Figure 3 - uploaded by Huidan Yu
Content may be subject to copyright.
(a) A representative neck bridge evolution for the case of g r ¼ 0:28. (b) Sequence of meniscus development and neck growth across development time (from a to d) and half power-law scaling time (from d to f).
Source publication
The effects of initial conditions on the coalescence of two equal-sized air micro-bubbles (R0) in water are studied using the lattice Boltzmann method. The focus is on effects of two initial set-ups of parent bubbles, separated by a small distance d and connected with a neck bridge radius r0, on the neck bridge growth at the early stage of the bubb...
Contexts in source publication
Context 1
... this section, five cases with the relative radii of the initial neck bridge, r ð¼ r 0 =RÞ ¼ 0:16, 0:20, 0:28, 0:33, and 0.38, are investigated. Figure 3 shows the neck bridge evolution of a representative case ( r ¼ 0:28). It can be seen in Figure 3(a) that after a development time, the relative growth of neck bridge, ðr À r 0 Þ=R 0 , becomes linear to ðt=t i Þ 1=2 , which is equivalent to the half power-law of ðr À r 0 Þ=R 0 ¼ 0:81ðt=t i Þ 1=2 . ...
Context 2
... 3 shows the neck bridge evolution of a representative case ( r ¼ 0:28). It can be seen in Figure 3(a) that after a development time, the relative growth of neck bridge, ðr À r 0 Þ=R 0 , becomes linear to ðt=t i Þ 1=2 , which is equivalent to the half power-law of ðr À r 0 Þ=R 0 ¼ 0:81ðt=t i Þ 1=2 . The half power-law scaling has been predicted analytically, 11 which has been confirmed in recent experiments. ...
Context 3
... order to understand the underlying physics of the early neck growth, the driving mechanism to the coalescence in this early stage is closely looked into. Figure 3(b) shows the neck bridge development in the development time from a to d and half power-law scaling regime from d to f indicated in Figure 3(a). As the neck bridge radius r increases gradually, pushing the bottom of the neck up, the meniscus gradually rounds up with increased diameter . ...
Context 4
... order to understand the underlying physics of the early neck growth, the driving mechanism to the coalescence in this early stage is closely looked into. Figure 3(b) shows the neck bridge development in the development time from a to d and half power-law scaling regime from d to f indicated in Figure 3(a). As the neck bridge radius r increases gradually, pushing the bottom of the neck up, the meniscus gradually rounds up with increased diameter . ...
Context 5
... the time period of half power-law scaling from time point d to f, it is seen that the ratio of the two curvatures is around 15. Thus, the time development before the half-power law scaling is due to the significantly unbalanced capillary force of the meniscus curvature and the neck curvature. The time evolutions of the neck bridge with different initial neck bridge radius are plotted in Figure 3, distinguished by the dimensionless parameter r ð¼ r 0 =R 0 Þ. The solid line corresponds to the representative case discussed above. ...
Context 6
... each initial radius case has a similar tendency of the neck growth to the representative case, it is seen that smaller r (from bottom up) results in faster growth of the neck bridge, meaning that smaller initial neck bridge leads to faster coalescence at the early stage. It is noticed that the plotted power-law scaling is Table 2. Curvature of meniscus (K ) vs. curvature of neck bridge (K r ) at representative time points indicated in Figure 3(a). ðr À r 0 Þ=R 0 ¼ A 0 ðt=t i Þ 1=2 for the purpose to compare different initial neck bridge radius r 0 . ...
Similar publications
Compound bubbles with a liquid coating in another continuous immiscible bulk phase are ubiquitous in a wide range of natural and industrial processes. Their formation, rise and ultimate bursting at the air–liquid interface play crucial roles in the transport and fate of natural organic matter and contaminants. However, the dynamics of compound bubb...
Citations
... Unlike the direct solution of the Navier-Stokes (NS)-based equations, LBM employs a discretized kinetic model on a regular cubic mesh with a Cartesian coordinate system to simulate incompressible fluid dynamics, effectively separating nonlinearity from non-locality. This approach has distinct modeling and computational advantages, particularly when dealing J o u r n a l P r e -p r o o f with complex boundaries and incorporating microscopic interactions in multiphase flows Chen et al., 2017Chen et al., , 2018Chen et al., , 2019Chen et al., , 2020Chen et al., , 2021, as well as flows involving mass and heat transfer with or without chemical reactions (Yu et al., 2002(Yu et al., , 2007(Yu et al., , 2008. One of the most attractive features of the LBM is its suitability for implementation on graphic processing units (GPUs) for parallel computing (Yu et al., 2002(Yu et al., , 2014aWang et al., 2015;An et al., 2017a). ...
