The Assumption of Negligible Acceleration Terms

In the equations of motion for the beads in Eq. (11.4), it seems reasonable to assume that the bead-acceleration terms on the left side (which have the general appearance of a substantial derivative ) are negligibly small compared to the individual terms on the right side. This assumption has been discussed in several publications [15-19]. When the acceleration terms are omitted, the bead equation of motion reduces to a simple force balance used in the publications of Kramers [1], Kirkwood [2], Rouse [3], Zimm [4], and others  

That is, the sum of the Brownian, external, intramolecular, and hydrodynamic forces acting on a bead is zero. The introduction of this assumption makes the solution of the equation for the singlet configuration-space distribution function simpler. It is also useful in developing alternative expressions for the stress tensor (see, e.g., DPL Tables 13.3-1 and 15.2-1). 

4 An Assumption for the Hydrodynamic Force — Introduction of the Friction Coefficient 

6) an expression is given for the hydrodynamic force on a bead. This expression involves the pair distribution function, which is not known. Therefore It has been standard practice to make use of an empincism. In its simplest form, this states that the average hydrodynamic force on a bead depends linearly on the difference between the average bead velocity and the velocity of the surrounding medium (Kuhn [20], Kramers [1], Kirkwood and coworkers [2])  

This expression is used in the next section m developing the equation for the singlet configuration-space distribution function. 

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