Elastic instability in crossflow of polymer solutions through periodic arrays of cylinders

Abstract

The kinematics of viscous and viscoelastic liquid flows transverse to periodic arrays of circular cylinders have been studied experimentally at Reynolds numbers ranging from 0.039 to 0.5. Streak photography was used to observe the flow of a dilute polyisobutylene solution in polybutene, through square and hexagonal arrays with a porosity of 70%. Unsteady flow patterns were observed at Deborah numbers above 0.5 for the hexagonal array and at Deborah numbers above 1.5 for the square array. In the case of the square array, the asymmetry of the particle paths was particularly striking. The flow resistance corresponding to each photograph has been recorded; progressively increasing flow resistance is seen to correspond to progressively increasing unsteadiness and asymmetry in the flow patterns. The velocity profiles along selected streamline segments of another concentrated solution of polyisobutylene in decalin flowing through the same arrays, were recorded with a laser Doppler velocimeter. The Reynolds number was less than 0.01 in all the runs. At Deborah numbers up to one within the square array, the average stretch rate between rows of cylinders, determined experimentally and normalized with the nominal strain rate, increases by up to 50%. At Deborah numbers of 1–2 within the hexagonal array, the average stretch rate measured between stagnation points is the same as the corresponding value for the Stokes field. The flow field becomes unsteady with this fluid also, at Deborah numbers where the fRe product increases for both arrays.