Ph.D Student | Marc Van Dyke |
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Subject | Transport and Dispersion of a Flexible Macromolecule under Gravity and in a Homogeneous, Unbounded Shear Flow |

Department | Department of Mechanical Engineering |

Supervisor | Professor Emeritus Haber Shimon |

Generalized Taylor dispersion theory is utilized in order to calculate the translational mobility and dispersivity tensors of a Brownian flexible chain particle under the influence of an external force or flow field whose net effect is to simultaneously realign and deform the particle. Numerical results are computed for two specific problems, the first of which is an inhomogeneously dense flexible polymer sedimenting in a quiescent fluid, where this particle is modeled as a non-neutrally buoyant inhomogneously weighted tethered dumbbell. It is shown that this density inhomogeneity

causes a novel coupling effect between the ‘shape-fluctuation’ and ‘size-fluctuation’ dispersion mechanisms. This coupling effect also plays a central role in the second problem, a flexible chain particle (modeled as a symmetric tethered dumbbell) in a linear shear flow.

In both problems, it is shown that when the ratio of tether length to constitutive sphere radius (l) is greater than 3,

the ‘size-fluctuations’ terms are of at least the same order of magnitude as the ‘shape-fluctuation’ terms. Therefore, in this limit, the oft-invoked ‘preaveraging’ approximation fails.

In general there is no closed form expression for the low Reynolds number hydrodynamic interactions between the constitutive spheres and the ambient fluid, and thus solutions for the mobility and dispersion coefficients were computed by using numerical approximations. Nevertheless, it was shown that for very long tether lengths (l>7) that one may neglect higher order hydrodynamic interactions between the constitutive spheres, and in this limit a fully analytical solution was presented. For intermediate values of l, the full numerical solution must be used.