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Register a new userOn the lateral migration of a slightly deformed bubble rising near a vertical plane wall
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Deformation-induced lateral migration of a bubble slowly rising near a vertical plane wall in a stagnant liquid is numerically and theoretically investigated. In particular, our focus is set on a situation with a short clearance $c$ between the bubble interface and the wall. Motivated by the fact that numerically and experimentally measured migration velocities are considerably higher than the velocity estimated by the available analytical solution using the Fax{e}n mirror image technique for $a/(a+c)ll 1$ (here $a$ is the bubble radius), when the clearance parameter $varepsilon(= c/a)$ is comparable to or smaller than unity, the numerical analysis based on the boundary-fitted finite-difference approach solving the Stokes equation is performed to complement the experiment. The migration velocity is found to be more affected by the high-order deformation modes with decreasing $varepsilon$. The numerical simulations are compared with a theoretical migration velocity obtained from a lubrication study of a nearly spherical drop, which describes the role of the squeezing flow within the bubble-wall gap. The numerical and lubrication analyses consistently demonstrate that when $varepsilonleq 1$, the lubrication effect makes the migration velocity asymptotically $mu V_{B1}^2/(25varepsilon gamma)$ (here, $V_{B1}$, $mu$, and $gamma$ denote the rising velocity, the dynamic viscosity of liquid, and the surface tension, respectively).
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Deformation-induced lateral migration of a bubble slowly rising near a vertical plane wall in a stagnant liquid is numerically and theoretically investigated. In particular, our focus is set on a situation with a small clearance $c$ between the bubble interface and the wall. Motivated by the fact that experimentally measured migration velocity (Takemura et al. (2002, J. Fluid Mech. {bf 461}, 277)) is higher than the velocity estimated by the available analytical solution (Magnaudet et al. (2003, J. Fluid Mech. {bf 476}, 115)) using the Fax{e}n mirror image technique for $kappa(=a/(a+c))ll 1$ (here $a$ is the bubble radius), when the clearance parameter $epsilon(=c/a)$ is comparable to or smaller than unit, the numerical analysis based on the boundary-fitted finite-difference approach by solving the Stokes equation is performed to complement the experiment. To improve the understandings of a role of the squeezing flow within the bubble-wall gap, the theoretical analysis based on a soft-lubrication approach (Skotheim & Mahadevan (2004, Phys. Rev. Lett. {bf 92}, 245509)) is also performed. The present analyses demonstrate the migration velocity scales $propto{rm Ca} epsilon^{-1}V_{B1}$ (here, $V_{B1}$ and ${rm Ca}$ denote the rising velocity and the capillary number, respectively) in the limit of $epsilonto 0$.
Series of experiments on turbulent bubbly channel flows observed bubble clusters near the wall which can change large-scale flow structures. To gain insights into clustering mechanisms, we study the interaction of a pair of spherical bubbles rising in a vertical channel through combined experiments and modeling. Experimental imaging identifies that pairwise bubbles of 1.0 mm diameter take two preferred configurations depending on their mutual distance: side-by-side positions for a short distance ($S<5$) and nearly inline, oblique positions for a long distance ($S>5$), where $S$ is the mutual distance normalized by the bubble radius. In the model, we formulate the motions of pairwise bubbles rising at $Re=O(100)$. Analytical drag and lift, and semi-empirical, spatio-temporal stochastic forcing are employed to represent the mean acceleration and the fluctuation due to turbulent agitation, respectively. The model is validated against the experiment through comparing Lagrangian statistics of the bubbles. Simulations using this model identify two distinct timescales of interaction dynamics which elucidate the preferred configurations. For pairs initially in-line, the trailing bubble rapidly escapes from the viscous wake of the leading bubble to take the oblique position. Outside of the wake, the trailing bubble travels on a curve-line path with a slower velocity driven by potential interaction and horizontally approaches the leading bubble to become side-by-side. Moreover, statistical analysis identifies that the combination of the wake and the agitation can significantly accelerate the side-by-side clustering of in-line pairs. These results indicate positive contributions of liquid viscosity and turbulence to the formation of bubble clusters.
Hard particle erosion and cavitation damage are two main wear problems that can affect the internal components of hydraulic machinery such as hydraulic turbines or pumps. If both problems synergistically act together, the damage can be more severe and result in high maintenance costs. In this work, a study of the interaction of hard particles and cavitation bubbles is developed to understand their interactive behavior. Experimental tests and numerical simulations using computational fluid dynamics (CFD) were performed. Experimentally, a cavitation bubble was generated with an electric spark near a solid surface, and its interaction with hard particles of different sizes and materials was observed using a high-speed camera. A simplified analytical approach was developed to model the behavior of the particles near the bubble interface during its collapse. Computationally, we simulated an air bubble that grew and collapsed near a solid wall while interacting with one particle near the bubble interface. Several simulations with different conditions were made and validated with the experimental data. The experimental data obtained from particles above the bubble were consistent with the numerical results and analytical study. The particle size, density and position of the particle with respect to the bubble interface strongly affected the maximum velocity of the particles.
Dynamics of a bubble impacting and sliding a tilted surface has been investigated through experimental and computational methods. textcolor{blue}{Specifically, shear stress generated on the wall has been calculated and compared with bacterium adhesion force in order to evaluate a potential sanitization function. In experiments, the bubble-wall interaction has been characterized for several different wall angles. We numerically solved a force balance including buoyancy, hydrodynamic inertia & drag, 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 of time. 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.
We discuss an inertial migration of oblate spheroids in a plane channel, where steady laminar flow is generated by a pressure gradient. Our lattice Boltzmann simulations show that spheroids orient in the flow, so that their minor axis coincides with the vorticity direction (a log-rolling motion). Interestingly, for spheroids of moderate aspect ratios, the equilibrium positions relative to the channel walls depend only on their equatorial radius $a$. By analysing the inertial lift force we argue that this force is proportional to $a^3b$, where $b$ is the polar radius, and conclude that the dimensionless lift coefficient of the oblate spheroid does not depend on $b$, and is equal to that of the sphere of radius $a$.
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