An Experimental Study of Viscoelastic Flow in a Conical Entrance Region

An experimental study has been made of the pressure drop in the conical entrance region to a capillary tube. Two fluids, a Newtonian oil and a viscoelastic polymer solution, were used. The entrance half angle was varied from 10.8° to 90°; the wall shear rate in the capillary was varied from 50 sec.^-1 to 1000 sec.^-1.

For Newtonian flow, Oka's creeping flow solution was shown to be of the correct form to predict viscous pressure drop effects, although it gave quantitative agreement only at the larger half angles (46.7°). An adaptation of this solution to the power law viscosity model provided a satisfactory prediction of non-Newtonian viscous effects. Weissberg's solution for flow in a sharp-edged entrance (∝ = 90°) gave excellent agreement with experimental data.

For viscoelastic flow, the data were correlated semiempirically using an equation that involved a non-linear viscous term and an elastic term. An attempt to solve the conical flow problem using the theory of Bernstein, Kearsley, and Zapas yielded an intractable result, but it was possible to identify a group with the character of a dimensionless normal deformation rate. This group, which also has the properties of a Deborah number, was found to characterize the elastic pressure drop reasonably well.