Flow onset for a single bubble in a yield-stress fluid

We use computational methods to determine the minimal yield stress required in order to hold static a buoyant bubble in a yield-stress liquid. The static limit is governed by the bubble shape, the dimensionless surface tension ( $\gamma$ ) and the ratio of the yield stress to the buoyancy stress ( $Y$ ). For a given geometry, bubbles are static for $Y > Y_c$ , which we determine for a range of shapes. Given that surface tension is negligible, long prolate bubbles require larger yield stress to hold static compared with oblate bubbles. Non-zero $\gamma$ increases $Y_c$ and for large $\gamma$ the yield-capillary number ( $Y/\gamma$ ) determines the static boundary. In this limit, although bubble shape is important, bubble orientation is not. Two-dimensional planar and axisymmetric bubbles are studied.

Deformation characteristics of a single bubble in immiscible fluids

In order to investigate characteristics of bubble deformation in immiscible fluids, the bubble shape change during the interface and the relationship between aspect ratio(E) and dimensionless number of forces is obtained. A three-dimensional model is established and the free-floating behavior of a single bubble in immiscible fluids is numerically simulated by phase-field method. The simulation results are in good agreement with experimental results. The research shows that, in the lower liquid, the relationship between E and We, Ta, Re is distributed between two intersecting lines. In the upper liquid, the relationship between E and We, Ta, Re is distributed between two parallel lines. Comparing the bubble deformation and the influence of the forces. Compared with gravity, the inertial force plays a leading role in the bubble shape in the lower liquid and upper liquid. Compared with the viscous force, the surface tension dominates the bubble shape in the lower liquid.

Collision of Bubbles with Solid Surface in the Presence of Specific Surfactants

The present work is motivated by the effort to understand basic processes occurring in three-phase systems where small bubbles interact with large particles. The simplified system of a single bubble rising in a stagnant liquid and colliding with a solid surface is studied. The effect of two specific surfactants, α-Terpineol and n-Octanol, is investigated. Two independent measurements are combined: (i) bubble–solid surface collision experiments and (ii) the bubble shape oscillations induced by a movable capillary. Both experiments are based on high-speed imaging resulting in the evaluation of the restitution coefficient characterizing the collision process and the relative damping time characterizing the bubble shape oscillations in the presence of surfactants. It was observed that even for small concentrations of a surfactant, both the bubble shape oscillations and the bubble bouncing on the solid surface are significantly suppressed. Two predictions for the restitution coefficient are proposed. The equations include a term characterizing the suppression of the damping time in the presence of surfactants and a term balancing the inertia, capillary and viscous forces in the liquid film separating the bubble and the solid surface. The proposed equations successfully predict the restitution coefficient of bubble bouncing on the solid surface in liquids with the addition of specific surfactants.

Numerical Study of Formation of a Series of Bubbles from an Orifice by Applying Dynamic Contact Angle Model

The dynamic contact angle model is applied in the formation process of a series of bubbles from Period-I regime to Period-II regime by using the VOF method on a 2D axisymmetric domain. In the first process of the current research, the dynamic contact angle model is validated by comparing the numerical results to the experimental data. Good agreement in terms of bubble shape and bubble detachment time is observed from a lower flow rate Q = 150.8 cm3/min (Re = 54.77, Period-I regime) to a higher flow rate Q = 603.2 cm3/min (Re = 219.07, Period-III regime). The comparison between the dynamic contact angle model and the static contact angle model is also performed. It is observed that the static contact angle model can obtain similar results as the dynamic contact angle model only for smaller gas flow rates (Q ≤ 150.8 cm3/min and Re ≤ 54.77)). For higher gas flow rates, the static contact angle model cannot produce good results as the dynamic contact angle model and has larger relative errors in terms of bubble detachment time and bubble shape.

3D Reconstruction of a Single Bubble in Transparent Media Using Three Orthographic Digital Images

This work proposed a method to reconstruct the 3D bubble shape in a transparent medium utilizing the three orthographic digital images. The bubble was divided into several ellipse slices. The azimuth angle and projection parameters were extracted from the top view image, while the formulas for dimensionless semi-axes were derived according to the geometric projection relationship. The elliptical axes of each layer were calculated by substituting the projection width into the formulas. All layers of slices were stacked to form the 3D bubble shape. Reconstruction accuracy was evaluated with spheres, ellipsoids, and inverted teardrops. The results show that the position contributes greatly to the reconstruction accuracy of the bubbles with serious horizontal deformation. The method in Bian et al. (2013) is sensitive to both horizontal and vertical deformations. The vertical deformation has little influence on the method in Fujiwara et al. (2004), whereas the horizontal deformation greatly impacts its accuracy. The method in this paper is negligibly affected by vertical deformation, but it does better in reconstructing single bubbles with large horizontal deformation. The azimuth angle affects the accuracy of the methods in Bian et al. (2013) and Fujiwara et al. (2004) more than the method in this paper.

On evolving size and shape of gas bubble in marine clay under multi-stage loadings: microcomputed tomography (μCT) characterization and cavity contraction analysis

Discrete bio-gas bubbles commonly form in fine-grained marine sediments and have modified many aspects of the behavior of these sediments, including strength, stiffness, and permeability. Although the level of such modifications is known to govern by bubble shape and size, limited studies have been undertaken, mainly due to difficulty in nondestructively characterizing bubbles within a soil under in situ stresses. In this study, a mini-loading device was developed to perform one-dimensional loading tests on gassy marine clay and gassy silt in a microcomputed tomography (μCT). The evolving bubble shape, size, and pressure during loading were quantified, and the resulting stress fields around the bubble cavities were evaluated via elliptical cavity contraction analysis considering stress anisotropy. As the vertical load increased, bubble cavities were found to compress predominantly along the vertical loading direction, with little horizontal compression, because localized soil failure (LSF) and thus cavity collapse occurred mainly near the roof of the at-rest lateral earth pressure coefficient (K0)-stressed elliptical bubble cavities. The evolution of bubble shape and size under loading is significantly affected by stress anisotropy, which governs the extent and location of the LSF. A Gaussian mixture model is adopted to quantify the evolving distributions of bubble structure parameters, which are essential for developing more physically rigorous gassy soil models.