Bubble impact on a tilted wall: Removing bacteria using bubbles

Dynamics of a bubble impacting and sliding on a tilted surface has been investigated through experimental and computational methods. In experiments, bubble-wall interaction has been characterized with an air bubble of about 550 $\mu \mathrm{m}$ in radius and a rising speed of about 30 cm/s as it impacts a solid substrate of a wall angle between $0^{\circ }$ and ${40}^{\circ }$. Specifically, shear stress generated on the wall has been calculated and compared with bacterium adhesion force in order to evaluate a potential sanitization function. We numerically solved a force balance including buoyancy, hydrodynamic inertia and drag, and lift and thin film force to determine the bubble motion. Results showed that the shear stress increases with the wall inclination. The maximum shear stress goes up to more than 300 Pa as a single bubble impacts and scrubs a tilted wall. We found that such a high shear stress is attributed to a rapid change in thin film curvature (flipping bubble-water interface) during the bouncing stage. Later, during the sliding stage, a smaller shear stress up to around 45 Pa is generated for a longer period. We also showed that the shear stress generated during the bouncing and sliding stages is high enough to remove bacteria from a surface as a potential method for removing bacteria from tilted surfaces.

Figure 1

(a) Large-scale schematic of a bubble rising and impacting a tilted surface; (b) zoom-in schematic of a bubble impacting a substrate with a coordinate system; (c) a liquid film between a bubble and a wall is squeezed and deformed due to the bubble impact.

Figure 2

A reminiscent wake flow behind a rising bubble makes the bubble rotate during the bouncing stage.

Figure 3

A bubble impacting a wall. (a) A bouncing bubble from a tilted wall at ${18}^{\circ }$. The blue dotted line shows a trajectory of the bubble centroid, and the light green dot shows the centroid at a given time; (b) a bubble impacting a horizontal wall.

Figure 4

Velocity profiles of a bubble with $R=520–550\mu \mathrm{m}$ at five different tilted angles. (a) Parallel velocity, (b) normal velocity. The reference time is the impact time, and all velocity profiles are shifted to start at time 0. For each angle, an error bar is calculated by the root-mean-square deviation method for five trials over the time. Then average error bar of all angle is plotted at left corner.

Figure 5

(a) Parallel and (b) normal velocities of a bubble $R=550\mu \text{m}$ impacting a solid wall at an angle of $\theta ={18}^{\circ }$. Gray circles are the averaged velocity of five experimental trials, and the corresponding error bar of twice the standard deviation is shown on the top-left corner in blue.

Figure 6

Particles are scrubbed off from a wall by a bubble bouncing and rotating in the clockwise direction, $\theta ={18}^{\circ }$.

Figure 7

(a) Vorticity structure around the bubble, obtained by a PIV test; (b) vorticity, ${\omega }_z\left(t\right)$, is calculated from the circulation around the bubble; two trials (PIV1 and PIV2) in the case of $\theta ={18}^{\circ }$ and $R\approx 520\mu \mathrm{m}$. The vorticity is related to circulation as $\mathrm{\Gamma }\left(t\right)={\omega }_z\left(t\right)\pi R^2$ where circulation is measured around the bubble on different closed paths by $\mathrm{\Gamma }\left(t\right)=\int u_s\left(t\right)ds$. Circles represent the average vorticity obtained by calculating the circulation along several closed paths with distances of $1.1R1.2R$, and $1.3R$ from the bubble center. The black line is a fitted Gaussian distribution $[{\omega }_z={\omega }_{0}exp(-{(t-t_c)}^2/C)]$, which is used in a lift force model. The best-fitted parameters are ${\omega }_0=90.30{\mathrm{s}}^{-1},t_c=9.07\times {10}^{-3}$ s, and $C=6.16\times {10}^{-5}{\mathrm{s}}^2$ with $95\%$ confidence intervals [83.78, 96.75]${\mathrm{s}}^{-1}$, $[8.50\times {10}^{-3},9.63\times {10}^{-3}]$ s, and $[3.80\times {10}^{-5}$, $8.52\times {10}^{-5}]{\mathrm{s}}^2$, respectively. Not enough data are available as the bubble gets close to the wall due to difficulty in tracking the particles in the gap between the bubble and the wall.

Figure 8

(a) Parallel velocity of a bubble for several $C_L$ values; (b) parallel velocity of the bubble ($C_L=0.5$) with $95\%$ confidence interval for vorticity fitting. The bubble ($\mathrm{R}=550\mu \mathrm{m}$) is impacting a solid wall at an angle of $\theta ={18}^{\circ }$.

Figure 9

Forces in $x$ and $y$ directions for the bubble at $\theta ={18}^{\circ }$. The results are for the model with constant added $C_m=0.62\chi -0.12$ including lift force (blue line in Fig. 5). (a) Forces in the $x$ direction; (b) forces in the $y$ direction.

Figure 10

Thin film profiles for a bubble with $R\approx$ 550 $\mu \mathrm{m}$ during the impacting and bouncing stage at the wall angle of $\theta ={18}^{\circ }$. $X$ is normalized by the size of the domain.

Figure 11

Experimental and simulated sliding velocities of a bubble at different wall angles.

Figure 12

Shear stress (${\tau }_{xy}$) propagation and thin film profiles for the bubble($R\approx$ 520 $\mu \mathrm{m}$) impacting a horizontal wall, $\theta =0$. $X$ and $Z$ are normalized by the size of domain; (a)–(c) the shear stress formation and thin film profile as the bubble impacts the wall; (d) the schematic of the bubble approaching the wall and two dimples propagate toward the outside; (e)–(g) the bouncing stage; (h) the schematic of a thin film as its curvature changes during the bubble bouncing from the wall, and two incoming dimples merge and result in a rapid curvature change of the thin film, concave to convex profile from $t_2$ to $t_3$.

Figure 13

Maximum normal and shear stress on a wall. (a) $R\approx$ 520 $\mu \mathrm{m}$ impacts on a horizontal surface, $\theta =0^{\circ }$; (b) $R\approx$ 550 $\mu \mathrm{m}$ impacts on a tilted surface, $\theta ={18}^{\circ }$.

Figure 14

Maximum shear stress generated during the first impact ($\blacksquare$) and sliding stages ($▴$) for several wall angles.

Figure 15

Pressure profile inside liquid thin film as the bubble $R\approx 520\mu \mathrm{m}$ bounces away from the horizontal wall.

Figure 16

Shear stress required to remove bacteria from a surface compared with the stress generated during the bubble impact at $\theta ={42}^{\circ }$.