TY - JOUR

T1 - Mixing of passive tracers in the decay Batchelor regime of a channel flow

AU - Jun, Yonggun

AU - Steinberg, Victor

N1 - Funding Information:
This work was partially supported by grants from the Israel Science Foundation, Lower Saxony Ministry of Science and Culture Cooperation, the Minerva Foundation, and the Minerva Center for Nonlinear Physics of Complex Systems.

PY - 2010/12/14

Y1 - 2010/12/14

N2 - We report detailed quantitative studies of passive scalar mixing in a curvilinear channel flow, where elastic turbulence in a dilute polymer solution of high molecular weight polyacrylamide in a high viscosity water-sugar solvent was achieved. For quantitative investigation of mixing, a detailed study of the profiles of mean longitudinal and radial components of the velocity in the channel as a function of Wi was carried out. Besides, a maximum of the average value as well as a rms of the longitudinal velocity was used to determine the threshold of the elastic instability in the channel flow. The rms of the radial derivatives of the longitudinal and radial velocity components was utilized to define the control parameters of the problem, the Weissenberg Wiloc and the Péclet Pe numbers. The main result of these studies is the quantitative test of the theoretical prediction about the value of the mixing length in the decay Batchelor regime. The experiment shows large quantitative discrepancy, more than 200 times in the value of the coefficient C, which appears in the theoretical expression for the mixing length, but with the predicted scaling relation. There are two possible reasons to this discrepancy. First is the assumption made in the theory about the δ-correlated velocity field, which is in odds with the experimental observations. Second, and probably a more relevant suggestion for the significantly increased mixing length and thus reduced mixing efficiency, is the observed jets, the rare, localized, and vigorous ejection of the scalar trapped near the wall, which protrudes into the peripheral region as well as the bulk. They are first found in the recent numerical calculations and then observed in the experiment reported. The jets definitely strongly reduce the mixing efficiency in particular in the peripheral region and so can lead to considerable increase of the mixing length. We hope that this result will initiate further numerical calculations of the mixing length. Finally, we analyze statistical properties of the mixing in the decay Batchelor regime by studying the power spectra, the decay exponents scaling, the structure functions of a tracer and moments of PDF of passive scalar increments, and the temporal and spatial correlation functions and find rather satisfactory agreement with theory.

AB - We report detailed quantitative studies of passive scalar mixing in a curvilinear channel flow, where elastic turbulence in a dilute polymer solution of high molecular weight polyacrylamide in a high viscosity water-sugar solvent was achieved. For quantitative investigation of mixing, a detailed study of the profiles of mean longitudinal and radial components of the velocity in the channel as a function of Wi was carried out. Besides, a maximum of the average value as well as a rms of the longitudinal velocity was used to determine the threshold of the elastic instability in the channel flow. The rms of the radial derivatives of the longitudinal and radial velocity components was utilized to define the control parameters of the problem, the Weissenberg Wiloc and the Péclet Pe numbers. The main result of these studies is the quantitative test of the theoretical prediction about the value of the mixing length in the decay Batchelor regime. The experiment shows large quantitative discrepancy, more than 200 times in the value of the coefficient C, which appears in the theoretical expression for the mixing length, but with the predicted scaling relation. There are two possible reasons to this discrepancy. First is the assumption made in the theory about the δ-correlated velocity field, which is in odds with the experimental observations. Second, and probably a more relevant suggestion for the significantly increased mixing length and thus reduced mixing efficiency, is the observed jets, the rare, localized, and vigorous ejection of the scalar trapped near the wall, which protrudes into the peripheral region as well as the bulk. They are first found in the recent numerical calculations and then observed in the experiment reported. The jets definitely strongly reduce the mixing efficiency in particular in the peripheral region and so can lead to considerable increase of the mixing length. We hope that this result will initiate further numerical calculations of the mixing length. Finally, we analyze statistical properties of the mixing in the decay Batchelor regime by studying the power spectra, the decay exponents scaling, the structure functions of a tracer and moments of PDF of passive scalar increments, and the temporal and spatial correlation functions and find rather satisfactory agreement with theory.

UR - http://www.scopus.com/inward/record.url?scp=79251587790&partnerID=8YFLogxK

U2 - 10.1063/1.3522400

DO - 10.1063/1.3522400

M3 - 期刊論文

AN - SCOPUS:79251587790

VL - 22

JO - Physics of Fluids

JF - Physics of Fluids

SN - 1070-6631

IS - 12

M1 - 123101

ER -