Modelling of Active Particles Near a Planar Wall

In most biological and synthetic settings involving chemically or mechanically active particles in a fluid, interactions with nearby walls and other obstacles are important. We discuss two such systems. In the first, we study the common mathematical model swimmer known as a squirmer under the effects of gravity and confinement by horizontal no-slip wall below the squirmer. We use a boundary integral method to numerically solve the equations of Stokes flow around the squirmer and systematically characterize the effects of the first two polar squirming modes, showing that multiple equilibrium configurations and oscillating states are possible. In the second study, we model photocatalytically active hematite particles that exhibit behaviors in experiments ranging from sticking to the glass surface to rising up when illuminated from below. By accounting for short-ranged wall interactions, rates of reaction, diffusiophoresis, and the effects of pH, our model shows qualitative agreement with experiments over a range of conditions.

Henry Shum is an Associate Professor in the Department of Applied Mathematics at the University of Waterloo. He studied Mathematics and Physics as an undergraduate at the University of Warwick, completed his doctoral degree in Mathematical Sciences at the University of Oxford, and gained postdoctoral experience at the University of Oxford (Department of Physics) and the University of Pittsburgh (Department of Chemical & Petroleum Engineering). His research interests are in modelling the locomotion of microorganisms with an emphasis on fluid mechanics and fluid-structure interactions. More generally, he is interested in modeling chemical and physical processes that govern biological functions and applying these principles in bio-inspired robotic systems.