The role played by the flexible polymer polyacrylamide (PAM) and the rigid polymer xanthan gum (XG) on drag in Taylor–Couette geometry: from Taylor’s vortexes to fully turbulent flow

We study how the flexible polymer polyacrylamide (PAM) and the rigid polymer Xanthan gum (XG) affect drag in a Taylor–Couette geometry, mainly for small Reynolds numbers, in which the Newtonian flow is characterized by laminar instabilities. Our study is focused on the range 145≤Re≤1200\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$145\le {\mathrm{Re}}\le 1200$$\end{document}. The role played by concentration is very complex for Re<600\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{Re}}<600$$\end{document}. We suppose that two distinct polymeric effects occur all together. One of them is the so-called elasto-inertial turbulence, small elasto-inertial instabilities that work to increase drag, and the other effect is related to changes in the large structures, which contributes to reduce drag. It seems that elasto-inertial turbulence is important at very small Re. In such regime, the drag reduction is not so clear, but for Re≥600\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{Re}}\ge 600$$\end{document}, the drag is clearly reduced and it is possibly related to changes in the large structures.