Research
My research interests lie in applied mathematics, fluid dynamics, and mathematical modeling, with applications to microfluidics, biological fluid mechanics, and deformable cells. My work combines asymptotic analysis, computational modeling, and scientific computing to study complex fluid-structure interactions and transport phenomena. I am also interested in interdisciplinary applications of mathematics and undergraduate research mentorship.
Research Areas
Inertial migration in microfluidic devices
To understand the flow in inertial microfluidic devices, I developed a hybrid numerical and asymptotic model for the inertial migration of a sphere in a rectangular channel. The resulting model showed strong agreement with experimental observations. And I used it to develop a model of pairwise dynamics in microfluidic crystals.
Flow past hairy surfaces
To understand how marine crustaceans use their hairy appendages for sensing and feeding, I modeled the flow past hairy surfaces.
Modeling deformable cells in microfluidic devices
To understand how mammalian cells deform in microfluidic devices, I am working on developing a reduced order model to represent the family of constant-volume shapes the cell could take. Current work uses spherical harmonics to represent families of constant-volume cell shapes.
Brijesh Patel applied edge detection techniques to determine the edges of cells from experimental and numerical data.
Open Source Research Code:
Matlab code for the inertial lift force on a particle in rectangular channels with aspect ratios AR = 1, 2, 4, 8, and 9 available on GitHub.
Mathematica code for computing Lamb's solution external to a sphere also available on GitHub.
HoodFlowLab on GitHub for most recent code on modeling deformable cells using spherical harmonics.
Undergraduate Research Opportunities
If you are interested in getting involved in undergraduate research in math, check out the following resources:
Due to current advising commitments, I am not currently taking additional undergraduate research students.
Past Undergraduate Mentoring
I have mentored undergraduate students in applied mathematics and computational modeling projects involving fluid mechanics, scientific computing, and deformable cell dynamics.
Brijesh Patel (2025)
- Project: Modeling Deformable Cells Using Spherical Harmonics
- SURF student summer 2025
- Poster presented at: Purdue Summer Undergraduate Research Symposium 2025
- Poster link
- Link to code on GitHub
- Current Position: Ph.D. student in Mathematics at UCLA
Alex Kelley (2023-2024)
- Project: Modeling Deformable Cells Using Spherical Harmonics
- Undergraduate Researcher
- Poster presented at: Purdue Spring Undergraduate Research Conference (2025), Fall Undergraduate Research Expo (2024), and SIAM Great Lakes Section Annual Meeting (2024)
- Poster link
- Current Postion: Software Engineer at Epic Systems
Olivia Chang (2023, 2024)
- Project: Modeling a Deformable Ellipse in Shear flow using IB2d