By R Byron Bird; et al
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7) to get the distribution function for a single polymer molecule. This cannot, however, be done until something is inserted for the double-bracket 56 C F Curtiss and R B Bird quantities indicating momentum-space averages. Up to now there is not sufficient information about the phase-space distribution function fx to allow for the calculation of these double-bracket quantities [16,19]. We therefore freely make use of the friction coefficient empricism in Eqs. 7): When Eqs. 10) are combined, we get-
6) as well as the expression for pxyx implied by Eqs. 6) Equation (6,3) for pv was also used. Hence Eq. 7) tit in which n(k\ the kinetic contribution to the stress tensor, is the first term on the right side of Eq. 5). This quantity, which is the momentum flux resulting from the motion of the beads across a surface moving with velocity v(r, t), can be put in the form of Eq. 9) or Eq. 11). M =1 mllW - v)(r; - v)]] at Pa(r - RÎ, Q", t)dQ* lim - v)(r? 8) J Note, however, that before writing out the higher terms in the expansion in second line of Eq.
3)). When this expression for ul = [[if]]" is inserted into Eq. 6), an equation for the configurational distribution function 4^, is obtained. The resulting equation is often referred to as the diffusion equation for 4*^. Often, however, we prefer to work with the center-of-mass vector rx and the connector vectors Qf By using Eqs. 13), we can obtain from Eq. 1) the following two equations (for models m which all bead masses, m, and friction coefficients, £, are identical). 3) In which the A]k = "LvBJVBk, are the elements of the Rouse matrix (see Eq.