Fund Project:Project supported by the National Natural Science Foundation of China (Grant No. 11462019) and the Inner Mongolia Graduate Research Innovation Fund, China (Grant No. S2018112002Z)
Received Date:14 March 2020
Accepted Date:21 May 2020
Available Online:12 June 2020
Published Online:20 September 2020
Abstract:In this paper, we observe and record the phenomenon of multi-bubble sonoluminescence in phosphoric acid solution which helium is injected into. It is found that a large number of cavitation bubbles are produced in the solution, which can form bubble groups with different shapes and structures, among them the spherical bubble group is a typical one. By the Rayleigh-Plesset equation of bubble group and any bubble in the group with the combination of van der Waals process equation, we study the variations of the bubble radius, temperature of the bubble, pressure pulse in the groups which are composed, respectively, of the bubbles with the same size and the same gas, the bubbles with the same size and different gases, the bubbles with different sizes and the same gas and the bubbles with different sizes and different gases. The results show that for the bubble group composed of the bubbles with the same size and the same gas and the bubble group composed of the bubbles with the same size and different gases, the gas contained in the bubble has a significant effect on the temperature inside the bubble, but has little effect on the bubble radius and the pressure pulse peak within the cluster. Bubble collapse depth of gas with low molecular weight is deeper than that of gas with high molecular weight, but the radius change of rebound stage is smaller than that of the latter. For the bubble group composed of the bubbles with different sizes and the same gas and the bubble group composed of the bubbles with different sizes and different gases, when the total number of bubbles in a bubble group is constant, for the case where there is only one large bubble in the group, the temperature in the large bubble is the highest, which can be higher than the temperature in a single bubble with the same size and the same gas; with the increase of the number of large bubbles in the group, the temperatures in the large and small bubbles both decrease rapidly: the temperature in the large bubbles approaches to the temperature in the bubbles of the bubble group composed of large bubbles with the same gas and the same size, and the temperature in the small bubble gradually approaches to the temperature in small bubble with the same gas under the radiation of many large bubbles. With the increase of the number of large bubbles, the peak value of the pressure pulse in the bubble group first decreases sharply to the inflection point, and then increases steadily to the peak value of the pressure pulse in the bubble group composed of large bubbles with the same gas and the same size. The proportion of large bubbles number in the bubble group has an important influence on the cavitation characteristics of the bubble group, only when the proportion of large bubbles reaches a certain value, can the bubbles of different sizes in the bubble group collapse at the same time, and this conclusion improve and perfect the previous conclusion. The results of this paper will provide some theoretical guidance and help to further explore the cavitation effect and luminescent mechanism of the bubble group. Keywords:spherical bubble group/ different types of bubbles/ expansion and collapse/ bubble temperature/ pressure in bubble group
表175%磷酸溶液的相关物理参数[22] Table1.Physical parameters of 75% phosphoric acid[22].
23.1.相同尺寸相同气体气泡组成泡群的空化特性
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3.1.相同尺寸相同气体气泡组成泡群的空化特性
为了解由相同尺寸相同气体气泡组成泡群的声空化特性, 选取初始半径为5 μm的氩气气泡和初始半径为5 μm的氦气气泡组成的两种泡群, 并用数值方法绘制了两种泡群的气泡半径变化、径向速度变化、泡内温度变化、泡群半径变化和群内压力变化, 如图2所示. 同时, 为了显示气泡初始半径不同所导致的影响, 图2中也给出了初始半径是10 μm的氩气气泡和初始半径是10 μm的氦气气泡组成的两种泡群的气泡半径变化、径向速度变化、泡内温度变化、泡群半径变化和群内压力变化. 图 2 相同尺寸相同气体气泡组成的四种泡群的声空化特性 (a) 气泡半径变化; (b) 气泡径向速度变化; (c) 气泡崩溃及回弹阶段的半径放大图; (d) 泡群半径变化; (e) 泡群径向速度变化; (f) 气泡内温度变化; (g) 泡群内压力变化 Figure2. Acoustic cavitation characteristics of four kinds of bubble groups composed of same size and same gas bubbles: (a) Change of bubbles radius; (b) change of bubbles radial velocity; (c) magnified figure of bubbles radius at the stage of collapse and rebound; (d) change of bubble group radius; (e) change of bubble groups radial velocity; (f) change of temperature in bubbles; (g) change of pressure in bubble groups.
