Department of Mathematics,
Office: 3266 SAS Hall
North Carolina State University
Raleigh, North Carolina 27695, USA
I am currently a Postdoctoral Research Scholar in the Department of Mathematics at North Carolina State University (Raleigh, NC, USA), working with Dr. Hangjie Ji.
I am also a member of The Center for Research in Scientific Computation at North Carolina State University (Raleigh, NC, USA).
My current research focuses on developing mathematical models to understand the Morphological changes in Eutectic Gallium Indium (EGaIn) droplets under applied voltage in an electrolyte solution and the Dynamics of asymmetric droplet coalescence.
Before joining NC State University, I received my Ph.D. (Mathematics) from Indian Institute of Technology Dharwad under the guidance of Dr. Amlan K. Barua.
My research interests lie in applied mathematics, specifically studying fluid dynamics problems involving moving interfaces. These flows are classified as free-boundary problems. We need to determine moving interfaces as part of the solution to obtain a quantitative description of the dynamics. Such problems are notoriously tricky mathematically for several reasons:
(a) The Navier-Stokes equations need to be solved in changing domains.
(b) In certain applications, we may need to also solve for the temperature/ electric/ magnetic/ electromagnetic fields.
(c) Several nonlinear boundary conditions must be specified at the unknown interface(s).
(d) The surface equation is highly nonlinear.
I use modeling, analysis, and computations to investigate the flow dynamics. The models I develop incorporate various physical effects, such as Marangoni forces resulting from surface tension gradients and electrostatic and electrokinetic effects that are crucial in micro- and nano-fluidic applications. Mathematically, these models are reduced systems of the Navier-Stokes equations and often lead to nonlinear PDEs of the "active-dissipative" type. These equations exhibit long-wave instabilities and short-wave damping, which results in low dimensional interfacial chaos. My primary objective is to understand the qualitative aspects of these solutions through analysis and construct quantitative solutions using accurate and efficient simulations.
Thermocapillary ultrathin self-rewetting film flows down a rotating fibre. Physica D: Nonlinear Phenomena, 2025. [Journal]
(with A. K. Gaonkar, H. Ji) Thermocapillary instabilities in thin liquid films on a rotating cylinder. International Journal of Heat and Mass Transfer, 2025. [Journal]
(with H. Ji) Thermocapillary weak viscoelastic film flows on a rotating substrate. Physica D: Nonlinear Phenomena, 2025. [Journal]
Thermocapillary thin films on rotating cylinders with wall slip and exothermic reactions. International Journal of Heat and Mass Transfer, 2024. [Journal]
Falling liquid film down a non-uniformly heated slippery inclined plane with odd viscosity effects. International Journal of Heat and Mass Transfer, 2024. [Journal]
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June 5 - 6, 2025: I presented a poster at the Frontiers in Applied and Computational Mathematics (FACM'25) at the Department of Mathematics, New Jersey Institute of Technology (Newark, New Jersey, USA).
Apr 3, 2025: I gave a talk at the CAM (Computational and Applied Mathematics) Seminar at the Department of Mathematics, North Carolina State University (North Carolina, USA).
Nov 24 - 26, 2024: I presented our work Stability and dynamics of thin film flow on a rotating cylinder at the 77th Annual Meeting of the Division of Fluid Dynamics in Salt Lake City, USA.
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Emails: sdipmath@gmail.com, schatto5@ncsu.edu
Go to my ResearchGate account.
Go to my Google Scholar profile.
