Bubble Drag Reduction Requires Large Bubbles

In the maritime industry, the injection of air bubbles into the turbulent boundary layer under the ship hull is seen as one of the most promising techniques to reduce the overall fuel consumption. However, the exact mechanism behind bubble drag reduction is unknown. Here we show that bubble drag reduction in turbulent flow dramatically depends on the bubble size. By adding minute concentrations (6 ppm) of the surfactant Triton X-100 into otherwise completely unchanged strongly turbulent Taylor-Couette flow containing bubbles, we dramatically reduce the drag reduction from more than 40% to about 4%, corresponding to the trivial effect of the bubbles on the density and viscosity of the liquid. The reason for this striking behavior is that the addition of surfactants prevents bubble coalescence, leading to much smaller bubbles. Our result demonstrates that bubble deformability is crucial for bubble drag reduction in turbulent flow and opens the door for an optimization of the process.

Figure 1

(a) Drag coefficient $c_f$ as a function of time (for $f_i=20\mathrm{Hz}$, corresponding to $\mathrm{Re}=2.0\times 10^6$ at $\alpha =0\%$) for different gas volume fractions $\alpha$. At $t=0\mathrm{s}$ the surfactant is injected, as indicated by the dashed vertical line. We then observe a large jump in the measured friction coefficient and within $\sim 20\mathrm{s}$ all curves overlap. (b) Drag reduction (DR) as function of time. Nearly all DR is lost after injection of the surfactant at $t=0\mathrm{s}$. Inset: averaged DR before (circles) and after (asterisks) addition of the surfactant, as a function of the gas volume fraction $\alpha$. The thin line equals $\mathrm{DR}=\alpha$, showing that after addition of the surfactant the small residual DR is accounted for by the reduced density of the fluid mixture. (c) The dimensionless torque ${\mathrm{N}\mathrm{u}}_{\omega }=\tau /{\tau }_{\text{lam}}$, which is the torque $\tau$ divided by the torque in the laminar and purely azimuthal case [20], as a function of the Reynolds number Re for various $\alpha =0\%$, 1%, 2%, 3%, both with (dashed lines) and without (solid lines) the surfactant Triton X-100. (a),(b) correspond to $\mathrm{Re}=2.0\times 10^6$ (at $\alpha =0\%$), shown by the thin vertical line in the plot.

Figure 2

Snapshots of the bubbly turbulence ($\alpha =1\%$, $\mathrm{Re}=2\times 10^6$) with increasing magnification (as shown by the scale bars). In the first row no surfactants are present in the turbulent flow, whereas the second row shows the (statistically stationary) situation after addition of 6 ppm Triton X-100. In the left photos the $\mathrm{T}{}^3\mathrm{C}$ apparatus can be seen.