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Diffusivity of polymers in dilute solutions undergoing homogeneous flows
Author(s) -
Öttinger Hans Christian
Publication year - 1989
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.690350212
Subject(s) - brownian motion , mechanics , shear flow , diffusion , thermal diffusivity , polymer , flow (mathematics) , chemistry , thermodynamics , momentum diffusion , tensor (intrinsic definition) , mass flux , classical mechanics , physics , mathematics , turbulence , geometry , organic chemistry , quantum mechanics
In order to describe the translational diffusion of polymers in dilute solution, an elastic dumbbell model is used for which the effects of both hydrodynamic interaction and a nonlinear connector force are treated in a self‐consistently averaged form. For this model, the diffusion tensor in the presence of a homogeneous flow field is obtained from ( i ) the mass flux caused by concentration gradients, ( ii ) the average polymer velocity caused by external forces, and ( iii ) the mean‐square displacement of a polymer caused by the Brownian forces. From the second and third approaches the same expression for the diffusion tensor is found, whereas a different expression is obtained from the first approach. This means that the Nernst‐Einstein equation cannot be generalized to the case of flowing solutions. The model predictions for the diffusion tensors in steady shear flow are discussed in detail.