微通道内气泡/液滴生成的理论研究
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摘要
微气泡(液滴)以其独特的流体力学特性及尺度效应,正在医学、化工、动力、环境、日常生活等领域获得越来越广泛的应用。与传统方法相比,利用微流体机械可以生成单一性更好、大小可调的微气泡(液滴),如MicrochannelEmulsification方式、Capillary Flow Focusing方式及T-junction Microchannel方式。但是限于目前的研究还较少,人们还无法完全解释这些微气泡(液滴)生成方式的机理、结果及过程中的一些“奇特”现象。目前已经有较多关于微通道内两相流动特性(两相流压降等)的研究,但在流型之间的转变机理上的研究还大部分停留在经验的试验图表阶段。基于以上这些问题,本文将采用理论分析的方法对各种微气泡(液滴)生成方式及微通道内两相流型进行研究。
对于Microchannel Emulsification方式生成微气泡(液滴):通过列写外界能量输入及生长过程中气泡(液滴)表面自由能增加的表达式,证实了对于气泡(液滴)在台阶上的可逆膨胀过程,表面自由能的增加等于外界做的总功;考查了气泡(液滴)表面积与体积的比,得出了若气泡(液滴)初始半径为O的话,其初始生长耗能将为无穷大的结论,而这在现实中是不能实现的,从而解释了每次生成过程均会在台阶上留有剩余分散相流体的原因;仔细分析了已有的液滴直径d随台阶长度L和微通道高度h变化的实验数据,通过使用无量纲数d/h及L/h,并采用对数形式重新整理这些数据,从而在没有假设条件的情况下得出了与试验数据符合较好的预测生成液滴大小的数量级关系式,并与文献中得出的关系式进行了比较;
对于T-junction Microchannel方式生成微气泡(液滴):分析了这种方式生成微气泡(液滴)的过程中各种起作用的力的大小,发现阻力与表面张力对气泡(液滴)的脱离起主导作用。将这两个力在微通道中合理的表达出来,从而利用力的平衡得出了预测微气泡(液滴)大小的数量级关系式,并发现与已发布的试验数据符合较好,从而解决了T型微通道中生成的较小的气泡(液滴)的体积计算问题。此外还对这个数量级关系式进行了讨论,发现最终生成的气泡(液滴)的体积随Capillary数减小而增大,随分散相流体与连续相流体的流量比增大而增大。
从宏观通道中两相流流型之间过渡的机理出发,发现在微通道中,也应满足两相邻气泡(液滴)间的连续相流体在其流动方向上足够“长”从而能使变形的速度分布重新恢复时,柱状流动流型才能稳定的条件,从而解释了微通道中由柱状流动流型向过渡流动流型转变的机理,并据此提出了过渡的数量级理论界线式。
Owing to their special hydrodynamic characteristics and scale effect,micro bubbles/droplets are having wider and wider applications in many fields such as medicine,chemistry,power engineering, environmental science,and,even our daily life.By using microfluidic devices,micro bubbles/droplets with finer monodispersity and more controllable size can be formed compared with the traditional formation methods.Microchannel emulsification,Capillary flow focusing and T-junction microchannel formation method are all good examples of the microfluidic-device-based formation methods.However,few investigations have been done on these methods up to now, which limits people from fully understanding the mechanisms,results and certain peculiar phenomena of the formation processes.On the other hand,although there have been a certain amount of researches on the two phase flow characteristics in microchannels,analysis on the transition boundaries among different flow regimes is still confined to superficial empirical experimental results.This paper will concentrate on these problems based on theoretical analysis.