... The novelty of this computational approach consists of (1) a unique extraction of flow domain and local wall normality from image data, (2) a seamless connection between the output of image processing and the input of CFD, (3) an en-route calculation of strain-rate tensor for wall stresses, and (4) GPU parallel computing processing [28][29][30][31] (not included in this paper) to significantly mitigate the computation burden. The kinetic-based LBM has emerged for simulating a broad class of complex flows including pore-scale porous media flow [32,33] , multiphase/multicomponent flows [34][35][36][37][38] , and turbulence [36,[39][40][41][42][43] . The main advantages of the LBM for this work are its amenability for modeling the intermolecular interactions at the two-phase interface to recover the appropriate multiphase dynamics without demanding computing cost and its suitability for scalable GPU (Graphics Processing Unit) parallelization [28,30,31,36,[39][40][41][42][43][44] to achieve fast computation. ...
Image-based computational fluid dynamics (CFD) has become a new capability for determining wall stresses of pulsatile flows. However, a computational platform that directly connects image information to pulsatile wall stresses is lacking. Prevailing methods rely on manual crafting of a hodgepodge of multidisciplinary software packages, which is usually laborious and error prone. We present a new technique to compute wall stresses in image-based pulsatile flows using the lattice Boltzmann method (LBM). The novelty includes: (1) a unique image processing to extract flow domain and local wall normality, (2) a seamless connection between image extraction and CFD, (3) an en-route calculation of strain-rate tensor, and (4) GPU acceleration (not included here). We first generalize the streaming operation in the LBM and then conduct an application study for laminar and turbulent pulsatile flows in an image-based pipe (Reynolds number: 10 to 5000). The computed pulsatile velocity and shear stress are in good agreement with Womersley solutions for laminar flows and concurrent laboratory measurements for turbulent flows. This technique is being used to study (1) the hemodynamic wall stresses in inner choroid endothelium, (2) the drag force in sand flows, and (3) effects of waste streams on ion exchange kinetics in porous media.
... The current work is part of the continuous efforts 21,46,47 to reveal the underlying physics of microbubble coalescence to support the design and optimization of microfluidics where microbubbles are involved. Motivated by a recent experimental observation 21 in the microbubble coalescence inside a polymer microfluidic gas generation device that CIMD occurs in some cases but not in others, we intend to explore the key factors that lead to CIMD and the corresponding mechanisms behind it. ...
This work is motivated by an experiment of microbubble transport in a polymer microfluidic gas generation device where coalescence-induced detachment exhibits. We numerically study three-dimensional microbubble coalescence using the graphics processing unit accelerating free energy lattice Boltzmann method with cubic polynomial boundary conditions. The focus is on the coalescence-induced microbubble detachment (CIMD) in microfluidics. From the experimental observation, we identified that size inequality between two-parent bubbles and the size of the father (large) bubble are key factors to determine if a CIMD will occur. First, the analytical relationship between equilibrium contact angle and dimensionless wetting potential and experimental results of coalescence with and without CIMD are employed for the verification and validation, respectively. From eighteen experimental and computational cases, we derive a new criterion for CIMD: CIMD occurs when the two-parent bubbles are (nearly) equal with a relatively large radius. The underlying mechanism behind this criterion is explored by the time evolution of the velocity vector field, vorticity field, and kinetic energy in the entire coalescence. It is found that the symmetric capillary force drives the formation of vertical flow stream to the horizontal alignment of parent bubbles and the blockage of the downward stream due to the solid interface promotes the intensity of the upward stream. Meanwhile, large-sized parent bubbles transfer a large amount of kinetic energy from the initial free surface energy, which is essential to lead a CIMD in the post-coalescence stage. Such a new criterion is expected to impact the design and optimization of microfluidics in various applications.
... There have been efforts to investigate different effects on the individual stages of microbubble coalescence through mathematical analyses, laboratory experiments, and numerical simulations. The majority efforts have been on the early coalescence to reveal various effects [6][7][8][9][10]. For instance, Paulsen et al. [8] studied the effects of the dense surrounding fluid on the formation of an infinitesimal neck bridge and discovered that outer fluid has a marginal impact on the dynamics * whyu@iupui.edu of neck bridge formation and evolution. ...
... We explore the underlying physics in the global process of microbubble coalescence to support the design and optimization of the prototype. Prior to this work, we have studied the temporal and spatial scalings of air microbubble coalescence in water [19], the effects of the initial conditions on the neck growth [9] in the early coalescence, and the mechanism of damping oscillation in the post coalescence [14] through numerical simulations using the lattice Boltzmann method (LBM) [20,21]. ...
