Flow of Dilute Polymer Solutions Through a Channel with a Large Obstacle at Small Reynolds Numbers

The addition of even small quantities of high-molecular-weight polymers can significantly alter the rheological properties of a fluid. When subjected to shear flow, polymers stretch, imparting elasticity to the fluid. At low Reynolds numbers, elastic forces may dominate over inertial effects. In this study, the pressure difference between two points in the channel and the average mass flow of fluid (with the average velocity \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\langle {v}\rangle $$\end{document}) have been measured in an obstacle-laden channel (channel with a width of 2.5 mm, a height of 1 mm and a vertically oriented cylindrical obstacle with a diameter \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d = 1$$\end{document} mm in the center of the channel). Beyond the critical Weissenberg number Wi \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ = \lambda \langle {v}\rangle {\text{/}}d$$\end{document} (where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda $$\end{document} is the longest relaxation time), the friction factor (calculated from the pressure difference and average flow) rose above laminar flow values which is concurrent with enhanced fluctuations in the pressure differential between two measurement points. Spectral analysis of pressure fluctuation dynamics has been performed to characterize these effects. The results demonstrate that polymers achieve a highly stretched conformation, reflected in pronounced viscoelastic behavior.