(83f) Thin Liquid Film Stability in Various Interaction Regimes Arising Due to Surface Active Agents

Thin
liquid film stability in various interaction regimes arising due to surface
active agents

Paidi
Venkatesh Kumar ¹, U. Hariharan¹, Anjishnu Choudhury²,
Harish N. Dixit², Sreeram K. Kalpathy¹*^#,  

¹ Dept.
of Metallurgical and Materials Engineering, Indian Institute of Technology
Madras, Chennai – 600036, India.

² Dept.
of Mechanical and Aerospace Engineering, Indian Institute of Technology Hyderabad,
Kandi, Sangareddy, Telangana  – 502285, India.

 *Corresponding author: sreeram@iitm.ac.in

^#  Presenting
author

A
hydrodynamic model that addresses the interplay between surface rheological
effects, and surface tension and its gradients is used to predict the stability
of a thin liquid film containing surface active agents.  The model traces the evolution
of a Newtonian liquid film, covered with insoluble surface active particles,
until rupture, assisted by a Van der Waals-type disjoining pressure. The particles
are assumed to have a significant effect on the surface viscosity of the film,
which in turn depends on the particle concentration. In addition, they may also
cause gradients in surface tension due to diffusion-driven local concentration
variations, and induce a Marangoni flow. Four distinct interaction regimes,
emerging from local concentration variations are identified, such that either,
both, or neither of Marangoni and surface viscosity effects would be present at
leading order in the lubrication limit.

In
the model, the liquid film is covered by a passive air phase above, and is either
bounded by a rigid solid below, or considered a free film in the squeezing mode¹,
symmetric about the horizontal axis (see Figure 1). For the former case, a
no-slip condition for the horizontal velocity is used at the solid surface, and
for the latter, a symmetry condition is used, wherein the vertical gradient of
the horizontal velocity vanishes at the symmetry plane. The surface tension is
assumed to decrease linearly with increasing concentration of the surface
active particles, whereas a nonlinear phenomenological model² is
used to examine the effect of particle concentration on surface viscosity. At
sufficiently high concentrations, the particles could form an apparently rigid
shell around the liquid free surface due to enhanced surface viscosity. Depending
on whether the Marangoni or surface viscosity effects are weak or strong, these
effects are correspondingly present or absent in the tangential stress balance
condition at the free surface.

Standard
linear stability analysis reveals the nature of growth or decay of small
amplitude interfacial perurbations. When the system has weak Marangoni and weak
surface viscosity effects, both these factors act as film stabilizers against Van
der Waals instability, with a characteristic interfacial perturbation wavelength
that grows the fastest. However, when either or both these effects are important
at leading order, the surface viscosity effect may act as a destabilizer, and
the characteristic wavelength is seen to be strongly influenced by their
magnitudes. The system may either exhibit a classical long-wave instability or
exhibit a sudden spike in growth rate at a certain wavenumber. The nonlinear
evolution of the film is seen to be a strong function of the relative
difference between the critical wavelength, the wavelength of the initial
perturbation, and the number of such wavelengths in the simulation domain.

Figure 1: Schematic
of the problem setup. (a) Film bounded by a rigid solid at the bottom  (b)
Symmetric free film in squeezing mode.

References

[1] De
Wit, A., Gallez D. (1994) Phys. Fluids. 6(10), 3256-3266.

[2] Maki,
K.L., and Kumar, S. (2011) Langmuir. 27, 11347-11363.