frame-work of Korteweg-de Vries (KdV), damped force Korteweg-de Vries (DFKdV), damped force modified Korteweg-de Vries (DFMKdV) and damped forced Zakharov-Kuznetsov (DFZK) equations in an unmagnetized collisional dusty plasma consisting of negatively charged dust grain, positively charged ions, Maxwellian distributed electrons and neutral particles. Using reductive perturbation technique (RPT), the evolution equations are obtained for DIAWs.

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