Abstract
For the measurement of normal stress difference by the capillary tube method, the basic equations are derived under the following two assumptions.
Assump. 1. Velocity profile is fully developed at the tube exit.
Assump. 2. Exit pressure on the center-line of the tube is a function of shear stress at the wall.
The results are shown in Table I. In this Table, the equations proposed by several investigators are also shown with their assumptions and approximations.
By using the nondimensional group N defined by Eq. (5), which represents the ratio of inertia force to normal stress difference, the exit stress Pw(L) is expressed by Eq. (6). For the range of N<<1, Pw(L) is approximately equal to the normal stress difference Tn and increases with wall shear rate. Generally, Pw(L) depends on N as well as on wall shear rate, and cannot be considered as the material function. It may be anticipated that there is the range of N where Pw(L) becomes a decreasing function of N.
Since the pressure term in Pw(L) cannot be neglected and it cannot be determined by the capillary tube method, it is impossible to determine each component of normal stress differences only by the capillary tube method.
