Study of Oscillating Flow of Viscoelastic Fluid With the Fractional Maxwell Model

The oscillating flow of the viscoelastic fluid in cylindrical pipes has been applied in many fields, such as industries of petroleum, chemistry, and bioengineering. It is studied using the fractional derivative Maxwell model in this paper. The exact solution is obtained utilizing a simpler and more reasonable technique. According to this velocity solution, the time-velocity profile of one kind of viscoelastic fluid is analyzed. From analysis, it is found that the flow behaves like the Newton fluid when the oscillating frequency is low, and the flow reversal occurs when the oscillating frequency is high. Moreover, two series approximations for the velocity are obtained and analyzed for different model parameters. In one series approximation, the velocity is parabolic in profile, while in the other series approximation, the velocity presents three characteristics: (1) it is independent of radius and at the centerline is smaller than that of steady Poiseuille flow, (2) the phase lags about 90deg with respect to the imposed pressure gradient, and (3) the Richardson annular effect is found near the wall.

ANNULAR EFFECT AND OTHER PATTERNS OF CURRENT DISTRIBUTION IN POINT CONTACTS

The experiments with point-contacts, containing type-II superconductors, gave possibility to study the conditions with different current density distributions in contact cross-section. The current density is constant over the cross-section of pure contacts with the ballistic electron transport: d < < li, where d is the contact diameter, li is the impurity (elastic) mean free path of electrons. A uniform current flow also occurs in contacts between pure electrodes separated with a thin layer of a metal (t < < d) having high resistivity. In dirty contacts (d > > li) an annular effect is observed: the current density is low in the centre and the highest at the contact section periphery. The relative width of the annulus of the flowing current is proportional to li/d. In contacts between two type-II superconductors in the zero external magnetic field, the current first flows over an annulus, whose width increases with the current. In the critical state preceding the superconductivity destruction in the contact, the current density reaches its highest value in the center and decreases towards the periphery as r−1/2.