Daniel Tam

Marangoni convection in droplets on superhydrophobic surfaces

We consider a small droplet of water sitting on top of a heated superhydrophobic surface. A toroidal convection pattern develops in which fluid is observed to rise along the surface of the spherical droplet and to accelerate downwards in the interior towards the liquid/solid contact point. The internal dynamics arise due to the presence of a vertical temperature gradient; this leads to a gradient in surface tension which in turn drives fluid away from the contact point along the interface. We develop a solution to this thermocapillary-driven Marangoni flow analytically in terms of streamfunctions. Quantitative comparisons between analytical and experimental results, as well as effective heat transfer coefficients, are presented.

Optimal feeding and swimming gaits of biflagellated organisms

Locomotion is widely observed in life at micrometric scales and is exhibited by many eukaryotic unicellular organisms. Motility of such organisms can be achieved through periodic deformations of a tail-like projection called the eukaryotic flagellum. Although the mechanism allowing the flagellum to deform is largely understood, questions related to the functional significance of the observed beating patterns remain unresolved. Here, we focus our attention on the stroke patterns of biflagellated phytoplanktons resembling the green alga Chlamydomonas. Such organisms have been widely observed to beat their flagella in two different ways—a breaststroke and an undulatory stroke—both of which are prototypical of general beating patterns observed in eukaryotes. We develop a general optimization procedure to determine the existence of optimal swimming gaits and investigate their functional significance with respect to locomotion and nutrient uptake. Both the undulatory and the breaststroke represent local optima for efficient swimming. With respect to the generation of feeding currents, we found the breaststroke to be optimal and to enhance nutrient uptake significantly, particularly when the organism is immersed in a gradient of nutrients.

AN EXTENSION OF THE GHOST FLUID METHOD FOR COUPLING FLUIDS WITH THIN, OPEN STRUCTURES

We propose a two dimensional extension of the ghost fluid method that enables the modeling of the dynamic interactions between a compressible flow and a thin flexible rod structure immersed in the flow. The modeling approach combines an Eulerian finite volume formulation for the fluid and a Lagrangian formulation for the finitedeformation dynamic response of the 2D rod structure. The coupling between the fluid and the solid response is achieved via an approach based on extrapolation and velocity reconstruction. As opposed to previously presented work, the proposed algorithm is not based on the existence of an exterior to the fluid domain and, thus, enables the consideration of very thin open boundaries and structures where the flow may be relevant on both sides of the interface. We demonstrate the ability of the method to properly describe disparate flow conditions across a thin fixed interface without cross pollution of the flow field. We also apply the coupling approach to the transient supersonic flow past a transverse, highly flexible rod.