My research focuses on analytical and computational modeling of problems in the dynamics of Newtonian and non-Newtonian fluids, and their interaction with suspended microstructures, interfaces, and boundaries. Feel free to reach out directly to me with questions or ideas.
Current research projects
- Thermal Fluctuations, Microrheology, Active Suspensions in Complex Flow with Scott McKinley (Tulane): rheology is the study of flow and deformation of soft matter in response to applied forces that is widely used to reconstruct a viscoelastic fluid mechanical properties.
- Elastic Pulsatile Branched Blood Flow Model with Filip Belik, Tyler Schuessler, Henry Crandall, Braxton Osting and Benjamin Sanchez: elasticity in the arterial wall and the oscillatory nature of blood pressure drive flow drive blood in a branched artery.
Completed research projects
- Newtonian Steady Streaming Flow with Nathan Willis: steady streaming refers to the time independent portion of the secondary flow measured around a cylinder in an oscillatory flow.
- Fluid Flushing with Surface Tension with Chee Han Tan and Braxton Osting: sloshing refers to the free surface motion of a fluid in a container.
- Ice Fishing Problem with Nathan Willis, Chee Han Tan, and Braxton Osting: the ice fishing problem refers to the frequency of oscillation of a liquid in a circular hole.
- Fluid Coupling in Motility Assays with Tamar Shinar (UC Riverside) and Steve Cook (UC Riverside): motility assays are suspensions of molecular motors, and tracks suspended in viscous fluid.
- Fractal Dimension of Melt Ponds with Ken Golden, Back Ali, and Kyle Steffen: melt ponds are melted water on top of ice which exhibit a fractal dimension.
- Stability of Active Suspensions with Michael Shelley (Flatiron Institute/NYU): active suspensions are populations of micro swimmer that exhibit instabilities due to their motility and coupling to the fluid
- Hydrodynamic Coupling in Viscoelastic Fluids with Greg Forest (UNC): chemically coated particles create a depletion layers that can be used to estimate viscoelastic properties.
- Particle Velocimetry and Wall Slip with Peter Mucha (Dartmouth University) and Miami Yoda (Georgia Tech): uncertainties in measurements leads to apparent wall slip.
Funding
- with Benjamin Sanchez and Braxton Osting (2023-2026), NSF-CBET
- RTG: Optimization and Inversion for the 21st Century Workforce with Ken Golden, Akil Narayan, Elena Cherkaev, and Fernando Guevara-Vasquez (2022-2027), NSF-DMS 2136198
- University of Utah SEED Funding: with Braxton Ostend (2022-2023)
- Collaborative Research: Diffusion of foreign particles in complex fluids with Scott McKinley (2014-2018), NSF-DMS 14112998
- Collaborative Grants for Mathematicians, Simons Foundation (2014), 317887
Collaborators
- Scott McKinley, Department of Mathematics, Tulane University
- Braxton Osting, Department of Mathematics, University of Utah
- Benjamin Sanchez, Department of Electrical and Computer Engineering, University of Utah