Modelling Pattern Formation in Dip-Coating Experiments
arXiv:1502.03632 · doi:10.1051/mmnp/201510402
Abstract
We briefly review selected mathematical models that describe the dynamics of pattern formation phenomena in dip-coating and Langmuir-Blodgett transfer experiments, where solutions or suspensions are transferred onto a substrate producing patterned deposit layers with structure length from hundreds of nanometres to tens of micrometres. The models are presented with a focus on their gradient dynamics formulations that clearly shows how the dynamics is governed by particular free energy functionals and facilitates the comparison of the models. In particular, we include a discussion of models based on long-wave hydrodynamics as well as of more phenomenological models that focus on the pattern formation processes in such systems. The models and their relations are elucidated and examples of resulting patterns are discussed before we conclude with a discussion of implications of the gradient dynamics formulation and of some related open issues.
References in corpus (10)
- Morphology changes in the evolution of liquid two-layer films
- Relaxation of a dewetting contact line Part 1: A full-scale hydrodynamic calculation
- Dynamical model for the formation of patterned deposits at receding contact lines
- Modelling the formation of structured deposits at receding contact lines of evaporating solutions and suspensions
- Thin film evolution equations from (evaporating) dewetting liquid layers to epitaxial growth
- Thermodynamically consistent description of the hydrodynamics of free surfaces covered by insoluble surfactants of high concentration
- Continuous and discontinuous dynamic unbinding transitions in drawn film flow
- Emergence of the bifurcation structure of a Langmuir-Blodgett transfer model
- Stability of liquid films covered by a carpet of self-propelled surfactant particles
- Dynamical Effects and Phase Separation in Thin Films
Cited by in corpus (19)
- Classical dynamical density functional theory: from fundamentals to applications
- Gradient dynamics models for liquid films with soluble surfactant
- Recent advances in and future challenges for mesoscopic hydrodynamic modelling of complex wetting
- Modelling of surfactant-driven front instabilities in spreading bacterial colonies
- Continuation for thin film hydrodynamics and related scalar problems
- Numerical Bifurcation Analysis of Marine Ice Sheet Models
- Order-of-magnitude speedup for steady states and traveling waves via Stokes preconditioning in Channelflow and Openpipeflow
- Connecting monotonic and oscillatory motions of the meniscus of a volatile polymer solution to the transport of polymer coils and deposit morphology
- From a thin film model for passive suspensions towards the description of osmotic biofilm spreading
- Self-organised dip-coating patterns of simple, partially wetting, nonvolatile liquids
- Universal wavenumber selection laws in apical growth
- Effects of time-periodic forcing in a Cahn-Hilliard model for Langmuir-Blodgett transfer
- Two-dimensional patterns in dip coating -- first steps on the continuation path
- Dip-coating with prestructured substrates: transfer of simple liquids and Langmuir-Blodgett monolayers
- Gradient dynamics approach to reactive thin-film hydrodynamics
- Bifurcation study for a surface-acoustic-wave driven meniscus
- Travelling-wave spatially periodic forcing of asymmetric binary mixtures
- Demixing of two species via reciprocally concentration-dependent diffusivity
- Strain and defects in oblique stripe growth