Hydrodynamics of rotational motion

As was discussed in Chapter 3, the first step in deriving the Smoluchowski equation is to obtain the phenomenological relation between the force and flux by using the hydrodynamics of the problem. 

Consider a rod plac in a quiescent viscous fluid. If an external field exerts a torque N on the rod, the rod will rotate with certain angular velocity to. For thin rod, we may neglect the rotation around u, and assume that both to and N are perpendicular to . If iV is small, is linear in N, and by symmetry, parallel to N. 

A simple estimation of tr is done for the shirii-kebab model illustrated in Fig. 8.2 the rod is regarded as made up of N = Lib beads , which are numbered from -JV/2 to NH. When the rod rotates with angular velocity d, the bead n which is separated from the centre by the distance nb moves with velocity — (to X nbu). 

If the hydrodynamic interaction is neglected, the frictional force acting on the segment n is oK where is the translational friction 

Rodlike polymer and shish-kebab model, which consists of N-Lib beads of diameter b placed along a straight line. 

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