Diffusion of macromolecules to the axis region of capillary is considered to be driven by an entropic potential arising from the stretching of the polymer chain near a capillary wall. The potential is obtained in case of Hookean dumbbell with a constant friction factor and with a conformation dependent friction factor, respectively. Such a radial potential field is governed by dimensionless Weissenberg number, defined as relaxation time of polymer at rest multiplied by a wall shear rate.
By the gradient of a potential field, the nonhomogeneous flow field produces a force that drive a polymer to the capillary inner region. From the result of flow-induced radial migration, concentration depletion layer is developed in a capillary wall and average velocity of a polymer is larger than that of solvent molecules. In order to quantify the elution character, the ratio of polymer velocity to fluid velocity is defined as a velocity enhancement factor.
Radial concentration profiles in a circular capillary flow are calculated at developing and fully developed stages. Concentration depletion layer near the wall is widened as flow strength is increased.
Predicted velocity enhancement factor considering a conformation dependent friction factor is more gradually increased with We number, and also the value is less than in comparison to the constant friction factor model. It is due to the fact that the extension of chain is hindered by hydrodynamic friction force acting on the dumbbell, expecially in a strong flow.
For experimental comparison, CHDF system is designed and flow experiments are performed using water-soluble polymers including polyelectrolyte. In order to determine a We number, the relaxation time is estimated from curve fitting of the plot of velocity enhancement factor versus wall shear rate.
In case of flexible polymer(PAAm), in a weak flow condition only surface-exclusion is responsible for the velocity enhancement. The increase in velocity enhancement factor in relatively low shear rate region(i.e., 1＜We＜5) is good agreement with theoretical prediction, which is based on a constant friction factor assumption. As We number increases, velocity enhancement factor depart from the constant fiction factor model behavior. Somewhat, velocity enhancement has a tendency to approach to prediction obtained by considering conformation dependent friction factor.
Velocity enhancement factor of weakly charged polyelectrolyte(HPAM) is affected by eluant salt concentration. The increase in velocity enhancement factor with wall shear rate become more shape as a salt added. This behavior indicates the increase in a chain flexibility of HPAM. It is related to the reduction of relaxation time. The increasing trend of velocity enhancement factor with We number is similar to the case of flexible non-polyelectrolyte PAAm.
But, in low We region, velocity enhancement factor shows some dependence on the ionic strength. It imply that colloidal force is also origin of velocity enhancement for polyelectroyte. At high We number, the magnitude of department from a theoretical prediction is larger than that of PAAm. For strongly charged polyelectrolyte(NaPSS), addition of salt just lowers the velocity enhancement factor. It may be that electrostatic repulsion between the polymer and the wall is dominant in this case.
Experimental result of the increase in a velocity enhancement factor with molecular weights is obtained using standard Pullulans. There is a room and need for theoretical analysis on velocity enhancement factor dependence on the molecular weight.