Interdisciplinary Applied Mathematics

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12n^akBT dt

where dt is    the    time    step    in    the    numerical    integration    of the    Lagrangian

tracking of the particles and £ is a random vector following a Gaussian distribution.

In addition to the factors already noted, beads and chains of particles in a microchannel will involve the hydrodynamic effects of the channel walls on the resistance or mobility tensors together with the hydrodynamic interaction of spherical beads with nonspherical chains. Magnetic beads that have formed a bound pair will be subject to both random displacements and rotations.

Dynamics of Particle Chaining

We present here a simulation of many particles placed in a periodic box of width L/a = 48, where a is the particle radius. The simulation is based on the force coupling method (FCM); see Section 14.3.2. The resolution is 1283 Fourier grid nodes for the solution of the fluid flow equations. Under the influence of hydrodynamic and magnetic forces the particles tend to aggregate in linear clusters. An averaging of ten initial random seedings was performed in order to evaluate the temporal growth of the mean cluster size (S(t)). This is defined as

E as2n{s)


where n(s)    denotes    the    number    of    clusters    of size s in    the    suspension    at

the sampled time.

In (Climent et al., 2004), several different configurations were considered corresponding to a particle volume fraction c ranging from 0.3% to 3% and dipole strength ratio A from 1 to 104. This concentration is in the range of the experiments of (Promislow et al., 1995), so that comparisons are    possible.    Figure    13.3(a)    shows    typical    initial    conditions    with    eighty

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