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

@article{Alshaikhi2021PatternsFI,
  title={Patterns formed in a thin film with spatially homogeneous and non-homogeneous Derjaguin disjoining pressure},
  author={Abdulwahed S. Alshaikhi and Michael Grinfeld and S. K. Wilson},
  journal={European Journal of Applied Mathematics},
  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

References

SHOWING 1-10 OF 56 REFERENCES
Auto07p: Continuation and Bifurcation for Ordinary Differential Equations
  • 2009
Singularities and Groups in Bifurcation Theory: Volume I
Nonlinear dynamics of dewetting thin films
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 solidsExpand
Bifurcation from an Orbit of Symmetry
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 anExpand
Mesoscopic hydrodynamics of contact line motion
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 boundaryExpand
Properties of steady states for thin film equations
We consider nonnegative steady-state solutions of the evolution equation formula here Our class of coefficients f, g allows degeneracies at h = 0, such as f(0) = 0, as well as divergences like g(0) =Expand
Spectral comparison principles for the Cahn-Hilliard and phase-field equations, and time scales for coarsening
We initiate a study of the instability properties of steady solutions of the Cahn-Hilliard (CH) equation and the phase field (PF) system in terms of the coarseness of those solutions. Other spectralExpand
Steady states of thin film droplets on chemically heterogeneous substrates
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 theExpand
3D Self-Assembled Microelectronic Devices: Concepts, Materials, Applications.
TLDR
Existing work in this field, with a focus on components constructed from 3D self-assembly, is reviewed, and an outlook on their application potential in tomorrow's microelectronics world is provided. Expand
Research on the fluid film lubrication between the piston-cylinder interface
The fluid film between piston and cylinder works simultaneously as bearing and lubricating functions, its thickness determines the lubrication efficiency and performance of an axial piston pump.Expand
...
1
2
3
4
5
...