Catherine Kamal

Slender bodies in viscous media

From the sorting of fibres particles in the paper industry, the dispersion of sheet-like graphene particles in specialised inks, to the locomotion of flagella or slender cells in biological fluids, predicting the motion of slender bodies in viscous media is crucial in various fields, including colloidal science and microbiology.  In this talk, we present three distinct examples of how slender bodies can be modelled within viscous media. We start with the classic example of a settling rod, demonstrating how environmental patchiness—such as a heterogeneous viscosity field—affects the rod's settling motion. To determine the leading effects of a viscosity gradient, we derive a new version of Resistive Force Theory (RFT) tailored for slender bodies in a spatial viscosity gradient field. This new RFT enables us to predict the orientation and drift of the settling rod under varying viscosity conditions. In our second example, we apply our RFT to theoretically compute the effect of viscosity gradients on the locomotion of an actively waving filament. Crucially, we find that the viscosity gradient introduces an additional time-averaged angular rotation, influencing waving locomotion. Over time, this angular rotation allows actively waving filaments to control their orientation and direction as they navigate through the medium, providing a physical mechanism for waving swimmers to navigate effectively through viscous media. Finally, in our third example, we show how slender body theory can be adapted to model two-dimensional ultra-thin sheets (2D SBT). We show how 2D SBT can offer valuable insights into the complex interactions of sheet-like 2D materials, such as graphene, in a viscous shear. Understanding these interactions has direct implications for advancing graphene production in the 2D nanomaterial industry.