气泡变形对泡状悬浮液表观黏度的影响
|
摘要
利用流体体积函数法研究了简单剪切场作用下、二维平行平板模型内,不同气液相黏度比(λ)和不同毛细数(Ca)工况下,气泡形态变化对泡状悬浮液表观黏度的影响,并探讨了气泡的加入对泡状悬浮液表观黏度的影响机理。实验结果表明,影响悬浮液表观黏度的因素主要有气相黏度、气泡对流动的阻碍和气泡提供滑移面三个因素;两种λ下,Ca相同时,表观黏度相同;相同λ下,当Ca=0.10时,气泡变形较小,对流动的阻碍占主导,导致整体黏性耗散增大,悬浮体系表黏度增大;当Ca=0.65时,气泡被拉长,对流动阻碍减小,且提供较大滑移面,导致整体黏性耗散与纯液体相近,表观黏度与纯液相相近;当Ca趋于气泡破碎临界毛细数时,气泡被进一步拉长,对流动阻碍很小,且提供很大的滑移面,导致整体黏性耗散减小,悬浮体系表观黏度减小。
In order to understand the mechanism of the effect of bubble addition on the apparent viscosity of bubble suspension,the effect of the bubble deformation on the apparent viscosity of bubbly suspension liquid in a two-dimensional parallel plate model in a simple shear field,under the conditions of different ratios of gas-liquid viscosity(λ) and different capillary numbers(Ca),was studied with the volume of fluid method. The results showed that the main factors affecting the apparent viscosity of suspension were the viscosity of the gas,the obstruction of the bubble to flow and the free slip surface provided by the bubble. The apparent viscosity was equal at the same Ca regardless of the λ. Under the same λ,when Ca was 0.10,the deformation of the bubble was weak,and its obstruction to flow was dominant,leading to the increase of the overall viscous dissipation and the increase of the apparent viscosity of the suspension. When Ca was 0.65,the bubble was elongated,which reduced the obstruction to flow and provided a larger free slip surface,which led to the overall viscous dissipation similar to that of the pure liquid,and the apparent viscosity was similar to the pure liquid phase. When Ca was closer to the critical capillary number,at which the bubble started to break up,the bubble was further elongated,whose obstruction to the flow was negligible,and it provided a large free slip surface,resulting in decrease in the overall viscous dissipation and decrease in the apparent viscosity of the suspension.
In order to understand the mechanism of the effect of bubble addition on the apparent viscosity of bubble suspension,the effect of the bubble deformation on the apparent viscosity of bubbly suspension liquid in a two-dimensional parallel plate model in a simple shear field,under the conditions of different ratios of gas-liquid viscosity(λ) and different capillary numbers(Ca),was studied with the volume of fluid method. The results showed that the main factors affecting the apparent viscosity of suspension were the viscosity of the gas,the obstruction of the bubble to flow and the free slip surface provided by the bubble. The apparent viscosity was equal at the same Ca regardless of the λ. Under the same λ,when Ca was 0.10,the deformation of the bubble was weak,and its obstruction to flow was dominant,leading to the increase of the overall viscous dissipation and the increase of the apparent viscosity of the suspension. When Ca was 0.65,the bubble was elongated,which reduced the obstruction to flow and provided a larger free slip surface,which led to the overall viscous dissipation similar to that of the pure liquid,and the apparent viscosity was similar to the pure liquid phase. When Ca was closer to the critical capillary number,at which the bubble started to break up,the bubble was further elongated,whose obstruction to the flow was negligible,and it provided a large free slip surface,resulting in decrease in the overall viscous dissipation and decrease in the apparent viscosity of the suspension.
引文
[1]Truby J M,Mueller S P,Llewellin E W,et al.The rheology of three-phase suspensions at low bubble capillary number[J].Proc R Soc London,Ser A,2015,471(2173):20140557.
[2]Tasaka Y,Kimura T,Murau Y.Estimating the effective viscosity of bubble suspensions in oscillatory shear flows by means of ultrasonic spinning rheometry[J].Exp Fluids,2015,56:867.
[3]Matsunaga D,Imai Y,Yamaguchi T,et al.Rheology of a dense suspension of spherical capsules under simple shear flow[J].J Fluid Mech,2016,786:110-127.
[4]Foglino M,Morozov A N,Henrich O,et al.Flow of deformable droplets:Discontinuous shear thinning and velocity oscillations[J].Phys Rev Lett,2017,119(20):208002.
[5]Rosti M E,Brandt L.Suspensions of deformable particles in a Couette flow[J].J Non-Newton Fluid,2018,DOI:10.1016/j.jnnfm.2018.01.008.
