Fingering instability of a suspension film spreading on a spinning disk - Kulkarni, Mayuresh; Sahoo, Subhadarshinee; Doshi, Pankaj; Orpe, Ashish V. (Physics of Fluids, 2016)
The spreading of a thin film of suspension on a spinning disk and the accompanying contact line instability is studied through flow visualization experiments. The critical radius for the onset of instability shows an increase with increase in the particle fraction (phi(p)) before decreasing slightly at the highest value of phi(p) studied, while the instability wavelength (lambda) exhibits a non-monotonic dependence. The value of lambda is close to that for a partially wetting liquid at lower phi(p), it decreases with increasing phi(p) to a minimum before increasing again at largest phi(p). The non-monotonic trends observed for lambda are discussed in light of the linear stability analysis of thin film equations derived for suspensions by Cook et al. [''Linear stability of particle-laden thin films,'' Eur. Phys. J.: Spec. Top. 166, 77 (2009)] and Balmforth et al. [''Surface tension driven fingering of a viscoplastic film,'' J. Non Newtonian Fluid Mech. 142, 143 (2007)]. Published by AIP Publishing.

Two-layer spin coating flow of newtonian liquids: a computational study - Sahoo, Subhadarshinee; Arora, Akash; Doshi, Pankaj (Computers & Fluids, 2016)
Spin coating is the most commonly used method in industries to form coating films of desired thickness and functionality. In case of two-layer spin coating process, stratified layers of two immiscible liquids are deposited onto the substrate simultaneously, which spread and thin to form two-layer coating film of finite thickness. Questions concerning the effect of surface/interfacial tension on uniformity of these films and contact line evolution are relevant and need thorough investigation. Therefore, an axisymmetric model governing the flow of two-layer spin coating process is developed here. Liquids used for the study are assumed to be Newtonian and fully wetting. The contact line singularity is resolved using a precursor layer model and the governing equations are simplified using lubrication approximation. A Galerkin finite-element method (G/FEM) based scheme is developed to solve the resulting fourth order non-linear PDEs. Simulation results reveal that the fluid properties like ratio of the viscosity of upper layer fluid to lower layer and ratio of the upper gas-liquid surface tension to inner liquid-liquid interfacial tension have profound impact on the time evolution of the film profile, contact radius and shape of the capillary ridges. It is observed that a uniform two-layer film surrounded by thin single layer film is formed when the viscosity ratio is small. On the contrary, when viscosity ratio is large, a thin two-layer film surrounded by bulky capillary ridges is formed. Similarly, the results also show that sharpness of capillary ridge increases with decrease in the surface tension ratio. Further, it is found that increase in the precursor layer thickness increases the spreading rate, thereby making the film more uniform. Finally, the uniformity of the final two-layer film does not get affected by the initial volume of fluid present in the upper layer. (C) 2016 Elsevier Ltd. All rights reserved.
Keywords: Axisymmetric flow; Mathematical modeling; Multi-layer coating; Precursor layer model; Thin-film flow; Two-layer spin coating

Spreading dynamics of superposed liquid drops on a spinning disk - Sahoo, Subhadarshinee; Orpe, Ashish V.; Doshi, Pankaj (Physics of Fluids, 2018)
We have experimentally studied simultaneous spreading of superposed drops of two Newtonian liquids on top of a horizontal spinning disk using the flow visualization technique. An inner drop of high surface tension liquid is placed centrally on the disk followed by a drop of outer liquid (lower surface tension) placed exactly above that. The disk is then rotated at a desired speed for a range of volume ratios of two liquids. Such an arrangement of two superposed liquid drops does not affect the spreading behavior of the outer liquid but influences that of the inner liquid significantly. The drop spreads to a larger extent and breaks into more fingers (Nf) as compared to the case where the same liquid is spreading in the absence of outer liquid. The experimentally observed number of fingers is compared with the prediction using available theory for single liquid. It is found that the theory over-predicts the value of Nf for the inner liquid while it is covered by an outer liquid. We provide a theoretical justification for this observation using linear stability analysis. Our analysis demonstrates that for small but finite surface tension ratio of the two liquids, the presence of the outer interface reduces the value of the most unstable wave number which is equivalent to the decrease in the number of fingers observed experimentally. Finally, sustained rotation of the disk leads to the formation of droplets at the tip of the fingers traveling outwards. Published by AIP Publishing.