Parasite ova caused to accumulate in a single microscopic field simplifies monitoring soil-transmitted helminthiasis by optical microscopy. Here we demonstrate new egg-accumulating geometries based on annular menisci formed on the surface of a wetted cone. Fluidic features extracted from profile images of the system provided mathematical representations of the meniscus gradient that were compared quantitatively to numerical solutions of an axisymmetric Young-Laplace equation. Our results show that the governing dynamics of these systems is dominated by the surface tension of the fluid. These image analysis and mathematical tools provide simple quantitative methods for system analysis and optimization.

Differential geometry is concerned with the calculus of smooth surfaces. The field rose to prominence through its incredible power to describe Einstein’s Theory of General Relativity, in which spacetime is considered to be a smooth four-dimensional manifold. More recently, differential geometry has been used to describe stress and strain for elastic bodies, in digital signals processing and in probability theory. Smooth surfaces appear in a variety of natural systems. This research focusses on the salvinia leaf, a floating fern whose skin has the unusual property that, when immersed in water, a stable, persistent air layer is retained on the surface of the leaf. This air-water interface is made possible by the phenomenon of surface tension and a forest-like structure on the surface of the leaf, which forms a ‘tent’ of air. This interface is a smooth surface that can be investigated using differential geometry, and has the particular property that it’s mean curvature is constant. The equation of capillary pressure, developed in the early nineteenth century by Thomas Young and Pierre-Simon Laplace, governs the system. However, the traditional formulation of the problem can be extremely difficult to solve. The project involved reformulating the Young-Laplace equation, a second-order nonlinear partial differential equation, in a coordinate independent fashion using differential geometry. Finite element analysis was then used to obtain numerical solutions for specific domain geometries. The ability to find domain geometries which form surfaces with specified properties will aid the design of effective bionic devices.