为了解相同尺寸气泡组成泡群内含有不同气体气泡时, 不同气体气泡对泡群的声空化特性的影响, 本节研究不同气体气泡(氩气和氦气)组成的初始半径为5和10 μm的两种混合泡群. 泡群内气泡总数仍为1000个, 其中氩气气泡和氦气气泡的比例为1∶1. 此时绘制的两种混合泡群的气泡半径变化、径向速度变化、泡内温度变化、泡群半径变化和群内压力变化, 如图3所示. 由图3可看出, 相同尺寸不同气体气泡组成的混合泡群中的气泡振荡规律和泡群振荡规律与图2显示的相同尺寸相同气体气泡组成泡群的变化规律都很相似, 所以这里不再进行分析. 详细比较可知, 两种泡群中的泡内最高温度以及群内最大压力脉冲峰值等都有一些差别, 如10 μm的相同气体泡群和不同气体泡群中的氩气泡内的温度差别约10 K, 氦气泡内的温度差别约6 K, 群内压力脉冲峰值差别约为$ 0.22 P_{0} $(氩气泡)和$0.16 P_{0} $(氦气泡). 在计算中还了解到, 泡群内气泡总数不变的情况下, 改变群内不同气体气泡数的比例对群内气泡的最大膨胀半径、最高温度以及群内的最大压力脉冲的影响也不是很明显. 图 3 相同尺寸不同气体气泡组成的两种混合泡群的声空化特性 (a) 气泡半径变化; (b) 气泡径向速度变化; (c) 气泡崩溃及回弹阶段的半径放大图; (d) 泡群半径变化; (e) 泡群径向速度变化; (f) 气泡内温度变化; (g) 泡群内压力变化 Figure3. Acoustic cavitation characteristics of two kinds of mixed bubble groups composed of same size and different gas bubbles: (a) Change of bubbles radius; (b) change of bubbles radial velocity; (c) magnified figure of bubbles radius at the stage of collapse and rebound; (d) change of bubble group radius; (e) change of bubble groups radial velocity; (f) change of temperature in bubbles; (g) change of pressure in bubble groups.
23.3.不同尺寸相同气体气泡组成的混合泡群的空化特性 -->
3.3.不同尺寸相同气体气泡组成的混合泡群的空化特性
对于不同尺寸气泡组成的泡群来讲, 群内不同尺寸气泡数的比例是影响泡群空化特性的重要因素. 为了解不同尺寸气泡数的比例对泡群内气泡半径变化、泡内温度以及群内压力脉冲变化造成的影响, 研究了10 和5 μm气泡组成的氩气泡群和氦气泡群, 相关结果如图4所示. 由图4(a)可看出, 不管氩气泡群还是氦气泡群, 当大气泡数为1 (小气泡数为999)时, 大气泡内的温度最高, 高于相同初始半径的单泡泡内温度, 接近文献[26]实验测得的大泡泡内温度. 随着大气泡数的增多, 两种泡群中大泡内的最高温度都快速下降, 并逐渐趋近于纯大气泡组成泡群的泡内温度, 即图2(f)所示温度. 这是因为随着大气泡数的增多, 群内气泡的空间分布变得更加密集, 气泡振动受到的抑制作用迅速增强, 气泡崩溃时间延长, 崩溃速度和半径压缩比减小, 导致大气泡内的温度快速下降. 群内大气泡数增加到一定比例之后, 大气泡的声响应逐渐占据主导地位, 整个泡群相当于纯大气泡组成的泡群, 群内大泡内温度平稳趋近于纯大气泡组成泡群的泡内温度. 对于泡群中的小气泡来讲(图4(b)), 开始时由于大气泡很少(1个大气泡), 泡群相当于纯小气泡组成的泡群, 所以泡群中小泡内温度接近于纯小气泡组成泡群的泡内温度, 即图2(f)所示温度. 随着大气泡数的增多, 两种泡群中小泡内的最高温度急速下降, 并达到400 K (氩气泡)和300 K (氦气泡)左右的平稳温度, 即趋近于许多大气泡辐射作用下的单一小气泡泡内温度. 