Phoretic self-propulsion of microbubbles may contribute to surface cleaning
Graphical abstract
Introduction
Small bubbles and droplets can move in an outer liquid phase in response to gradients of a quantity such as a temperature or chemical concentration generated at their interface, a phenomenon known as phoretic propulsion (Moran and Posner, 2017). Such motions mediated by interfacial gradients are relevant to both natural processes such as propulsion of microorganisms (Angelini et al., 2009), and technological processes such as transport in microfluidic devices (Anna, 2016), microbubble-based technologies (Qiao et al., 2021), and collective dynamics in active-matter systems (Michelin, 2022). Recently, Ubal et al. (2021) studied the phoretic motion of microbubbles that self-propel through an unbounded viscous fluid in response to gradients of contamination with surface active species (surfactants) at their interface. Here, we extend that study for the case in which the bubble contamination occurs in the immediate vicinity of a solid surface in a fluid of moderate viscosity. Our objective is to analyze the complex free-surface flow generated by the active bubble self-propelling toward the adjacent solid surface to determine whether the generated shear stresses are strong enough to remove microorganisms from fouled surfaces.
Although the magnitude of the shear stress required to remove fouling biofilms depends strongly on the physicochemical and biological particularities of the system, Esmaili et al. (2019) recently demonstrated that the impact of a freely rising bubble on a solid wall could generate strong enough shear stresses (∼300 Pa) to detach common microorganisms from contaminated surfaces. Motivated by the recent findings of Esmaili et al. (2019) and Ubal et al. (2021), here we seek to quantify the fluid stresses generated by an active bubble that self-propels towards a solid wall due to phoretic effects and characterize the interfacial phenomena involved. Our model system, sketched in Fig. 1a, resembles the spontaneous phoretic motion of a microbubble in the vicinity of a fouled solid surface. The surfactant contamination at the front of the bubble generates the surface-tension gradient (Marangoni stress) that propels the bubble forward (Scriven and Sternling, 1960).
To accurately describe the interaction between the microbubble and the solid surface, this highly nonlinear free-boundary problem is solved by direct numerical simulations. By simultaneously solving the full Navier-Stokes system governing the free-surface flow and the convection-diffusion equation governing the interfacial surfactant transport, the direct numerical simulations enable accurate characterization of the interplay of inertial, viscous, capillary, and Marangoni forces on the impact dynamics. Results show that the impact and subsequent deformation of the active bubble on the solid surface generate shear stresses that may contribute strongly to cleaning of fouled surfaces. Results also demonstrate that this effect is weakly influenced by inertia and decreases rapidly as the initial separation between the bubble and the solid surface increases.
Section snippets
Marangoni propulsion
We consider Marangoni self-propulsion driven by the spreading of a dilute, insoluble surfactant monolayer on the surface of a small bubble of radius R. The bubble is immersed in a Newtonian liquid of constant density ρ and viscosity μ. Spreading of the surfactant at the front of the bubble creates the surface-tension gradient (Marangoni stress) that propels the bubble forward. The initial surfactant concentration on the contaminated front cap is with corresponding surface tension , as
Results and discussion
The active bubble and the surrounding fluid in our initial numerical experiments were chosen to represent a moderately viscous dynamics of . We will discuss systems with larger inertia up to order later in the paper. For microbubbles with , a Reynolds number of order unity is representative of a range of viscosities between approximately (for ) and (for ). For reference, the viscosity of a 60% sucrose solution is about .
Conclusion
Using an idealized model setup for phoretic propulsion, we have analyzed the possibility that fluid stresses generated by the spontaneous active motion of a microbubble toward a fouled solid surface could contribute to surface cleaning. As a model system, we considered the self-propulsion of a microbubble driven to the solid surface by the Marangoni effect. The solution of the free-surface model using high-fidelity simulations enabled a comprehensive picture of the fluid dynamical and
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
References (28)
- et al.
Effects of microbubbles on removal of viscous oil adhering to channel wall
Chem. Eng. Res. Des.
(2023) - et al.
Orientation and detachment dynamics of bacillus spores from stainless steel under controlled shear flow: modelling of the adhesion force
Int. J. Food Microbiol.
(2011) - et al.
Bacterial adhesion and growth on a polymer brush-coating
Biomaterials
(2008) - et al.
Detachment of listeria innocua and pantoea agglomerans from cylinders of agar and potato tissue under conditions of Couette flow
J. Food Eng.
(2008) - et al.
Active motion of contaminated microbubbles
Chem. Eng. Sci.
(2021) - et al.
Coalescence preference in surfactant-laden bubbles of equal size
Chem. Eng. Sci.
(2022) - et al.
Physical Chemistry of Surfaces, vol. 150
(1967) - et al.
Bacillus subtilis spreads by surfing on waves of surfactant
Proc. Natl. Acad. Sci. USA
(2009) Droplets and bubbles in microfluidic devices
Annu. Rev. Fluid Mech.
(2016)- et al.
Influence of surfactants on dip coating of fibers: numerical analysis
Ind. Eng. Chem. Res.
(2016)