Research Projects

The study of thin film flows is one of the most vibrant branches of fluid mechanics. These flows are characterised by a very short length scale in one direction as compared to other directions and are ubiquitous in nature and technical applications. The dynamics of such films are quite complex and display rich behaviour. The investigation approaches include modelling and analytical work, numerical simulations, and experiments to explain the instabilities that the film can exhibit. Special analytical and numerical techniques are needed to handle them. The experimental results are available but are quite sparse. In this project we propose to investigate certain thin fluid film flow problems in the areas of (a) compliant substrate, (b) non-Newtonian fluids and (b) evaporation. First we wish to investigate the previous-mentioned problems through analytical means and predict the important parameters of the flow related to the instability. We wish to carry out linear and weakly nonlinear analysis, investigation of travelling waves and Orr-Sommerfeld eigenvalue analysis as required. We will also focus our attention to the dynamical systems aspect of these problems which is typically not investigated in-depth. This has the potential to enrich our knowledge in these areas and act as guidelines for experimental researchers to verify the results. The second aspect we wish to explore is a very new numerical approach by Pal et al. using the radial basis functions (RBF). We wish to take their method further and check if this can be extended to the computation of other interesting features of the problem like travelling wave solution. We also wish to investigate important numerical aspects of RBF based approach like stability, adaptability in space-time to expedite the simulations and to check if desirable properties like discrete conservation can be embedded in the approach in the context of the current and other related problems. Apart from the scientific merit, these problems are important in application areas like chip manufacturing where the coating of the semiconductor chips requires the use of paints. Understanding of the heating mechanism is highly desirable as uneven coating reduces the life-span of the components. In all cases, we will start modelling the physical phenomena by means of partial differential equations of flow and couple the flow problems with other fields as necessary. Then we will carry out the simplifications of the equations and obtain a surface equation for film height and subject this equation to investigation using linear and non-linear methods. After that, the numerical investigation will also be carried out with two goals in mind: (a) confirmation of analytical results and (b) demonstration of the efficacy of the numerical algorithm. We further mention that we already have some interesting results in the area of compliant substrates.