For the Microchannel emulsification formation method,work this paper has done is as follows. By reasonably expressing the external energy input and the increasing of the bubble/droplet surface free energy during the formation process,it is confirmed that for the reversible inflation process of bubbles/droplets on the terrace,increasing of the surface free energy equals the total external work, which is believed to also apply to other systems in which surface tension dominants.Then,by analyzing the increasing of surface area per unit volume of bubble/droplet fluid,it is found that if the initial volume of the bubble/droplet is zero,energy consumption of the initial expansion will be infinite,which is,however,very difficult to realize in natural world.Thus we can obtain the reason why there is always remaining dispersed phase fluid on the terrace during each formation process. Lastly,available experimental data relating bubble/drop diameter d to terrace length L and microchannel depth h in the literature are carefully analyzed.Through using nondimensional numbers d/h and L/h,and re-expressing these data in logarithm form,a scaling relation predicting the sizes of the formed bubbles/droplets without any assumptions is proposed which agrees well with experimental data.Then a comparison between this scaling relation and that deduced by other authors was made.
For the T-junction microchannel formation method,we compared the magnitudes of different kinds of forces in the formation process and then found that drag force of the continuous phase fluid and surface tension force dominant the detachment of micro bubbles/droplets.By expressing these two forces reasonably in micro scale,we then obtained a scaling relation for the sizes of bubbles/droplets which are not big enough to occupy the entire microchannel cross section based on force balance,which agrees well with experimental results.Afterward,a discussion was conducted,which found that the final sizes of the micro bubbles/droplets increase while the Ca number decrease and increase while the flow rate ratio between the dispersed phase fluid and the continuous phase fluid increase.
On the basis of transition mechanisms of different two phase flow regimes in macrochannels, we found that it is also applicable in microchannels that only when the length of the fluid bulk is long enough so that the deformed continuous phase velocity distribution can be fully reestablished, can the velocity of the bubbles/droplets be the same and the length of the fluid bulk remain constant with time and position in the direction of flow so as to remain a stable slug flow.Accordingly,we explained the transition mechanism from slug flow pattern to transition flow pattern in microchannels and then proposed a theoretical transition boundary scaling relation.
对于Microchannel Emulsification方式生成微气泡(液滴):通过列写外界能量输入及生长过程中气泡(液滴)表面自由能增加的表达式,证实了对于气泡(液滴)在台阶上的可逆膨胀过程,表面自由能的增加等于外界做的总功;考查了气泡(液滴)表面积与体积的比,得出了若气泡(液滴)初始半径为O的话,其初始生长耗能将为无穷大的结论,而这在现实中是不能实现的,从而解释了每次生成过程均会在台阶上留有剩余分散相流体的原因;仔细分析了已有的液滴直径d随台阶长度L和微通道高度h变化的实验数据,通过使用无量纲数d/h及L/h,并采用对数形式重新整理这些数据,从而在没有假设条件的情况下得出了与试验数据符合较好的预测生成液滴大小的数量级关系式,并与文献中得出的关系式进行了比较;
对于T-junction Microchannel方式生成微气泡(液滴):分析了这种方式生成微气泡(液滴)的过程中各种起作用的力的大小,发现阻力与表面张力对气泡(液滴)的脱离起主导作用。将这两个力在微通道中合理的表达出来,从而利用力的平衡得出了预测微气泡(液滴)大小的数量级关系式,并发现与已发布的试验数据符合较好,从而解决了T型微通道中生成的较小的气泡(液滴)的体积计算问题。此外还对这个数量级关系式进行了讨论,发现最终生成的气泡(液滴)的体积随Capillary数减小而增大,随分散相流体与连续相流体的流量比增大而增大。
从宏观通道中两相流流型之间过渡的机理出发,发现在微通道中,也应满足两相邻气泡(液滴)间的连续相流体在其流动方向上足够“长”从而能使变形的速度分布重新恢复时,柱状流动流型才能稳定的条件,从而解释了微通道中由柱状流动流型向过渡流动流型转变的机理,并据此提出了过渡的数量级理论界线式。
Owing to their special hydrodynamic characteristics and scale effect,micro bubbles/droplets are having wider and wider applications in many fields such as medicine,chemistry,power engineering, environmental science,and,even our daily life.By using microfluidic devices,micro bubbles/droplets with finer monodispersity and more controllable size can be formed compared with the traditional formation methods.Microchannel emulsification,Capillary flow focusing and T-junction microchannel formation method are all good examples of the microfluidic-device-based formation methods.However,few investigations have been done on these methods up to now, which limits people from fully understanding the mechanisms,results and certain peculiar phenomena of the formation processes.On the other hand,although there have been a certain amount of researches on the two phase flow characteristics in microchannels,analysis on the transition boundaries among different flow regimes is still confined to superficial empirical experimental results.This paper will concentrate on these problems based on theoretical analysis.
