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Register a new userOn viscid-inviscid interactions of a pair of bubbles rising near the wall
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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.
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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).
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 $epsilonto 0$.
We present accurate measurements of the relative motion and deformation of two large bubbles released consecutively in a quiescent liquid confined in a thin-gap cell. Though the second bubble injected is smaller, we observed that in all cases it accelerates and catches up with the leading bubble. This acceleration is related to the wake of the leading bubble which also induces significant changes in the width and curvature of the trailing bubble. On the contrary, the velocity of the leading bubble is unaltered during the whole interaction and coalescence process. Shape adaptation of the two bubbles is observed just prior to coalescence. After pinch-off, the liquid film is drained at a constant velocity.
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.
An extended volume of fluid method is developed for two-phase direct numerical simulations of systems with one viscoelastic and one Newtonian phase. A complete set of governing equations is derived by conditional volume-averaging of the local instantaneous bulk equations and interface jump conditions. The homogeneous mixture model is applied for the closure of the volume-averaged equations. An additional interfacial stress term arises in this volume-averaged formulation which requires special treatment in the finite-volume discretization on a general unstructured mesh. A novel numerical scheme is proposed for the second-order accurate finite-volume discretization of the interface stress term. We demonstrate that this scheme allows for a consistent treatment of the interface stress and the surface tension force in the pressure equation of the segregated solution approach. Because of the high Weissenberg number problem, an appropriate stabilization approach is applied to the constitutive equation of the viscoelastic phase to increase the robustness of the method at higher fluid elasticity. Direct numerical simulations of the transient motion of a bubble rising in a quiescent viscoelastic fluid are performed for the purpose of experimental code validation. The well-known jump discontinuity in the terminal bubble rise velocity when the bubble volume exceeds a critical value is captured by the method. The formulation of the interfacial stress together with the novel scheme for its discretization is found crucial for the quantitatively correct prediction of the jump discontinuity in the terminal bubble rise velocity.
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