Showing papers by "J. L. Ericksen published in 1957"

Steady shear flow of non-Newtonian fluids

Abstract: In recent years, considerable effort has been expended in attempting to gain an understanding of the behavior of non-Newtonian fluids in shear. MARKOVITZ [1] recently attempted to collect and organize experimental data and to compare it with predictions of existing theories. One difficulty is that conclusions which can be drawn from different types of experiments seem to disagree. Theoretical work on the steady flow of non-Newtonian fluids has brought to light a new phenomenon. According to the linear theory of viscous fluids, it is always possible for a fluid flowing through a cylindrical tube, to which it adheres, to undergo steady rectilinear motion, each particle moving with constant speed in a straight line parallel to the generators of the cylinder. Analyses made by ERICKSEN [2] and by GREEN • RIVLm [31 show that, for many ideal fluids described by the REINER [41 -RIVLIN [5] theory, this simple type of motion is possible only for very special shapes of tubes and that, in general, it is replaced by a flow consisting of such a rectilinear motion combined with a secondary flow in cross-sectional planes. Using the more general theory of fluids proposed by RIVLIN & ERICKSEN [61, LANGLOIS [7] has obtained solutions involving secondary flows in tubes and other types of "boundary geometries. As has been discussed by RIVLIN [8], similar secondary flows have been observed in the mean flow of fluids through non-circular tubes when the motion is turbulent. To our knowledge, it is not known whether secondary flows occur in the steady flow of any real fluid through tubes. Our analysis indicates that, if the conclusions which ROBERTS [9] drew from his experiments ai-e correct, the fluids which he observed should be capable of undergoing rectilinear motionthrough tubes of any shape. MARKOVITZ [11 draws self-consistent conclusions from other experimental data which contradict some of ROBERTS' conclusions. Calculations made in accordance with these conclusions suggest that secondary flows are to be expected in some shapes of tubes. We offer a partial proof that if secondary flows do not occur in elliptical tubes, they will not occur in tubes of any other shape.