Effect of angle in removing proteins or bacteria on a tilted surface using air bubbles

Cleaning surfaces with air bubbles in an aqueous medium has been a topic of discussion in recent years due to the growing interest in sustainable methods for cleaning biological surfaces such as agricultural produce. Specifically, in a bubble-injection method, inclined surfaces are targeted by many millimetric air bubbles that collide with and slide along the surface. The collision and subsequent sliding of these air bubbles exert shear stress on the surface, causing contaminants to be removed. The shear stress is proportional to the tangential speed of the bubble with respect to the surface divided by the thickness of the thin film of liquid between the bubble and the solid surface. In this study, we conduct experiments to test the cleaning efficacy at different angles of inclination of a contaminated surface. We use two different types of surface coated with either a protein solution or a bacterial biofilm. Our experimental results indicate that bubbles exhibit the highest cleaning efficacy at the surface angle of $\theta \approx {20}^{\mathrm{o}}$ with respect to the horizontal plane for polydisperse bubbles in the range of 0.3–2 mm and with an average radius of 0.6 mm. To gain a better understanding of the underlying mechanism, we perform a numerical analysis of a single air bubble colliding with a clean surface at various angles. Our numerical and theoretical results show that the average shear force that the bubble exerts on the surface reaches a maximum at $\theta \approx 22.5^{\mathrm{o}}$ which agrees well with the experiments. We also compare the maximum shear stress in sliding phase with the shear stress required for removing different types of bacteria as a fluid-mechanics-based guideline for geometrical design of bubble cleaning devices.

Figure 1

(a) Side-view and top-view schematics of the experiments. (b) Schematics of the slide imaging setup. (c) Pretest and posttest images of a protein-coated slide for $\theta ={20}^{\mathrm{o}}$ and 6 min of bubble testing. (d) Pretest and posttest images of a biofilm coated slide for $\theta ={20}^{\mathrm{o}}$ and 6 min of testing. The red dots in the posttest images show the location of the bubble releaser.

Figure 2

Schematics of a bubble impacting a tilted surface from the bouncing to the sliding regime.

Figure 3

(a) Snapshot of bubbles moving along a clean surface with $\theta ={10}^{\mathrm{o}}$. (b) Trajectory of air bubbles for 0.4 s presented using an arbitrary color with a Gaussian blurring method at bubble centers. The Gaussian distribution has a root mean square width equal to a bubble radius. The red circles highlight the collision point of bubbles on the surface. (c) Histogram of bubbles radius, $a$, for five different tests and approximately 200 bubbles.

Figure 4

(a) The cleaning efficacy, $\lambda$, for varying test time, $T$, at $\theta ={20}^{\mathrm{o}}$. (b) Pretest and posttest images of a surface coated with protein for $T=5$ min, and $\theta ={20}^{\mathrm{o}}$. The scale bar shows 1 cm. (c) Pretest and posttest images of a surface coated with protein for $T=6$ min, and $\theta ={20}^{\mathrm{o}}$. The red dots in posttest images show the location of the bubble releaser. The scale bar shows 1 cm.

Figure 5

(a) The efficacy of cleaning, $\lambda$, on surfaces coated with proteins for varying surface angles, $\theta$, with $T=6$ min. (b) Pretest and posttest images for $\theta ={10}^{\mathrm{o}}$, and $T=6$ min. The scale bar shows 1 cm. (c) Pretest and posttest images for $\theta ={20}^{\mathrm{o}}$, and $T=6$ min. The red dots in the posttest images show the location of the bubble releaser. The scale bar shows 1 cm.

Figure 6

(a) The cleaning efficacy, $\lambda$, on surfaces coated with bacteria for varying surface angles, $\theta$, with $T=6$ min. (b) Pretest and posttest images for $\theta ={10}^{\mathrm{o}}$, and $T=6$ min. The scale bar shows 1 cm. (c) Pretest and posttest images for $\theta ={20}^{\mathrm{o}}$, and $T=6$ min. The red dots in posttest images show the syringe needle projection on the surface. The scale bar shows 1 cm.

Figure 7

Bubble profile for $a=0.6$ mm and $\theta ={20}^{\mathrm{o}}$ during the steady-state sliding. The inset shows the zoom-in view of the dimple formed on the bubble, near the solid surface.

Figure 8

The bubble profile during the steady-state sliding in $x\text{−}z$ planes at $y=0\mu \mathrm{m}$ (solid line), $y=\pm 100\mu \mathrm{m}$ (dashed line), and $y=\pm 200\mu \text{m}$ (dotted dashed line) with $a=0.6\mathrm{mm}$ for $\theta ={10}^{\mathrm{o}}$ (violet), $\theta ={20}^{\mathrm{o}}$ (yellow), and $\theta ={30}^{\mathrm{o}}$ (red). The inset shows the zoom in view of the profile near the centerline.

Figure 9

The bubble profile during the steady-state sliding in $y\text{−}z$ planes at $x=0\mu \mathrm{m}$ (solid line), $x=\pm 100\mu \mathrm{m}$ (dashed line), and $x=\pm 200\mu \text{m}$ (dotted dashed line) with $a=0.6\mathrm{mm}$ for $\theta ={10}^{\mathrm{o}}$ (violet), $\theta ={20}^{\mathrm{o}}$ (yellow), and $\theta ={30}^{\mathrm{o}}$ (red). The inset shows the zoom-in view of the profile near the centerline.

Figure 10

Comparison of the steady-state sliding velocity, $u_{\mathrm{s}}$ for varying $\theta$ between the experiments (symbols), the model (solid line), and the scaling laws (dashed line). The dashed line shows $u_{\mathrm{s}}=0.25sin\theta$. The error bars represent three trials.

Figure 11

(a) Numerical model (solid line) and scaling law (dashed line) results for the steady film thickness in the center of the bubble, $h_0$, at varying $\theta$. (b) Model results (solid line) and scaling law (dashed line) for the average shear force, ${\overline{F}}_{\mathrm{s}}$, normalized by maximum ${\overline{F}}_{\mathrm{s}}$ at varying $\theta$. The dashed line shows ${\overline{F}}_{\mathrm{s}}=7\times {10}^{-6}sin\theta cos\left(2\theta \right)$. (c) The maximum shear stress in the steady sliding phase for $a=0.6\mathrm{mm}$ and varying $\theta$. The shaded areas show limits reported for removing E. coli [51], Listeria [54, 61], and Bacillus spores [62]. The inset shows ${\overline{F}}_{\mathrm{s}}$ magnitude vs $\theta$.

Figure 12

${\overline{F}}_{\mathrm{s}}$ vs $\theta$ for different bubble sizes, $a=0.5$, 0.6, and 0.7 mm.