Kirkwood theory of macromolecular friction

The theoretical approach to calculating the friction coefficient, /, of a macromolecule is based on the derivation of the force exerted by tire particle on the fluid when it is moving with a center-of-mass velocity, u F=fu. The macromolecule is divided into m subchains, with subchain friction coefficient The total force is obtained as the vector sum of the forces on the subchains  

All the subchains move with the center-of-mass velocity. 

The solvent is characterized by a velocity field, The force exerted 

The perturbation of the fluid velocity at one of the subchains is the sum of the perturbations from all the other subchains. The local fluid velocity is then  

There are then m coupled equations for the local fluid velocity and the force exerted by each subchain  

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