Resistive Force theory & swimming of biflagellated green algae
Friday 7th November, 2008 14:30-15:30 Mathematics Building, room 516
Green Algae plays an important role in the development of the Earth's atmosphere by photosynthesizing and acting as a sink for carbon dioxide. They are estimated to make up more than half of the Earth's biomass and acts as a potential source for Hydrogen gas production. They can be the most efficient source of feedstock for Biofuel or Biodiesel industry. The green biflagellated algae Chlamydomonas nivalis has a prolate spheroidal body and has two long, thin flagella attached at one end which are propelled to cause the swimming of the organism. The length of the cell body and flagella is approx. same as 10 micro meter and the flagella beat at approx. 50 hertz. C. nivalis is usually considered to swim in a human breast-stroke manner with an effective-recovery style, approximately in the direction of its axis of symmetry. However, the latest research proved that this is not exactly the accurate swimming stroke. The approximation known as Resistive Force Theory (RFT) was established by Gray & Hancock (1953) and states that the normal and tangential components of force and torque on an element of a flagellum is directly proportional to the normal and tangential components of the fluid velocity relative to that element. RFT was used by Jones et al. (1994) to model the swimming of a single cell of C. nivalis in a viscous flow of low Reynolds number. Analytical and numerical techniques were used to calculate the magnitude and direction of the cell's swimming velocity and angular velocity. The aim of our work is to extend the Jones et al. model to calculate the the cell's swimming velocity and angular velocity in the vicinity of a stationary no-slip boundary or sphere using appropriate image system techniques. Finally, we will model interactions of two algae cells using RFT and image systems and calculate the magnitude and direction of both cell's swimming velocity and angular velocity.