Hydrodynamics of translational motion

It is straightforward to include the translational motion into the Smoluchowski equation. Again the hydrodynamics is considered first. Suppose the rod is moving with the velocity F in a quiescent fluid (see Fig. 8.4). If the rod moves along , the rod will feel a hydrodynamic drag, which is parallel to V and is written as C F. On the other hand if F is perpendicular to u, the drag is again parallel to V and is written as Cj. V- 

In general the coefficients and are not equal to each other. They are called the parallel and perpendicular components of the translational friction constant, respectively. 

Given t and Cj. the hydrodynamic drag for a translational motion in a general direction is obtained as follows. Since the Stokes equation (eqn (3.102)) is a linear equation, the hydrodynamic drag must be linear in V. Thus if V and V i are the parallel and the perpendicular components of V, the drag is written as 

The calculation of and based on the Kirkwood theory is given in Appendix 8.1. The result is  

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