Research
My research focuses on analytical and computational modeling of problems in the dynamics of Newtonian and nonNewtonian fluids and their interaction with suspended microstructures, interfaces and boundaries.Current research projects
Thermal fluctuations and microrheology in a viscoelastic fluid
with Scott A. McKinley (Tulane), Adam R. Lee (undergraduate), D. Michael Senter (past undergraduate), Ryan Durr (past undergraduate)
Rheology is the study of the flow and deformation of soft matter, especially in response to applied forces. Many complex fluids (blood, mucus, silly putty, cake batter) have prominent viscoelastic properties. As a consequence, immersed particles exhibit subdiffusive behavior, which is to say, the variance of the particle displacement grows sublinearly with time. We study the inverse problem of relating the statistics of individual particle paths to bulk fluid properties. We are also interested in developing a viscoelastic generalization of the Landauâ€“Lifschitz Navierâ€“Stokes fluid model and tractable numerical simulations.Fluid sloshing with surface tension
with Braxton Osting, Chee Han Tan (graduate), Max Carlson (undergraduate)
Sloshing refers to the free surface motion of a fluid in a container. We study the linearized sloshing problem of an incompressible, inviscid, irrotational fluid, where we focus on the regime where the effect of surface tension dominates the effect of gravity. This is especially important in a microgravity environment, where scientists and engineers have worked to improve our understanding of the behavior of a liquid propellant within a rocket. We are interested in studying the properties of sloshing frequencies and the corresponding modes both analytically and numerically.
Biological microbots
with Rebecca Terry (graduate)
Microbots are small particles that can be controlled via an electric and/or magnetic field. They represent a controlled model system for complex biological species, where diversity is easy to achieve. We are interested in developing a continuum model to describe separation among two or more species and in studying the possible phase transitions in the resulting dynamical system.
Flow past axisymmetric biconcave shapes
with Alex Henabray (undergraduate, Honor's thesis)
Stokes flow past a sphere is a wellstudied and solved problem. We apply a recently proposed method using coordinate transforms and decomposition into Gegenbauer polynomials to numerically find the flow past axisymmetric biconcave shapes. We are interested in computing the drag and comparing with methods using singularity solutions.Completed research projects

Fluid coupling in active cytoskeletal network and motility assays:
with Tamar Shinar (UC Riverside) and Steve Cook (UC Riverside, graduate)
We studied steric and hydrodynamics effects in a continuum model coupling the dynamics of microtubule filaments, molecular motors and fluid flow, which we derived from first principles. We performed numerical simulations of our model and reproduce experimentally observed behaviors like clump formation, breakup and motion. 
Hydrodynamic response of elongated partices near a wall
with Kyle Steffen (graduate)
We studied the behavior of a few elongated particles interacting together near a wall by applying an asymptotic expansion to the nonlocal slender body theory equation to include wall effects. We applied the expansion to the sedimentation of particles near a wall. 
Fractal dimensions of melt ponds
with Ken Golden, Bacim Allali (postdoc) and Kyle Steffen (undergraduate)
We studied a large set of images from melt ponds in the Antartic, which we processed in Matlab, and extracted the fractal exponent between the perimeter and the area of melt ponds. 
Stability of active suspensions
with Mike Shelley (Courant)
We studied the linear stability of a system of active swimmers described by a continuum model and established the dependence of the onset of the instability with the domain size and a physical parameter describing the swimming mode. 
Hydrodynamic coupling in viscoelastic fluids
with Greg Forest (UNC)
We studied how the depletion layer surrounding a particle in a viscoelastic fluid can be best estimated using crosscorrelation information from multiple particles paths. 
Particle velocimetry and wall slip
with Peter Mucha (UNC) and Minami Yoda (Georgia Tech)
We studies a simple PDE model with noise to describe how to correct for apparent wall slip near a wall due to uncertainties in measurements.
Collaborators
 Braxton Osting, Department of Mathematics, University of Utah
 Scott A. McKinley, Department of Mathematics, Tulane University
 Tamar Shinar, Department of Computer Sciences, University of California Riverside