RESEARCH

My research centers 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.

Research Projects

Current

Swimmers in Stokes flow

with Holly Vanlooy (g) and Fernando Guevara VasquezLong range hydrodynamics forces between suspended microswimmers and fluid are transmitted instantaneously.

Keywords: Fluid dynamics, Boundary integrals, Singularity solutions, Simulations, Structure interactions.

Elastic model of pulsatile blood flow in branched arteries

with Filip Belik (g), Tyler Schuessler (g), Henry Crandall (g), Victoria Kala (postdoc), Braxton Osting and Benjamin Sanchez (UCI)The elasticity of the arterial wall and the oscillatory nature of blood pressure drive blood flow through a small branched arterial trees with outflow boundary conditions.

Keywords: Fluid dynamics, Coupling with elastic wall structure, Simulation, Dimensional analysis, Fourier series, Bessel functions.

Thermal fluctuations, microrheology, active suspensions in complex flows

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. Complex fluid exhibits both elastic (storage) and viscous (loss) response to an applied force.

Keywords: Fluid dynamics, Stochastic calculus, Fluctuations, Suspensions

Completed

Newtonian steady streaming flow

with Nathan Willis (g)

Steady streaming refers to the time independent portion of the secondary flow measured around a cylinder in an oscillatory flow.

Fluid sloshing with surface tension

with Chee Han Tan (g) and Braxton OstingSloshing refers to the free surface motion of a fluid in a container.

Ice fishing problem

with Nathan Willis (g), Chee Han Tan (g), and Braxton Osting

The ice fishing problem refers to maximizing/minimizing the frequency of oscillation of a liquid over a circular hole.

Fluid coupling in motiliy assays

with Steve cook (g, UC Riverside) and Tamar Shinar (UC Riverside)

Motility assays are suspensions of molecular motors and tracks suspended in a viscous fluid.

Fractal dimension of melt ponds

with Kyle Steffen (g), Bacim Alali, and Ken Golden

Melt ponds are melted water on top of ice which exhibit a fractal dimension.

Stability of active suspensions

with Mike 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 (Michigan State University)

Uncertainties in measurements leads to apparent wall slip.

Funding

Current

NSF-CBET, 2023-2026: Engineering Models to Link Blood Pressure and Bioimpedance with Benjamin Sanchez (University of Illinois at Chicago) and Braxton Osting
NSF-DMS-RTG, 2022-2027: Optimization and Inversion for the 21st Century Workforce with Ken Golden, Akil Narayan, Elena Cherkaev, and Fernando Guevara-Vasquez

Past

University of Utah SEED Funding, 2022-2023: with Braxton Ostend (2022-2023)
NSF-DMS, 2014-2018: Collaborative Research: Diffusion of foreign particles in complex fluids with Scott McKinley (Tulane University)
Simons Foundation, 2014: Collaborative Grants for Mathematicians

Collaborators

Fernando Guevara-Vasquez, Department of Mathematics, University of Utah
Victoria Kala (postdoc), Department of Mathematics, University of Utah
Scott McKinley, Department of Mathematics, Tulane University
Braxton Osting, Department of Mathematics, University of Utah
Benjamin Sanchez, Electrical and Biomechanical Engineering, University of Illinois at Chicago

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