Research topics

  • Microorganism locomotion and cellular mechanics
  • Suspensions of interacting and active particles
  • Mechanics of soft materials and complex fluids
  • Low Reynolds number hydrodynamics
  • Numerical methods and computational mathematics

Research description
Broadly speaking, my research interests lie in the development and usage of computational techniques to study the dynamics of microscopic objects in fluid. These objects can interact with each other through a variety of interparticle forces allowing them to self-assemble to form structures, they can be sufficiently small that they move stochastically through the fluid due to thermal fluctuations, they can be deformable, allowing for shape changes in reponse to applied forces, or they can have an interesting shape that allows them to move through the surrounding fluid in peculiar ways. I have particular interest when these objects are biological, especially swimming cells and microorganisms that can generate fluid flows as they move through their surrounding environment.

The computational techniques I develop address the problem of simulating the dynamics of these objects both at the individual level using highly resolved schemes, as well as at the large-scale (up to hundreds of thousands in some cases) to study how their coupled motion may lead to collective dynamics.

Possible PhD projects

  • Interacting particles in viscoelastic fluids: Many biological fluids, as well as those arising in industrial processes, are viscoelastic due to the presence of polymers suspended in the liquid. The project will entail developing techiques for large-scale simulation that resolve the motion and interactions of either rigid or deformable bodies suspended in these fluids. The project will require a background in fluid mechanics and transport processes, as well as in numerical methods for PDEs. Strong programming skills are also highly desirable.
  • Exact resolution of near-contact hydrodynamics in suspension simulations: Hydrodynamics interactions between particles become challenging to resolve when the particles come close to contact. This project will entail developing methods to resolve these near-contact interactions whilst retaining scalability in the computation. A strong background in fluid mechanics, especially at low Reynolds number, asymptotic methods, and numerical methods, particularly those for solving linear systems, are required. Strong programming skills are also highly desirable.
  • Dynamics and interactions of shape-changing particles: While many tiny objects, such as microorganisms, change their shape with time, the models we use to understand their interactions are based on rigid particles. This project entails developing models for their interactions that account for the shape change and the timescale over which they occur. The project requires a background in fluid mechanics, especially at low Reynolds number, asymptotic methods, and a background in numerical methods for PDEs.
  • Stochastic simulation of Brownian particles: Including the effects of Brownian motion in suspension simulations has traditionally been a computationally intensive endeavour. Only recently in the past 5-10 years have Brownian computations have been accelerated by using ideas from fluctuating hydrodynamics. The project builds on this work and aims at extending these ideas to new scenarios and problems in this burgeoning research area. This project requires a background in fluid mechanics and/or statistical mechanics, applied stochastic processes, and numerical methods for ODEs and SDEs.