[6]徐磊,庞明军.旋转圆环内分散气泡对液相表观黏度的影响[J].化学工程,2017,45(6):32-38.
[7]Hinch E J,Acrivos A.Long slender drops in a simple shear flow[J].J Fluid Mech,1980,98(2):305-328.
[8]Zhao Jianfu,Zhang Lang,Li Zhendong,et al.Topological structure evolvement of flow and temperature fields in deformable drop Marangoni migration in microgravity[J]Int J Heat Mass Transfer,2011,54(21/22):4655-4663.
[9]Llewellin E W,Mader H M,Wilson S D R.The constitutive equation and flow dynamics of bubbly magmas[J].Geophys Res Lett,2002,29(24):23-1-23-4.
[10]Frankel N A,Acrivos A.The constitutive equation for a diluteemulsion[J].J Fluid Mech,1970,44(1):65-78.
[11]赵大勇,李维仲.VOF方法中几种界面重构技术的比较[J].热科学与技术,2003,2(4):318-323.
[12]Hirt C W,Nichols B D.Volume of fluid(VOF)method for the dynamics of free boundary[J].J Comput Phys,1981,39(1):201-225.
[13]Brackbill J U,Kothe D B,Zemach C.A continuum method for modeling surface tension[J].J Comput Phys,1992,100(2):335-354.
[14]Taylor G I.The viscosity of a fluid containing small drops of another fluid[J].Proc R Soc London,Ser A,1932,138(834):41-48.
[15]Rallison J M.A numerical study of the deformation and burst of a viscous drop in general shear flows[J].J Fluid Mech,1981,109(1):465-482.
[16]Liu Jingru,Zhu Chunying,Fu Taotao,et al.Numerical simulation of the interactions between three equal-interval parallel bubbles rising in non-Newtonian fluids[J].Chem Eng Sci,2013,93(4):55-66.
[2]Tasaka Y,Kimura T,Murau Y.Estimating the effective viscosity of bubble suspensions in oscillatory shear flows by means of ultrasonic spinning rheometry[J].Exp Fluids,2015,56:867.
[3]Matsunaga D,Imai Y,Yamaguchi T,et al.Rheology of a dense suspension of spherical capsules under simple shear flow[J].J Fluid Mech,2016,786:110-127.
[4]Foglino M,Morozov A N,Henrich O,et al.Flow of deformable droplets:Discontinuous shear thinning and velocity oscillations[J].Phys Rev Lett,2017,119(20):208002.
[5]Rosti M E,Brandt L.Suspensions of deformable particles in a Couette flow[J].J Non-Newton Fluid,2018,DOI:10.1016/j.jnnfm.2018.01.008.
[6]徐磊,庞明军.旋转圆环内分散气泡对液相表观黏度的影响[J].化学工程,2017,45(6):32-38.
[7]Hinch E J,Acrivos A.Long slender drops in a simple shear flow[J].J Fluid Mech,1980,98(2):305-328.
[8]Zhao Jianfu,Zhang Lang,Li Zhendong,et al.Topological structure evolvement of flow and temperature fields in deformable drop Marangoni migration in microgravity[J]Int J Heat Mass Transfer,2011,54(21/22):4655-4663.
[9]Llewellin E W,Mader H M,Wilson S D R.The constitutive equation and flow dynamics of bubbly magmas[J].Geophys Res Lett,2002,29(24):23-1-23-4.
[10]Frankel N A,Acrivos A.The constitutive equation for a diluteemulsion[J].J Fluid Mech,1970,44(1):65-78.
[11]赵大勇,李维仲.VOF方法中几种界面重构技术的比较[J].热科学与技术,2003,2(4):318-323.
[12]Hirt C W,Nichols B D.Volume of fluid(VOF)method for the dynamics of free boundary[J].J Comput Phys,1981,39(1):201-225.
[13]Brackbill J U,Kothe D B,Zemach C.A continuum method for modeling surface tension[J].J Comput Phys,1992,100(2):335-354.
[14]Taylor G I.The viscosity of a fluid containing small drops of another fluid[J].Proc R Soc London,Ser A,1932,138(834):41-48.
[15]Rallison J M.A numerical study of the deformation and burst of a viscous drop in general shear flows[J].J Fluid Mech,1981,109(1):465-482.
[16]Liu Jingru,Zhu Chunying,Fu Taotao,et al.Numerical simulation of the interactions between three equal-interval parallel bubbles rising in non-Newtonian fluids[J].Chem Eng Sci,2013,93(4):55-66.