For the Microchannel emulsification formation method,work this paper has done is as follows. By reasonably expressing the external energy input and the increasing of the bubble/droplet surface free energy during the formation process,it is confirmed that for the reversible inflation process of bubbles/droplets on the terrace,increasing of the surface free energy equals the total external work, which is believed to also apply to other systems in which surface tension dominants.Then,by analyzing the increasing of surface area per unit volume of bubble/droplet fluid,it is found that if the initial volume of the bubble/droplet is zero,energy consumption of the initial expansion will be infinite,which is,however,very difficult to realize in natural world.Thus we can obtain the reason why there is always remaining dispersed phase fluid on the terrace during each formation process. Lastly,available experimental data relating bubble/drop diameter d to terrace length L and microchannel depth h in the literature are carefully analyzed.Through using nondimensional numbers d/h and L/h,and re-expressing these data in logarithm form,a scaling relation predicting the sizes of the formed bubbles/droplets without any assumptions is proposed which agrees well with experimental data.Then a comparison between this scaling relation and that deduced by other authors was made.
For the T-junction microchannel formation method,we compared the magnitudes of different kinds of forces in the formation process and then found that drag force of the continuous phase fluid and surface tension force dominant the detachment of micro bubbles/droplets.By expressing these two forces reasonably in micro scale,we then obtained a scaling relation for the sizes of bubbles/droplets which are not big enough to occupy the entire microchannel cross section based on force balance,which agrees well with experimental results.Afterward,a discussion was conducted,which found that the final sizes of the micro bubbles/droplets increase while the Ca number decrease and increase while the flow rate ratio between the dispersed phase fluid and the continuous phase fluid increase.
On the basis of transition mechanisms of different two phase flow regimes in macrochannels, we found that it is also applicable in microchannels that only when the length of the fluid bulk is long enough so that the deformed continuous phase velocity distribution can be fully reestablished, can the velocity of the bubbles/droplets be the same and the length of the fluid bulk remain constant with time and position in the direction of flow so as to remain a stable slug flow.Accordingly,we explained the transition mechanism from slug flow pattern to transition flow pattern in microchannels and then proposed a theoretical transition boundary scaling relation.
引文
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2. J. H. Xu, S. W. Li, J. Tan, Y. J. Wang, G. S. Luo, Preparation of highly monodisperse droplet in a T-junction microfluidic device, AICHE Journal 52, 3005(2006).
3. J. H. Xu, S. W. Li, J. Tan, Y. J. Wang, G. S. Luo, Controllable preparation of monodisperse O/W and W/O emulsions in the same microfiuidic device, The ACS journal of surfaces and colloids 22, 7943(2006).
4. T. Nisisako, T. Torii, T. Higuchi, Droplet formation in a microchannel network, Lab chip 2, 24(2002).
5. S. van der Graaf, M. L. J. Steegmans, R. G. M. van der Sman, C. G. P. H. Schroen, R. M. Boom, Droplet formation in a T-shaped microchannel junction: a model system for membrane emulsification, Colloids and surfaces A: physicochem. Eng. Aspects 226,106(2005).
6. J. Husny, J. J. Cooper-White, The effect of elasticity on drop creation in T-shaped microchannels, J. Non-Newtonian Fluid Mech. 137, 121 (2006).
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