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Stability of thin fluid films characterised by a complex form of effective disjoining pressure

Published online by Cambridge University Press:  01 March 2018

Michael-Angelo Y.-H. Lam Open the ORCID record for Michael-Angelo Y.-H. Lam [Opens in a new window] ,
Linda J. Cummings  and
Lou Kondic
Michael-Angelo Y.-H. Lam
Affiliation:
Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, NJ 07102, USA
Linda J. Cummings
Affiliation:
Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, NJ 07102, USA
Lou Kondic*
Affiliation:
Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, NJ 07102, USA
*
†Email address for correspondence: [email protected]
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Abstract

We discuss instabilities of fluid films of nanoscale thickness, with a particular focus on films where the destabilising mechanism allows for linear instability, metastability, and absolute stability, depending on the mean film thickness. Our study is motivated by nematic liquid crystal films; however, we note that similar instability mechanisms, and forms of the effective disjoining pressure, appear in other contexts, such as the well-studied problem of polymeric films on two-layered substrates. The analysis is carried out within the framework of the long-wave approximation, which leads to a fourth-order nonlinear partial differential equation for the film thickness. Within the considered formulation, the nematic character of the film leads to an additional contribution to the disjoining pressure, changing its functional form. This effective disjoining pressure is characterised by the presence of a local maximum for non-vanishing film thickness. Such a form leads to complicated instability evolution that we study by analytical means, including the application of marginal stability criteria, and by extensive numerical simulations that help us develop a better understanding of instability evolution in the nonlinear regime. This combination of analytical and computational techniques allows us to reach novel understanding of relevant instability mechanisms, and of their influence on transient and fully developed fluid film morphologies. In particular, we discuss in detail the patterns of drops that form as a result of instability, and how the properties of these patterns are related to the instability mechanisms.

JFM classification

Complex Fluids: Complex Fluids Non-Newtonian Flows: Non-Newtonian Flows Interfacial Flows (free surface): Thin films
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 841 , 25 April 2018 , pp. 925 - 961
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Copyright
© 2018 Cambridge University Press 

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Lam et al. supplementary movie 1

Evolution of the film thickness in the reference frame traveling with the linear spreading speed V (4.19). The initial condition is given in (4.1) with an initial film thickness of H0=0.6. Simulation resembles a traveling wave, with a stationary envelope

Download Lam et al. supplementary movie 1(Video)
Video 28.8 MB

Lam et al. supplementary movie 2

Evolution of the film thickness in the reference frame traveling with the linear spreading speed V (4.19). The initial condition is given in (4.1) with an initial film thickness of H0=0.24. Note that the oscillations ahead of the drop grow in magnitude before reaching some threshold value, initiating dewetting.

Download Lam et al. supplementary movie 2(Video)
Video 22.6 MB

Lam et al. supplementary movie 3

Evolution of the film thickness in the reference frame traveling with the linear spreading speed V (4.19). The initial condition is given in (4.1) with an initial film thickness of H0=0.15. A subtype of the R II regime, however, the front (eventually) alternates between two different breakup times, tMSC, and height of drop centers, Hl.

Download Lam et al. supplementary movie 3(Video)
Video 24.6 MB

Lam et al. supplementary movie 4

Evolution of the film thickness in the reference frame traveling with the linear spreading speed V (4.19). The initial condition is given in (4.1) with an initial film thickness of H0=0.45. Simulation resembles thin films in the R I regime. However, the expanding wave packet is sporadically interrupted.

Download Lam et al. supplementary movie 4(Video)
Video 27.8 MB