Advected bioconvection and the hydrodynamics of bounded biflagellate locomotion

The recent developments in using micro-organisms effectively for biofuels is the main motivation to carry out this research work. In this thesis, we have investigated two main aspects related micro-organisms: swimming behavior and bioconvection pattern formation. In the first aspect, we have discussed the swimming of a biflagellated green algae named as Chlamydomonas augustae in a Stokes flow in the absence and presence of the no-slip stationary plane boundary. For a micro-organism with similarly sized spherical cell body and flagella we have used Resistive Force Theory (RFT) for modelling the idealized flagellar beat pattern. The unbounded swimming analysis was used to calculate the organism's swimming velocity and angular velocity by balancing the forces and torques acting on the organism at every instant, and is a revision and improvement of the work carried out by Jones et al. The model was developed in general terms for uniplanar locomotion of the micro-organism. To facilitate analytical calculation a code in the software Maple was developed, which produced results consistent with the results in Jones et al. as discussed in chapter 2. The model predicts a realistic swimming speed and showed that viscous torque acting on the flagellum has significant contribution to the angular velocity of the organism. The trajectories of swimming for one beat and for multiple beats were also plotted. In chapter 3 we have extended the same swimming model for the case of the presence of a no-slip stationary plane boundary. In order to satisfy conditions at the no-slip plane boundary we have incorporated the image system singularities solution. Again using RFT and the software Maple, we have calculated the micro-organism's swimming velocity and angular velocity for the different geometries such as swimming away/towards, angled and parallel to the no-slip stationary plane boundary. The results were further compared with the unbounded swimming case and found that the micro-organism's swimming velocity regressed close to the boundary and approaches the unbounded values, whereas angular velocity approaches to zero, as it swims far from the plane boundary. For nutrient uptake and to optimize light for photosynthesis these micro-organisms swim in directions biased by environmental cues, termed taxes. These taxes inevitably lead to accumulations of micro-organisms that induce hydrodynamic instabilities due to their density difference. The large scale fluid flow and intricate patterns formed are called bioconvection. In chapter 4, we have for the first time, experimentally investigated pattern formation in thin, long, horizontal tubes with and without imposed flow. With no flow, the dependence of the dominant pattern wavelength at pattern onset on cell concentration is established for the three different tubes of variable diameter. The vertical plumes of micro-organisms are observed merely to bow in the direction of flow for the case of weak imposed flow. However, for sufficiently large flow rates, the plumes progressively fragment into piecewise linear diagonal plumes, inclined at constant angle and translating at fixed speeds. The pattern wavelength generally grows with flow rate, with transitions at critical rates that depend on concentration. The bioconvection is not wholly suppressed and perturbs the flow field, even at large imposed flow rates. The contents of this chapter have already been published in Physical Biology international journal with co authors Dr Ottavio A Croze and Dr Martin A Bees. In chapter 5, we have attempted for the first time to theoretically examine bioconvection in horizontal tubes in the presence of imposed flow to compare and verify the results of the experimental investigations discussed in chapter 4. To avoid the cumbersome calculation, we modelled the situation by considering the suspension flow between two plates instead of tube. The aim is to predict a particular most unstable mode from equilibrium solution and average inclination, speed of the plumes and flow transitions observed. The investigation is still not finished as modelling of the problem is complete but numerical analysis for the solution of the problem need to be done at this stage

New Solutions of Stokes Problem for an Oscillating plate using Laplace Transform

An exact solution of the flow of a Newtonian fluid on a porous plate is obtained when the plate at y = 0 is oscillating with the amplitude \u3b2 and oscillating frequency \u3c9 with the assumption that the plate initially is at rest and that the velocity approaches zero as we go far from the boundary region. The fluid flow problem is solved with the help of Laplace transform technique. Here we discuss two cases: first case corresponds the oscillating porous plate with superimposed suction or blowing and second deals with an increasing or decreasing velocity amplitude of the oscillating flat plate. @JASE