We systematically study the effects of liquid viscosity, liquid density, and surface tension on global microbubble coalescence using lattice Boltzmann simulation. The liquid-gas system is characterized by Ohnesorge number Oh≡ηh/ρhσrF with ηh,ρh,σ, and rF being viscosity and density of liquid, surface tension, and the radius of the larger parent bubble, respectively. This study focuses on the microbubble coalescence without oscillation in an Oh range between 0.5 and 1.0. The global coalescence time is defined as the time period from initially two parent bubbles touching to finally one child bubble when its half-vertical axis reaches above 99% of the bubble radius. Comprehensive graphics processing unit parallelization, convergence check, and validation are carried out to ensure the physical accuracy and computational efficiency. From 138 simulations of 23 cases, we derive and validate a general power-law temporal scaling T*=A0γ−n, that correlates the normalized global coalescence time (T*) with size inequality (γ) of initial parent bubbles. We found that the prefactor A0 is linear to Oh in the full considered Oh range, whereas the power index n is linear to Oh when Oh<0.66 and remains constant when Oh>0.66. The physical insights of the coalescence behavior are explored. Such a general temporal scaling of global microbubble coalescence on size inequality may provide useful guidance for the design, development, and optimization of microfluidic systems for various applications.
Image-based computational fluid dynamics (CFD) has become a new capability for determining wall stresses of pulsatile flows. However, a computational platform that directly connects image information to pulsatile wall stresses is lacking. Prevailing methods rely on manual crafting of a hodgepodge of multidisciplinary software packages, which is usually laborious and error-prone. We present a new computational platform, to compute wall stresses in image-based pulsatile flows using the volumetric lattice Boltzmann method (VLBM). The novelty includes: (1) a unique image processing to extract flow domain and local wall normality, (2) a seamless connection between image extraction and VLBM, (3) an en-route calculation of strain-rate tensor, and (4) GPU acceleration (not included here). We first generalize the streaming operation in the VLBM and then conduct application studies to demonstrate its reliability and applicability. A benchmark study is for laminar and turbulent pulsatile flows in an image-based pipe (Reynolds number: 10 to 5000). The computed pulsatile velocity and shear stress are in good agreements with Womersley's analytical solutions for laminar pulsatile flows and concurrent laboratory measurements for turbulent pulsatile flows. An application study is to quantify the pulsatile hemodynamics in image-based human vertebral and carotid arteries including velocity vector, pressure, and wall-shear stress. The computed velocity vector fields are in reasonably well agreement with MRA (magnetic resonance angiography) measured ones. This computational platform is good for image-based CFD with medical applications and pore-scale porous media flows in various natural and engineering systems.
Inlet and outlet boundary conditions (BCs) play an important role in newly emerged image-based computational hemodynamics for blood flows in human arteries anatomically extracted from medical images. We developed physiological inlet and outlet BCs based on patients’ medical data and integrated them into the volumetric lattice Boltzmann method. The inlet BC is a pulsatile paraboloidal velocity profile, which fits the real arterial shape, constructed from the Doppler velocity waveform. The BC of each outlet is a pulsatile pressure calculated from the three-element Windkessel model, in which three physiological parameters are tuned by the corresponding Doppler velocity waveform. Both velocity and pressure BCs are introduced into the lattice Boltzmann equations through Guo’s non-equilibrium extrapolation scheme. Meanwhile, we performed uncertainty quantification for the impact of uncertainties on the computation results. An application study was conducted for six human aortorenal arterial systems. The computed pressure waveforms have good agreement with the medical measurement data. A systematic uncertainty quantification analysis demonstrates the reliability of the computed pressure with associated uncertainties in the Windkessel model. With the developed physiological BCs, the image-based computation hemodynamics is expected to provide a computation potential for the noninvasive evaluation of hemodynamic abnormalities in diseased human vessels.
This work is part of our continuous research effort to reveal the underlying physics of bubble coalescence in microfluidics through the GPU-accelerated lattice Boltzmann method. We numerically explore the mechanism of damped oscillation in microbubble coalescence characterized by the Ohnesorge (Oh) number. The focus is to address when and how a damped oscillation occurs during a coalescence process. Sixteen cases with a range of Oh numbers from 0.039 to 1.543, varying in liquid viscosity from 0.002 to 0.08kg/(m · s) correspondingly, are systematically studied. First, a criterion of with or without damped oscillation has been established. It is found that a larger Oh enables faster/slower bubble coalescence with/without damped oscillation when (Oh < 0.477)/(Oh > 0.477) and the fastest coalescence falls at Oh ≈ 0.477. Second, the mechanism behind damped oscillation is explored in terms of the competition between driving and resisting forces. When Oh is small in the range of Oh < 0.477, the energy dissipation due to viscous effect is insignificant, sufficient surface energy initiates a strong inertia and overshoots the neck movement. It results in a successive energy transformation between surface energy and kinetic energy of the coalescing bubble. Through an analogy to the conventional damped harmonic oscillator, the saddle-point trajectory over the entire oscillation can be well predicted analytically.