泡群中小泡内最高温度出现这样的变化规律, 主要是因为大泡数的逐渐增加, 群内气泡的空间分布变得愈加密集, 泡群对气泡的抑制和大泡对小泡的辐射作用迅速增强, 使得小泡的振动被有效抑制, 导致小泡泡内温度迅速下降并趋于完全被抑制的小气泡泡内温度. Ida 等[27]研究发现在液体中注入大气泡能够抑制空化的发生与发展, 表明了大泡确实对小泡有很强的抑制作用. 总体上讲, 不管是大气泡还是小气泡, 氩气泡群中的泡内最高温度要高于氦气泡群中的泡内最高温度, 这与我们在声致发光实验中观察到的实验现象相符. 从图4(c)可知, 两种泡群中气泡崩溃时产生的压力脉冲峰值, 随着大气泡数的增多, 先急剧减小, 达到拐点之后平稳增加并逐渐趋近于纯氩气大气泡和纯氦气大气泡组成泡群的压力脉冲峰值, 即图2(g)所示的压力脉冲峰值. 整体上, 在拐点之后氩气泡群中的压力脉冲峰值略高于氦气泡群中的压力脉冲峰值. 图 4 不同尺寸相同气体气泡组成的两种混合泡群的声空化特性 (a) 大泡内最高温度随大气泡数的变化; (b) 小泡内最高温度随大气泡数的变化; (c) 泡群内压力脉冲峰值随大气泡数的变化 Figure4. Acoustic cavitation characteristics of two kinds of mixed bubble groups composed of different size and same gas bubbles: (a) The change of the maximum temperature in the large bubble with the number of large bubbles; (b) the change of the maximum temperature in the small bubble with the number of large bubbles; (c) the change of the peak of pressure pulse with the number of large bubbles in a bubble groups.
对不同尺寸相同气体气泡组成泡群声空化特性的研究基础上, 本节研究不同尺寸(10 和5 μm)不同气体(氩气和氦气)气泡组成的两种混合泡群的声空化特性. 这两种泡群中的第一种是大气泡含氩气、小气泡含氦气的泡群, 第二种是大气泡含氦气、小气泡含氩气的泡群. 研究了两种泡群中大泡泡内最高温度、小泡泡内最高温度以及群内压力脉冲峰值随大气泡数的变化规律, 如图6所示. 可以看出, 图6反映的泡内最高温度和群内压力脉冲变化规律与图4反映的规律基本相同, 不同的是第一种泡群中大泡泡内温度高于第二种泡群中大泡泡内温度, 而第一种泡群中小泡泡内温度低于第二种泡群中小泡泡内温度. 这主要是气泡含有的气体不同导致的. 总体上讲, 在初始半径相同的情况下, 不管是大气泡还是小气泡, 含分子量大的惰性气体气泡的泡内温度要高于含分子量小的惰性气体气泡的泡内温度, 发光也强于后者. 同样, 对泡群中大小气泡数比例不同的情况下, 给出了大小气泡半径和群内压力脉冲随时间的变化规律(图略), 发现大小气泡的半径变化规律和群内压力脉冲变化规律与图5中显示的变化规律相同. 图 6 不同尺寸不同气体气泡组成的两种混合泡群的声空化特性 (a) 大泡内最高温度随大气泡数的变化; (b) 小泡内最高温度随大气泡数的变化; (c) 泡群内压力脉冲峰值随大气泡数的变化 Figure6. Acoustic cavitation characteristics of two kinds of mixed bubble groups composed of different size and different gas bubbles: (a) The change of the maximum temperature in the large bubble with the number of large bubbles; (b) the change of the maximum temperature in the small bubble with the number of large bubbles; (c) the change of the peak of pressure pulse with the number of large bubbles in a bubble groups.