Location of Repository

The dynamics of semi-flexible fibres in shear flow and the effect of flexibility on the\ud swimming speed of helical flagella are investigated. High aspect ratio particles such as\ud carbon and glass fibres are often added as fillers to processed polymers. Although these\ud materials have high rigidity, the large aspect ratiomakes the fibres liable to bending during\ud flow. Other high aspect ratio fibres that behave as semi-flexible fibres include carbon\ud nano-tubes, paper fibres and semi-flexible polymers such as the muscle protein f-actin.\ud Most theoretical studies assume that fibres are either rigid or completely flexible, but in\ud this thesis fibres with a finite bending modulus are considered.\ud \ud A semi-flexible fibre is modelled as a chain of shorter rods linked together. A bending\ud torque is included at the joints between the rods to account for the rigidity. In shear flow\ud the simulation reproduces the C and S turns observed in experiments on semi-flexible\ud fibres. The results for finite aspect ratio fibres predict changes to the period of rotation\ud and drift between Jeffery orbits. The direction of drift for a flexible fibre depends on both\ud the intial orientation and the fibre’s flexiblity.\ud \ud We also present a linear analysis of how small distortions to a straight semi-flexible fibre\ud grow when the flow places the fibre under compression. These results are in agreement\ud with our full simulations and the growth rates of the distortions to a straight fibre allow us\ud to predict the most unstable mode at a particular flow rate.\ud \ud To allow for intrinsically bent or helical equilibrium shapes a second simulation method\ud is developed that includes a twisting torque at the joints between the rods as well as a\ud bending torque. Using this simulation we measure the period of rotation and orbit drift of\ud permanently deformed fibres in shear flow and show that due to the asymmetry of a helix,\ud shear induced rotation results in translation and orbit drift for both rigid and semi-flexible\ud fibres.\ud \ud Bacteria such as Vibrio alginolyticus and Escherichia coli swim by rotating one or more helical flagella. Vibrio alginolyticus has only one flagella and changes direction by\ud altering its sense of rotation. Experimental observations of Vibrio alginolyticus have\ud found that backwards swimming is 50% faster than forwards swimming speed however,\ud previous numerical simulation results have shown only a 4% difference for flagella of the\ud same dimensions. We use our simulation to consider how flexiblity affects the swimming\ud speed of helical flagella and show that for a constant angular velocity, difference between\ud forwards and backwards swimming speed ranges between 0-23%depending on the exact\ud stiffness chosen. We explain the differences in swimming speeds of semi-flexible fibres\ud by investigating the shape changes which occur and comparing them to the results for\ud swimming speeds of rigid flagella of varying dimensions

Publisher: Applied Mathematics (Leeds)

Year: 2007

OAI identifier:
oai:etheses.whiterose.ac.uk:53

Provided by:
White Rose E-theses Online

Downloaded from
http://etheses.whiterose.ac.uk/53/1/SamFinalThesis.pdf

- (1987). A boundary-element analysis of ﬂagellar propulsion.
- (1979). A hydrodynamic analysis of ﬂagellar propulsion.
- (1971). A note on the helical movement of micro-organisms.
- (2003). Analysis of small deformation of helical ﬂagellum of swimming Vibrio alginolyticus.
- (1951). Analysis of the swimming of microscopic organisms.
- (1970). Axial and transverse Stokes ﬂow past slender axisymmetric bodies.
- (1992). Boundary integral and singularity methods for linearised viscous ﬂow.
- (2001). Difference between forward and backward swimming speeds of the single-polar-ﬂagellated bacterium.
- Dynamic simulation of ﬂexible ﬁbers composed of linked rigid bodies.
- (1922). Ellipsoidal paricles immersed in a viscous ﬂuid.
- (2001). Instability of elastic ﬁlaments in shear ﬂow yields ﬁrst-normal-stress differences.
- (1992). Laminar ﬂow and convective transport processes.
- (1977). Life at low Reynolds number.
- (2001). Mechanics of motor proteins and the cytoskeleton. Sinauer Associates,
- (2005). Microscopic artiﬁcial swimmers.
- (2000). Numerical analyis of bacterium motion based on the slender body theory.
- (2003). Numerical analysis of small deformation of ﬂexible helical ﬂagellum of swimming bacteria.
- (1992). Numerical recipes in Fortran: The art of scientiﬁc computing.
- (2007). of Art Design. “Computer Animation QCA 7008, Basic Modelling”,
- (1938). On the motion of small particles of elongated form suspended in a viscous liquid. Second report on viscosity and plasticity,
- (1959). Orbits of ﬂexible threadlike particles. J.Colloid Sci.,
- (1951). Particle motions in sheared suspensions.
- (2006). Propulsion with a rotating elastic nanorod.
- (2002). Real-time imaging of ﬂuorescent ﬂagellar ﬁlaments of Rhizobium lupini H13-3: Flagellar rotation and pH-induced polymorphic transitions.
- (1999). Self-organised beating and swimming of internally driven ﬁlaments.
- (1997). Simulation of single ﬁber dynamics.
- (2000). Simulations of ﬁber ﬂocculation: Effects of ﬁber properties and interﬁber friction. J.Rheol.,
- (1970). Slender-body theory for particles of arbitrary cross-section in Stokes ﬂow.
- (1959). Spin and Deformation of Threadlike Particles.
- (1970). Stress system in a suspension of force-free particles.
- (1952). The action of waving cylindrical tails in propelling microscopic organisms.
- (1976). The distortion of a ﬂexible inextensible thread in a shearing ﬂow.
- (1979). The hydrodynamics of ﬂagellar propulsion: helical waves.
- (1948). The Intrinsic Viscosities and Diffusion Constants of Flexible Macromolecules in Solution.
- The motion of long slender bodies in a vicous ﬂuid. Part 1. General theory.
- (1962). The motion of rigid particles in a shear ﬂow at low Reynolds number.
- (1955). The propulsion of sea-urchin spermatozoa.
- (1953). The self propulsion of microscopic organisms through liquid.
- (2001). Writhing geometry at ﬁnite temperature: Random walks and geometric phases for stiff polymers.

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.