The growth or absence of elastic secondary flows is documented for flows of dilute and semi-dilute polymer solutions in sharp 90° micro-bends in channels of rectangular cross-section; secondary flows are not present for Newtonian flows under similar conditions. Flow visualization shows that a vortex is present in the inner, upstream corner of the bend and grows with increasing Reynolds (Re) and Weissenberg (Wi) numbers for flows of shear-thinning, semi-dilute polymeric solutions containing λ -DNA (9.9× 10 -7 <Re<3.1× 10-2, 0.42<Wi<126) or high molecular weight poly(ethylene) oxide (PEO) (3.5× 10-4 <Re<4.7× 10-3, 1.8<Wi<17.7). Rheological differences, likely due to differences in the flexibility of DNA and PEO, influence the degree of vortex enhancement with increasing Wi. The vortex is absent for flow of a dilute, non-shear-thinning PEO solution over a large Re and Wi range (3.3× 10-4 <Re<1.6× 10-2, 1.1<Wi<52.8) that includes conditions where vortices are observed for the semi-dilute, shear-thinning solutions. Hence, shear-thinning appears to be central to the presence of an elastic secondary flow in this geometry.
Bibliographical noteFunding Information:
S.G. would like to acknowledge financial support from Laboratory Directed Research and Development (LDRD) Grant No. 03-ERI-003 of the U.S. Department of Energy, through the Lawrence Livermore National Laboratory, and useful discussions with the Principal Investigator of the grant Dr. David Trebotich. Throughout the course of this work, C.S.D. has held a National Science Foundation Graduate Research Fellowship and an American Association of University Women Selected Professions Engineering Dissertation Fellowship. The authors are also grateful to Kenneth I. Pettigrew for fabrication of the test devices; all fabrication works were completed at the Microfabrication Laboratory at the University of California, Berkeley. The authors are also grateful to Malvern Instruments for the loan of the Malvern Gemini rheometer.