טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentAvshalom Manela
SubjectDispersion in Shear Flows of Dilute Suspensions of Dipolar
Particles
DepartmentDepartment of Aerospace Engineering
Supervisors Full Professor Frankel Itzchak
Full Professor Almog Yaniv


Abstract

        We calculate the effective phenomenological coefficients characterizing the transport of swimming gyrotactic micro-organisms suspended in a homogeneous (simple) shear flow. The micro-organisms are modelled as rigid axisymmetric particles possessing a permanent embedded dipole. It is further assumed that the swimming speed is uniform. The stochastic elements in the rotary motion of the micro-organisms are represented by an effective Brownian diffusivity whose value is, however, much larger than that corresponding molecular diffusivity (cf. Pedley & Kessler 1990).

        The requisite phenomenological coefficients, i.e. the average swimming velocity and Taylor dispersivity, are obtained via application of the generalized Taylor dispersion scheme (cf. Brenner 1980, Frankel & Brenner 1991). The effects of such factors as magnitude and direction of external field, shear rate and particle shapes are thereby studied. The results indicate

that, for sufficiently large shear rates, dispersivity is not monotonically decreasing with external-field intensity, a trend which seems rather counter-intuitive. An exceptional mode of  variation of the dispersivity with the shear rate (which is unique to non-spherical particles) appears at a certain interval of external-field orientations. This behaviour is related to the ‘intermediate domain’ in the corresponding deterministic problem (i.e. in the absence of Brownian rotations) where particle rotary motion is affected by the coexistence of multiple stable attractors (cf. Almog & Frankel 1995).