Cooperative drag reduction in turbulent flows using polymer additives and superhydrophobic walls

Anoop Rajappan and Gareth H. McKinley

Phys. Rev. Fluids 5, 114601 – Published 6 November 2020

Abstract

The addition of soluble long chain polymers to a Newtonian fluid, and the incorporation of aerophilic textures on submerged solid boundaries, have both been successfully employed as independent, stand-alone methods for drag reduction in turbulent aqueous flows. In this paper, we explore the possibility of combining the two strategies additively to obtain enhanced levels of frictional drag reduction in wall-bounded turbulence. By means of skin friction measurements in fully turbulent Taylor-Couette flow, we show that dissolved polymer chains act in concert with superhydrophobic walls to yield a net reduction in turbulent drag that is up to $50 %$ greater than that obtainable from either method employed independently. Cooperative drag reduction measurements are presented for various combinations involving one of two common water-soluble polymers (either polyacrylamide or polyethylene oxide) paired with one of two prototype drag-reducing superhydrophobic surfaces—either a regular pattern of streamwise microgrooves or a scalable random superhydrophobic texture possessing hierarchical multiscale roughness. The surface activity of polyethylene oxide is observed to adversely influence the wall slip on the randomly textured surface, leading to significant diminution in the overall drag reduction efficacy of this polymer-surface combination. In cases where such interfacial effects are absent, an additive friction law in Prandtl-von Kármán coordinates is proposed that yields fairly accurate predictions of the combined drag reduction performance anticipated from a given polymer-surface pair, each possessing known individual drag-reducing characteristics.

Received 24 April 2020
Accepted 1 September 2020

DOI:https://doi.org/10.1103/PhysRevFluids.5.114601

Physics Subject Headings (PhySH)

Taylor-Couette system Turbulence Wall slip

Polymer solutions

Fluid DynamicsPolymers & Soft Matter

Authors & Affiliations

Anoop Rajappan and Gareth H. McKinley ^*

Hatsopoulos Microfluids Laboratory, Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

