scholarly journals Dynamics of thin liquid films on vertical cylindrical fibres

2019 ◽  
Vol 865 ◽  
pp. 303-327 ◽  
Author(s):  
H. Ji ◽  
C. Falcon ◽  
A. Sadeghpour ◽  
Z. Zeng ◽  
Y. S. Ju ◽  
...  
Keyword(s):  
Thin Films ◽  
Stability Analysis ◽  
Wave Solution ◽  
Liquid Films ◽  
Travelling Wave ◽  
Thin Liquid Films ◽  
Travelling Wave Solution ◽  
Slip Boundary Conditions ◽  
Slip Boundary ◽  
Physical Effects

Recent experiments on thin films flowing down a vertical fibre with varying nozzle diameters present a wealth of new dynamics that illustrate the need for more advanced theory. We present a detailed analysis using a full lubrication model that includes slip boundary conditions, nonlinear curvature terms and a film stabilization term. This study brings to focus the presence of a stable liquid layer playing an important role in the full dynamics. We propose a combination of these physical effects to explain the observed velocity and stability of travelling droplets in the experiments and their transition to isolated droplets. This is also supported by stability analysis of the travelling wave solution of the model.

scholarly journals AN ANALYSIS TO THE TRAVELLING WAVE SOLUTION OF A DIFFUSIVE MODEL OF AN EPIDEMIC

1998 ◽  
Vol 29 (1) ◽  
pp. 65-68
Author(s):  
M. S. ABUAL-RUB
Keyword(s):  
Stability Analysis ◽  
Wave Solution ◽  
Sir Model ◽  
Travelling Wave ◽  
Travelling Wave Solution ◽  
Spatial Spread ◽  
Diffusive Model

An SIR model of an epidemic with spatial spread is considered, an equilibrium and stability analysis has been done and then the behavior to the travelling wave solution of the model is obtained.

scholarly journals Double flow reversal in thin liquid films driven by megahertz-order surface vibration

2014 ◽  
Vol 470 (2169) ◽  
pp. 20130765 ◽  
Author(s):  
Amgad R. Rezk ◽  
Ofer Manor ◽  
Leslie Y. Yeo ◽  
James R. Friend
Keyword(s):  
Thin Films ◽  
Acoustic Waves ◽  
Surface Acoustic Waves ◽  
Intermolecular Forces ◽  
Liquid Films ◽  
Thin Liquid Films ◽  
Propagation Direction ◽  
Flow Reversal ◽  
Order Surface ◽  
Over Time

Arising from an interplay between capillary, acoustic and intermolecular forces, surface acoustic waves (SAWs) are observed to drive a unique and curious double flow reversal in the spreading of thin films. With a thickness at or less than the submicrometre viscous penetration depth, the film is seen to advance along the SAW propagation direction, and self-similarly over time t 1/4 in the inertial limit. At intermediate film thicknesses, beyond one-fourth the sound wavelength λ ℓ in the liquid, the spreading direction reverses, and the film propagates against the direction of the SAW propagation. The film reverses yet again, once its depth is further increased beyond one SAW wavelength. An unstable thickness region, between λ ℓ /8 and λ ℓ /4, exists from which regions of the film either rapidly grow in thickness to exceed λ ℓ /4 and move against the SAW propagation, consistent with the intermediate thickness films, whereas other regions decrease in thickness below λ ℓ /8 to conserve mass and move along the SAW propagation direction, consistent with the thin submicrometre films.

scholarly journals EVOLUTION OF MODULATIONAL INSTABILITY IN TRAVELLING WAVE SOLUTION OF NON-LINEAR PARTIAL DIFFERENTIAL EQUATION

2020 ◽  
Vol 5 (1) ◽  
pp. 1-7
Author(s):  
Ram Dayal Pankaj ◽  
Arun Kumar ◽  
Chandrawati Sindhi
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Wave Solution ◽  
Modulational Instability ◽  
Nonlinear Partial Differential Equation ◽  
Linear Partial Differential Equation ◽  
Travelling Wave ◽  
Travelling Wave Solution ◽  
Partial Differential ◽  
Jacobian Elliptic Functions

The Ritz variational method has been applied to the nonlinear partial differential equation to construct a model for travelling wave solution. The spatially periodic trial function was chosen in the form of combination of Jacobian Elliptic functions, with the dependence of its parameters

Spin-coating of vertically stratified thin liquid films

2010 ◽  
Vol 647 ◽  
pp. 265-285 ◽  
Author(s):  
A. McINTYRE ◽  
L. N. BRUSH
Keyword(s):  
Thin Films ◽  
Spin Coating ◽  
Lower Layer ◽  
Liquid Films ◽  
Thin Liquid Films ◽  
Uniform Thickness ◽  
Viscous Forces ◽  
Liquid Free Surface ◽  
Device Applications ◽  
Lower Liquid

Spin-coating is a process used to fabricate thin films for device applications. In this paper, lubrication theory is used to derive an axisymmetric model for the spin-coating of two immiscible vertically stratified Newtonian thin films. The model includes gravitational, van der Waals, capillary and viscous forces, differences in liquid layer properties and evaporation/condensation effects. Thinning calculations focus on the effects of viscosity and condensation/evaporation. In this case, for layers of uniform thickness, the lower layer thins monotonically yet never reaches zero thickness. With evaporation mass loss the upper layer disappears in finite time, whereas with condensation effects the upper layer approaches a steady-state thickness. Fully nonlinear calculations are carried out for films with non-uniform thickness and the deviation of the interfaces from the flat state is monitored. In general, disturbances to the lower layer have a greater effect on the upper layer than those of disturbances of the upper layer on the lower layer. Disturbances along the upper gas–liquid free surface propagate outward more rapidly than those along the lower liquid–liquid interface and disturbances that decrease the film thickness tend to dissipate more slowly.

scholarly journals Stability Analysis on Nonequilibrium Supersonic Boundary Layer Flow with Velocity-Slip Boundary Conditions

Fluids ◽  
2019 ◽  
Vol 4 (3) ◽  
pp. 142
Author(s):  
Xin He ◽  
Kai Zhang ◽  
Chunpei Cai
Keyword(s):  
Boundary Layer ◽  
Stability Analysis ◽  
Boundary Conditions ◽  
Boundary Layer Flow ◽  
Velocity Slip ◽  
Linear Stability Theory ◽  
Resonance Phenomenon ◽  
Slip Boundary Conditions ◽  
Slip Boundary ◽  
Layer Flow

This paper presents our recent work on investigating velocity slip boundary conditions’ effects on supersonic flat plate boundary layer flow stability. The velocity-slip boundary conditions are adopted and the flow properties are obtained by solving boundary layer equations. Stability analysis of two such boundary layer flows is performed by using the Linear stability theory. A global method is first utilized to obtain approximate discrete mode values. A local method is then utilized to refine these mode values. All the modes in these two scenarios have been tracked upstream-wisely towards the leading edge and also downstream-wisely. The mode values for the no-slip flows agree well with the corresponding past results in the literature. For flows with slip boundary conditions, a stable and an unstable modes are detected. Mode tracking work is performed and the results illustrate that the resonance phenomenon between the stable and unstable modes is delayed with slip boundary conditions. The enforcement of the slip boundary conditions also shortens the unstable mode region. As to the conventional second mode, flows with slip boundary conditions can be more stable streamwisely when compared with the results for corresponding nonslip flows.

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