Research our contributions to discovery
Dynamics of fluid interfaces, multiphysics interactions & control
We elucidated the physics underlying the (in)stability of fluid-fluid interfaces in the presence of multiphysics interactions, such as deformable geometries, external forcing, imposed magnetic fields, etc. Our ultimate objective is to enable non-invasive control of patterns. Specifically, we were the first to demonstrate the generation of nonlinear periodic waves on a ferrofluid interface via an external magnetic field. Research supported by the National Science Foundation.
Fluid–structure interactions in cerebral aneurysms
Through a unique data set featuring patients with multiple aneurysms (with one growing and one stable, acting as "self-controls"), using patient-specific, high-resolution numerical simulations of fluid–structure interactions, we demonstrated that regions of combined low wall shear stress and oscillatory shear index correlate with aneurysmal growth. Research was supported by the Brain Aneurysm Foundation.
Micro- and nano-scale flows through deformable confinements
Flows through deformable confinements arise in microfluidics. We derived a nonlinear differential equation for a soft coating’s interface, in the presence of both fluid–structure interaction and hydrodynamic slip, to determine the conduit shape during flow. This joint research between Purdue and IIT Kharagpur was supported by the Scheme for Promotion of Academic and Research Collaboration (SPARC).
Nonlinear waves; PDEs with Hamiltonian structure; stochastics
Domain walls play a key role in condensed matter physics, cosmology, and biological physics. Their dynamics determine bulk properties of materials undergoing phase transitions, as theorized by Nobel Laureate Lev Landau. We characterized a new class of weakly localized domain walls and formulated a new theory of their interactions, overturning decades of intuition.
Particle-laden flows and heat transfer in complex and 3D geometries
We enabled predictive simulation of flows and thermal transport in dense suspensions via two-fluid continuum models by developing open-source computational codes using the OpenFOAM framework (twoFluidsNBSuspensionFoam). We discovered that thermal and shear gradients in dense suspensions can have both synergistic and antagonistic effects on particle migration. Research supported by the American Chemical Society's Petroleum Research Fund.
Anomalous scalings in the diffusion of granular materials
Check out our paradigm-shifting paper on the intermediate asymptotics of non-degenerate diffusion equations, contributed to the Proceedings of the National Academy of Sciences of the USA by G. I. Barenblatt himself. Research supported by the National Science Foundation.