Superparamagnetic filament

The dynamic Eq. (9.21) for particle velocity Vi can be written in reduced form [57]. It shows that the dynamics of the superparamagnetic filament depends on three characteristic numbers. One of them is the sperm number... 

It determines the influence of the external magnetic field on the superparamagnetic filament. The number Bj compares dipolar to bending forces and it is proportional to the magnetoelastic number introduced in Refs [4, 73, 74]. An alternative dimensionless number for characterizing the influence of the magnetic field is the Mason number introduced in the literature on magnetorheological suspensions [75, 88],... 

It is the ratio of frictional to magnetic forces and determines the behavior of the superparamagnetic filament when magnetic forces dominate over bending forces. Finally, a reduced spring constant... 

Application of ideas from polymers has begun to revolutionize bio-related disciplines. Therefore, this review book will not be complete without a chapter detailing such an application. The last chapter ( Modeling the Hydrodynamics of Elastic Filaments and its Application to a Biomimetic Flagellum ) by Stark attempts to model Nature s successful strategies for propulsion such as of sperm cells and fluid transport such as of mucus. The artificial cilium is based on a superparamagnetic filament, actuated by an external magnetic field the latter allows one to explore the filament s capacity to transport fluid. 

In Section 9.1.3, we introduced a filament made of superparamagnetic colloidal particles that are linked to each other by double-stranded DNA. We have modeled this filament as a bead-spring configuration with bending elasticity as described in Section 9.2.3. In addition, we have to include now the forces on the beads due to the dipole-dipole interaction induced by the external magnetic field. Our model very well describes the constructed artificial swimmer [4] and allows to explore the filament s capacity for transporting fluid. 

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