Fluids with Varying Temperature and Concentration Gradients

2 Fluids with Varying Temperature and Concentration Gradients 

This IS now substituted into Eq (106), which then becomes (when the external forces are neglected) AEFMPXC T V  

It should be observed that in this equation the vector a = Vln r appears, but the vector bj, = Vln , has dropped out. Equation (13.17) is valid for any bead-spring model for which all beads and friction coefficients are the same also external forces have been neglected in developing this result. 

We now give the solution to Eq. (13.17) for the simplest possible model, namely Hookean dumbbells, for which there is but one element in the D-matnx and it is identically equal to zero. For this equation we can postulate a Gaus-sian-form solution  

It should be noted that we have taken the faction coefiiaent C and the spring constant H to be mdependent of the temperature, and therefore the time constant Ajj is temperature independent. Although it might be appropnate to take into account the variation of the time constant with temperature, it does not seem to be possible to do so in the present formulation of the kmetic theory, because of the assumption made in Eq. (2.24) that the intramolecular potential depends only on the interbead distances and not on the position in space or on the time. Allowing H to be a function of T i,t) would be in violation of the assumption in Eq. (2.24) Numerous papers have appeared in the literature in which H IS taken to be temperature-dependent, and we question the correctness of the results. 

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