“…Under ultrasound excitation, two bubbles with initial radii (R 10 and R 20 ) and positions (bubble centers x 10 and x 20 ) could occur radial and translational motions (i.e., R 1 (t), R 2 (t) and x 1 (t), x 2 (t)) over time, respectively. It is assumed that both bubbles remain spherical during their oscillations, and the mass exchange (i.e., evaporation/condensation and gas diffusion) at the gas–liquid interfaces and chemical reactions inside the bubbles are neglected for simplicity as demonstrated in earlier works [28] , [34] , [35] , [36] , [39] , [40] , [41] , [42] . Fig.…”
Section: Theory and Methodsmentioning
confidence: 99%
“…The translational motions of bubbles were always neglected in previous studies [30] , [31] , [32] , [34] , [35] , [36] , [39] , [40] , nevertheless, the radial and translational motions of bubbles, as well as the viscoelastic drag experienced by bubbles while moving in the viscoelastic medium were comprehensively considered herein. The Keller-Miksis equations coupled with the bubble–bubble interactions were used as follows [28] , [42] : where R i (t), R j (t) and x i (t), x j (t) are the radii and center positions of the i th and j th bubble, respectively. The indexes i = 1, 2 and j = 3 − i denote the bubble number.…”
Section: Theory and Methodsmentioning
confidence: 99%
“…Regarding the translational motion of bubbles in a viscoelastic medium, the viscoelastic drag D e , i experienced by the i th bubble in Eq. (2) is given by [28] , [42] : where U i (t) is the translational velocity of the moving i th bubble. For the Kelvin-Voigt viscoelastic model, the relaxation modulus function is E(t) = G + μδ(t), where δ(t) is the Dirac delta function.…”
Section: Theory and Methodsmentioning
confidence: 99%
“…Specifically, the expansion ratios of bubbles can be suppressed or enlarged, which largely depends on the ultrasound parameters, the ambient bubble radii, the distances between bubbles and the number of bubbles [35] , [39] , [40] . Recently, several studies have attempted to clarify the impacts of the viscoelasticity of the surrounding medium on the translational and/or radial motions of bubbles with considering bubble–bubble interactions [41] , [42] . It was found that increasing elasticity, viscosity or both would significantly reduce the translational and radial motions of bubbles and consequently reduce the bubble–bubble interactions [42] .…”
Section: Introductionmentioning
confidence: 99%
“…Recently, several studies have attempted to clarify the impacts of the viscoelasticity of the surrounding medium on the translational and/or radial motions of bubbles with considering bubble–bubble interactions [41] , [42] . It was found that increasing elasticity, viscosity or both would significantly reduce the translational and radial motions of bubbles and consequently reduce the bubble–bubble interactions [42] . However, less attention has been paid to the characteristics of the nonlinear bubble dynamics and the resultant acoustic emissions while considering the impacts of the bubble–bubble interactions and the viscoelasticity of the surrounding medium simultaneously.…”
Highlights
The radial and translational motions of two interacting bubbles are studied.
Bubble dynamics is analyzed by bifurcation structures and acoustic emission spectra.
Small bubble is remarkably suppressed, while large bubble is slightly enlarged.
Bubble−bubble interaction reduces the nonlinear dynamics and acoustic emissions.
Viscoelasticity of the medium reduces the radial and translational bubble motions.
“…Under ultrasound excitation, two bubbles with initial radii (R 10 and R 20 ) and positions (bubble centers x 10 and x 20 ) could occur radial and translational motions (i.e., R 1 (t), R 2 (t) and x 1 (t), x 2 (t)) over time, respectively. It is assumed that both bubbles remain spherical during their oscillations, and the mass exchange (i.e., evaporation/condensation and gas diffusion) at the gas–liquid interfaces and chemical reactions inside the bubbles are neglected for simplicity as demonstrated in earlier works [28] , [34] , [35] , [36] , [39] , [40] , [41] , [42] . Fig.…”
Section: Theory and Methodsmentioning
confidence: 99%
“…The translational motions of bubbles were always neglected in previous studies [30] , [31] , [32] , [34] , [35] , [36] , [39] , [40] , nevertheless, the radial and translational motions of bubbles, as well as the viscoelastic drag experienced by bubbles while moving in the viscoelastic medium were comprehensively considered herein. The Keller-Miksis equations coupled with the bubble–bubble interactions were used as follows [28] , [42] : where R i (t), R j (t) and x i (t), x j (t) are the radii and center positions of the i th and j th bubble, respectively. The indexes i = 1, 2 and j = 3 − i denote the bubble number.…”
Section: Theory and Methodsmentioning
confidence: 99%
“…Regarding the translational motion of bubbles in a viscoelastic medium, the viscoelastic drag D e , i experienced by the i th bubble in Eq. (2) is given by [28] , [42] : where U i (t) is the translational velocity of the moving i th bubble. For the Kelvin-Voigt viscoelastic model, the relaxation modulus function is E(t) = G + μδ(t), where δ(t) is the Dirac delta function.…”
Section: Theory and Methodsmentioning
confidence: 99%
“…Specifically, the expansion ratios of bubbles can be suppressed or enlarged, which largely depends on the ultrasound parameters, the ambient bubble radii, the distances between bubbles and the number of bubbles [35] , [39] , [40] . Recently, several studies have attempted to clarify the impacts of the viscoelasticity of the surrounding medium on the translational and/or radial motions of bubbles with considering bubble–bubble interactions [41] , [42] . It was found that increasing elasticity, viscosity or both would significantly reduce the translational and radial motions of bubbles and consequently reduce the bubble–bubble interactions [42] .…”
Section: Introductionmentioning
confidence: 99%
“…Recently, several studies have attempted to clarify the impacts of the viscoelasticity of the surrounding medium on the translational and/or radial motions of bubbles with considering bubble–bubble interactions [41] , [42] . It was found that increasing elasticity, viscosity or both would significantly reduce the translational and radial motions of bubbles and consequently reduce the bubble–bubble interactions [42] . However, less attention has been paid to the characteristics of the nonlinear bubble dynamics and the resultant acoustic emissions while considering the impacts of the bubble–bubble interactions and the viscoelasticity of the surrounding medium simultaneously.…”
Highlights
The radial and translational motions of two interacting bubbles are studied.
Bubble dynamics is analyzed by bifurcation structures and acoustic emission spectra.
Small bubble is remarkably suppressed, while large bubble is slightly enlarged.
Bubble−bubble interaction reduces the nonlinear dynamics and acoustic emissions.
Viscoelasticity of the medium reduces the radial and translational bubble motions.
Hydrocarbon resin (HR) is an essential fine chemical. The preparation and application process of HR involves lots of gas–liquid heterogeneous reactions, and the bubbly flow behavior influences them significantly. Using high‐speed photography and digital image processing techniques, the motion and interaction of in‐line bubbles in non‐aqueous solutions of HR are examined in this article. The results show a critical gas flow rate that can change the bubbling regime. It can be observed that viscosity features prominently in changing the shape of bubbles and their motion. As the viscosity increases, the bubbles are more prone to coalescence, and the bubble coalescence process gradually changes from connected slip‐rising coalescence to connected‐rising coalescence. The viscosity transition region between non‐coalescent and coalescent systems in non‐aqueous solutions of HR occurs at 3.6–9.2 mPa·s. Further, a force analysis shows that in paired bubbles, the leading bubble can be viewed as an individual bubble unaffected by trailing bubble before the two bubbles collide, but in the wake of the leading bubble, the drag force on the trailing bubble decreases and the added mass force increases.
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