Citation
Chwang, Allen TseYung (1971) Helical movements of flagellated propelling microorganisms. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd03262007141206
Abstract
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The helical motion of an infinitely long flagellum with a crosssectional radius b, along which a helical wave of amplitude h, wavelength [lambda] and phase velocity c is propagated, has been analyzed by using Stokes' equations in a helical coordinate system (r,[xi],x). In order to satisfy all the boundary conditions, namely the noslip condition on the flagellum surface and zero perturbation velocity at infinity, the flagellum must propel itself with a propulsion velocity U in the opposite direction to the phase velocity c. For small values of kb (where k = 2[pi]/[lambda] is the wave number), by a singleharmonic approximation for the outer region (r > h), the ratio of the propulsion velocity U to the phase velocity c is found to be[...], where K[n](kh) is the modified Bessel function of the second kind.
A modified and improved version of the Gray and Hancock method has been developed and applied to evaluate helical movements of a freely swimming microorganism with a spherical head of radius a and a tail of finite length and crosssectional radius b. The propulsion velocity U and the induced angular velocity [omega] of the organism are derived. In order that this type of motion can be realized, it is necessary for the head of the organism to exceed a certain critical size, and some amount of body rotation is inevitable. For fixed kb and kh, an optimum headtail ratio a/b, at which the propulsion velocity U reaches a maximum, has been discovered. The power required for propulsion by means of helical waves is determined, based on which a hydromechanical efficiency [eta] is defined. This [eta] reaches a maximum at kh [...] 0.9 for microorganisms with optimum headtail ratios. In the neighborhood of kh = 0.9, the optimum headtail ratio varies in the range 15 < a/b < 40, the propulsion velocity in 0.08 < U/c < 0.2, and the efficiency in 0.14 < [eta] < 0.24, as kb varies over 0.03 < kb < 0.2.
The modified version of the Gray and Hancock method has also been utilized to describe the locomotion of spirochetes. It is found that although a spirochete has no head to resist the induced viscous torque, it can still propel by means of helical waves provided that the spirochete spins with an induced angular velocity [omega]. Thus the 'Spirochete paradox' is resolved. In order to achieve a maximum propulsion velocity, it is discovered that a spirochete should keep its amplitudewavelength ratio h/[lambda] around 1:6 (or kh [...] 1). At kh = 1, the propulsion velocity varies in the range 0 < U/c < 0.2, and the induced angular velocity in 0.4 < [omega]/[lowcase omega] < 1 (where [lowcase omega] = kc is the circular frequency of the helical wave), as the radiusamplitude ratio varies over 0 < b/h < 1.
A series of experiments have been carried out to determine by simulation the relative importance of the socalled 'neighboring' effect and 'end' effect, and results for the case of uniform helical waves are presented
Item Type:  Thesis (Dissertation (Ph.D.)) 

Degree Grantor:  California Institute of Technology 
Division:  Engineering and Applied Science 
Major Option:  Mechanical Engineering 
Thesis Availability:  Public (worldwide access) 
Research Advisor(s): 

Thesis Committee: 

Defense Date:  25 March 1971 
Record Number:  CaltechETD:etd03262007141206 
Persistent URL:  http://resolver.caltech.edu/CaltechETD:etd03262007141206 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  1148 
Collection:  CaltechTHESIS 
Deposited By:  Imported from ETDdb 
Deposited On:  27 Mar 2007 
Last Modified:  26 Dec 2012 02:35 
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