# Patterns formed in a thin film with spatially homogeneous and non-homogeneous Derjaguin disjoining pressure

@inproceedings{Alshaikhi2021PatternsFI, title={Patterns formed in a thin film with spatially homogeneous and non-homogeneous Derjaguin disjoining pressure}, author={A. Alshaikhi and M. Grinfeld and S. K. Wilson}, year={2021} }

We consider patterns formed in a two-dimensional thin film on a planar substrate with a Derjaguin disjoining pressure and periodic wettability stripes. We rigorously clarify some of the results obtained numerically by Honisch et al. [Langmuir 31: 10618–10631, 2015] and embed them in the general theory of thin-film equations. For the case of constant wettability, we elucidate the change in the global structure of branches of steady state solutions as the average film thickness and the surface… Expand

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SHOWING 1-10 OF 48 REFERENCES

Auto07p: Continuation and Bifurcation for Ordinary Differential Equations

- 2009

Instabilities of Layers of Deposited Molecules on Chemically Stripe Patterned Substrates: Ridges versus Drops.

- Chemistry, Physics
- Langmuir : the ACS journal of surfaces and colloids
- 2015

It is shown that the transport process does neither influence the linear stability thresholds nor the sequence of morphologies observed in the time simulation, but only the ratio of the time scales of the different process phases. Expand

Bifurcation from an Orbit of Symmetry

- Physics
- 1985

We explore two different approaches to investigating what happens to an orbit of critical points of a symmetric function when the continuous symmetry of the function is broken, and outline an… Expand

Nonlinear dynamics of dewetting thin films

- Materials Science
- 2020

Fluid films spreading on hydrophobic solid surfaces exhibit complicated dynamics that describe transitions leading the films to break up into droplets. For viscous fluids coating hydrophobic solids… Expand

Steady states of thin film droplets on chemically heterogeneous substrates

- Physics, Materials Science
- 2020

We study steady-state thin films on a chemically heterogeneous substrates of finite size, subject to no-flux boundary conditions. Based on the structure of the bifurcation diagram, we classify the… Expand

Finite-time thin film rupture driven by modified evaporative loss

- Materials Science, Physics
- 2017

Abstract Rupture is a nonlinear instability resulting in a finite-time singularity as a film layer approaches zero thickness at a point. We study the dynamics of rupture in a generalized mathematical… Expand

Global attractor for the 1-D thin film equation

- Physics, Computer Science
- Asymptot. Anal.
- 2007

The existence of global attractor is proved and the fourth-order degenerate parabolic equation which describes the dewetting phenomenon of a thin film under the long-range attractive force and the short-range stabilizing effect of Born repulsion is described. Expand

Collision versus collapse of droplets in coarsening of dewetting thin films

- 2005

Thin films of viscous fluids coating solid surfaces can become unstable due to intermolecular forces, leading to break-up of the film into arrays of droplets. The long-time dynamics of the system can… Expand

Mesoscopic hydrodynamics of contact line motion

- Physics
- 2002

Abstract We review the paradoxes of the problem of a moving gas–liquid–solid contact line, and the ways to eliminate them by modifying both hydrodynamic equations at mesoscopic distances and boundary… Expand