'Thin Films of Liquid' - An amazing wonder

Vedant

Jun 1, 2024

Liquid, when we heard this name the first thing appear in our mind is the water, since water is one of the most common and useful liquid humans encounter, liquid exists everywhere from largest of the dams to small glass on your table. The physics behind how the liquid behaves in different condition is always been an topic of interest to many centuries, we consider the liquid as a 'Continuum', which defines the liquid as substance which completely occupies the space and is evenly distributed. However if we zoom enough we find out that there are molecules of liquid that behaves like this. One of the phenomena that exists at the continuum scale is the formation of 'Thin-films'.




    Fig-1: A picture of dam, holding enormous
     amount of water

One of the most common example of thin films are the gasoline on water, when small amounts of gasoline is accumulated on the water surface due to density difference and surface tension these two liquid namely water and gasoline do not mix. But the gasoline forms a thin film over the water that produces vibrant colors reminding of Rainbow. This happens due to refraction of light from that film.














Fig-2 : A thin film of gasoline or oil produces 
vibrant colors

However the thin-films are not just limited to creating small rainbow on water surface, there are tremendous application of them, ranging from Lithography (semiconductor manufacturing), Coating of film on screens, spectacles, paints, etc. This small structure has wide range of applications in our daily life.

The physics behind the thin films can be explained by the 'Partial differential equations', studies are made for the stability of thin-films called Stability analysis, it is a mathematical technique that studies how films get destabilized from the different forces acting on it, manipulating parameters such as the type of substrate, intensity of the electric field will provides us the different scenarios. We need to ensure the stability of thin films to use them in different applications, research has been going on since decades in the field of stability of thin-films. Basically we need to deal with convoluted mathematics to solve the partial differential equation obtained so far from the fundamental balance principle of physics. One of the most common type of PDE (Partial differential equation) is the wave equation.
The one dimensional wave equation which tells us about a point how it varies with time and position looks like:
\begin{align} \frac{\partial^2 u}{\partial t^2} &= c^2 \frac{\partial^2 u}{\partial x^2} \end{align}

And its solution is:

\begin{align} u(x,t) &= \frac{1}{2} \sum_{n=0}^{\infty} b_n \sin \left(n\pi \frac{x + ct}{L}\right) + b_n \sin \left(n\pi \frac{x - ct}{L}\right) \\ b_n &= \frac{2}{L} \int_0^L f(x) \sin \left(\frac{n\pi x}{L}\right) dx \end{align}

Mathematical treatment gives us an idea about the structure and other parameters, however these equations do not provides us with the actual picture, through microscopes we can see the thin-films that whose size is order of nanometers. Mathematical modeling and simulation produces results based on some of the assumptions and generates appropriate results that can be used further in application.


  








Fig-3: Ripples of water

Thin-films are truly wonderful structures that enables us fabricate important electronics and sensors and so much more, many researches are their dedicating their life for the development of new technology involving thin-films.