^*gareth@mit.edu

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 5, Iss. 11 — November 2020

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
(a) Schematic sectional view of the bespoke TC apparatus used for turbulent drag measurements. The entire fixture is mounted on a commercial rotational rheometer, which is not shown. (b) A water drop, dyed blue, placed on the surface of the superhydrophobic grooved rotor. A reflective plastron is visible at the circular base of the drop. (c) A closer image of the basal surface of the drop in panel (b). The individual plastrons filling the groove troughs appear magnified due to optical refraction through the spherical drop cap. (d) Scanning electron micrograph of the grooved surface shown in panels (b) and (c). The grooves are aligned circumferentially along the exterior rotor surface. (e) A drop of water, colored blue, deposited on the superhydrophobic random texture. (f) Scanning electron micrograph of the random texture before hydrophobization with Glaco solution. The characteristic crossed leaflet nanostructure of boehmite is clearly visible. (g) The random texture in panel (f) after treatment with Glaco solution, showing the underlying boehmite layer completely covered by hydrophobic silica nanoparticles.
Reuse & Permissions
Figure 2
(a), (b) Huggins-Kramer plots for (a) aqueous PAM and (b) aqueous PEO solutions, used in the experimental determination of the intrinsic viscosity $[η]$ . (c), (d) Experimental friction curves for the smooth no-slip rotor in aqueous solutions of (c) PAM and (d) PEO of various concentrations, showing turbulent drag reduction induced by the dissolved polymer chains. The black hollow circles in both panels denote the baseline friction data for the smooth rotor in deionized water. Data are averaged over two replicates. (e) The slope $M_{P}$ of the polymeric friction curve as a function of the normalized concentration $c / c^{*}$ , obtained by linear least-squares regression of Eq. (2) to the experimental data in panels (c) and (d).
Reuse & Permissions
Figure 3
(a) Experimental friction curves for the grooved rotor ( $S_{G}$ ) and the randomly textured rotor ( $S_{R}$ ) in air-saturated deionized water, showing drag reduction induced by wall slip. The baseline data for the no-slip rotor (N) are also included for comparison. (b) The nondimensional slip length $b^{+}$ for the two superhydrophobic rotors, derived from the data in panel (a), shown as a function of the shear Reynolds number ${Re}_{τ}$ . The dashed curves represent least-squares quadratic polynomial fits to the data. The two gray bands denote, respectively, the expected linear variation of $b^{+}$ for a constant (dimensional) slip length of $b = (17 \pm 1) μ m$ for the grooved rotor $S_{G}$ , and $b = (25 \pm 1) μ m$ for the randomly textured rotor $S_{R}$ . Error bars in both panels show the full range of observations across multiple replicate tests (ten replicates for $S_{G}$ , and six for $S_{R}$ ).
Reuse & Permissions
Figure 4
(a) Combined drag reduction data (labeled $C_{G}$ ) for the superhydrophobic grooved rotor in a 50-ppm solution of aqueous PAM. Also included for comparison are the individual friction curves for the no-slip rotor in water (N) and in 50-ppm aqueous PAM (P), as well as for the superhydrophobic grooved rotor in deionized water ( $S_{G}$ ). (b) The percentage drag reduction $D$ corresponding to the data shown in panel (a). The solid curves in panels (a) and (b), respectively, denote the ideal drag reduction estimates ${(V_{C}^{+})}^{\circ}$ and $D_{C}^{\circ}$ predicted by Eqs. (4) and (9). (c) Percentage drag reduction for the grooved rotor in PAM solutions of various concentrations. (continued) The individual numbers denote the polymer concentration $c$ in ppm. (d) The ratio $D_{C} / D_{C}^{\circ}$ of the actual drag reduction achieved as compared to the ideal estimate, for the data shown in panel (c). (e), (f) Drag reduction data for the grooved rotor in aqueous PEO, analogous to those presented for PAM in panels (c) and (d). Drag reduction data in panels (a)–(d) were averaged over at least three replicates, and those in panels (e) and (f) were averaged over six replicates.
Reuse & Permissions
Figure 5
(a) Combined drag reduction data (labeled $C_{R}$ ) for the randomly textured superhydrophobic rotor in a 50-ppm solution of aqueous PAM. The individual friction curves for the no-slip rotor in water (N) and in 50-ppm aqueous PAM (P), and for the randomly textured rotor in deionized water ( $S_{R}$ ), are also included for comparison. (b) The percentage drag reduction $D$ corresponding to the data shown in panel (a). The solid curves in panels (a) and (b), respectively, denote the ideal additive estimates ${(V_{C}^{+})}^{\circ}$ and $D_{C}^{\circ}$ predicted by Eqs. (4) and (9). (c), (d) Drag reduction curves for the randomly textured rotor in 50-ppm aqueous PEO, analogous to the data for PAM shown in panels (a) and (b). In the case of PEO, the actual drag reduction observed in experiments (labeled $C_{R}$ ) falls considerably short of the ideal estimate denoted by the solid curves (separately labeled $C_{R}^{\circ}$ for clarity). Drag reduction data in panels (a) and (b) were averaged over six replicates, and those in panels (c) and (d) were averaged over eight replicates.
Reuse & Permissions
Figure 6
(a) Surface tension $σ$ of aqueous PAM and PEO solutions as a function of the polymer concentration $c$ . The surface tension of water is unaltered by the addition of PAM, and that of the PEO solution is largely independent of $c$ within the range of concentrations employed in flow tests. (b) Surface tension of a binary solution of 2-butanol in water, as a function of the percentage volume of butanol. (c, d) Experimentally determined slip length $b^{+}$ on the grooved rotor (c) and the randomly textured rotor (d) in a $0.5 %$ solution of butanol in water. The original slip length curves for the two rotors as measured in pure water—and shown in Fig. 3—are also included for comparison. In panel (d), the gray and orange bands denote the expected variation of $b^{+}$ for constant slip lengths of $b = (25 \pm 1) μ m$ and $(18 \pm 1) μ m$ , for the randomly textured rotor in water and in the butanol solution, respectively. (e, f) Ideal drag reduction estimates for the randomly textured superhydrophobic rotor in 50-ppm aqueous PEO, recomputed based on the diminished slip length determined from panel (d). The revised predictions are denoted by the orange solid curves labeled ${(C_{R}^{\circ})}^{'}$ ; all other curves are identical to those in Figs. 5 and 5.
Reuse & Permissions

Physical Review Fluids