实验室研究与探索 2017 , 36 (5): 28-31

实验技术

球体在肥皂泡体中的运动

王心华, 金武, 李博斌, 盛英卓

兰州大学物理科学与技术学院, 兰州 730000

A Study on the Movement of the Sphere in Soap Bubbles

WANG Xinhua, JIN Wu, LI Bobin, SHENG Yingzhuo

School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, China

中图分类号: O351.2

文献标识码: A

文章编号: 1006-7167(2017)05-0028-04

收稿日期: 2016-09-12

网络出版日期: 2017-05-20

基金资助: 中央高校基本科研业务费专项资金项目(lzujbky-2016-117)

作者简介:

作者简介:王心华(1979-)男,青海海东人, 实验师,从事大学物理实验教学及磁性纳米材料研究。Tel.:18919999598; E-mail:xhwang@lzu.edu.cn

展开

摘要

肥皂泡体作为非线性流体,对于外界的作用有着极其复杂的非线性响应。研究肥皂泡体中运动物体的动力学行为能够解释和解决生产和生活中的很多相关问题。通过理论建模、实验设计和数值模拟对于小而轻且与肥皂泡大小相差不大的球体在与肥皂泡体中的运动过程进行研究。首先从统计力学的系综角度给出了三维肥皂泡体动力学行为的理论解释,再从实验上验证了在重力场作用下,小球在肥皂泡中的动力学行为关系式,具有普遍性。

关键词： 重力场 ; 肥皂泡体 ; 球体 ; 统计描述

Abstract

The soap bubble, as a nonlinear fluid, has a very complex non-linear response to external actions. This paper attempts to give a theoretical explanation to this process by a small and light sphere which has similar size of soap bubble and travels in suds, from the view point of statistics. The experiments show that the original description thought is reasonable.

Keywords： gravity field ; soap bubbles ; spheres ; statistical description

PDF (906KB) 元数据多维度评价相关文章收藏文章

本文引用格式导出 EndNote Ris Bibtex

王心华, 金武, 李博斌, 盛英卓. 球体在肥皂泡体中的运动[J]. , 2017, 36(5): 28-31 https://doi.org/

WANG Xinhua, JIN Wu, LI Bobin, SHENG Yingzhuo. A Study on the Movement of the Sphere in Soap Bubbles[J]. 实验室研究与探索, 2017, 36(5): 28-31 https://doi.org/

0 引言

肥皂泡体类似于普通的流体,但又有普通流体无法相比拟的特性。近年来,肥皂泡体常用于粉体矿物分离、消防器材、工业清洁、交通工具的生产和油井中原油的回收等^[1-5]。同时,肥皂泡体作为复杂流体介质的典型例子,普遍受到国内外理论研究领域的关注,尤其是肥皂泡体对其中运动物体的动力学行为的影响^[6-10]。然而,肥皂泡体作为非线性流体,其对于外界的作用有着极其复杂的非线性响应,从而导致动力学系统近乎无规律的随时演化行为,这是肥皂泡体对动力学系统的影响描述的困难所在。对此无序三维肥皂泡体的研究,国内外的研究人员大多并未从理论上进行系统的描述,而是从实验的角度,采取唯象的研究策略,从而得到描述三维肥皂泡体对动力学的经验关系^[11-13]。本文论述了在重力场作用下球体在肥皂泡体中的运动现象,从统计力学的系综角度上给出理论的解释,并从实验上证明其合理性。

1 理论分析

由于肥皂泡体结构的复杂性,而本文研究的对象是肥皂泡体中和肥皂泡大小差不多的小而轻的球体在重力场中的运动,这导致系统更加复杂。面对如此复杂的过程,我们放弃对于小球在肥皂泡体之中的精确运动描述,转而从统计的系综角度描述小球在肥皂泡体之中的运动。

肥皂泡因其内部含水量的不同而呈现完全迥异的形态和完全不同的物理特性。在此引入物理量液相比Φ,定义:

$\begin{matrix} \frac{1}{3} Φ = \frac{σ_{f}}{σ_{l}} \end{matrix}$

其中:σ_f是肥皂泡体的传导性度量;σ_l是流体中无气体时的传导性^[14]。

肥皂泡具有独特的可以发生形变和流动的网状结构(见图1);而肥皂泡体是具有弹性体与流体双重结构的连续媒质。所以把小球在肥皂泡中的受力分为由泡沫的网状结构和黏滞作用两大类因素引起。这也是肥皂泡体对其中运动小球的相互作用的基本分类。

显示原图| 下载原图ZIP| 生成PPT

图1 肥皂泡网状结构

由肥皂泡体的物理特性分析可直接得到,小球在肥皂泡氛围之中的受力分为黏滞作用和弹性作用。黏滞作用一般同流体一样,与小球下落的速度成幂次关系;弹性作用源于肥皂泡的网络结构形变,与小球下落速度无关,即该作用是单向的。小球的动力学行为不会影响肥皂泡,首先得到量化关系:

$\begin{matrix} \begin{matrix} F = F_{o} + χ (R, Φ, A, r) v^{n}, mg > F_{0} (1) \\ v = 0, mg \leq F_{o} (2) \end{matrix} \end{matrix}$

式中:F为小球所受到肥皂泡体的总作用;F₀是肥皂泡体由于网络结构形变而引起的弹性作用;χ·vⁿ项为小球受到的黏滞作用。由分析可知,χ·vⁿ项中的χ系数必定与小球的半径R,表面浸润性A,肥皂泡体中肥皂泡的平均半径r,液相比Φ等相关。而式(2)表示当小球的重力小于F₀时,小球将被肥皂泡体撑住而无法下落。

进一步对弹性作用分析可知,弹性作用由两部分组成,即由肥皂泡壁的表面张力的净合力和球接触的气泡内的挤压净合力组成(见图2)。

显示原图| 下载原图ZIP| 生成PPT

图2 肥皂泡受力情况

对于二维气泡壁的净合力的经验关系为^[15]:

$\begin{matrix} F_{0}^{n} = \frac{0.516}{Φ^{\frac{1}{4}}} \frac{μ (σ, siz e_{气泡}) siz e_{障碍物}}{\sqrt{\overset{a_{气泡}}{are}}} \end{matrix}$

对于研究的三维情况,由于物理情形的相似性,将其直接推广为:

$\begin{matrix} {F^{n}}_{0} = \frac{const}{Φ^{\frac{1}{4}}} \frac{σR}{r} (3) \end{matrix}$

而对于气泡内的净挤压合力,选取球坐标积分,面元方向为外法向,得:

$\begin{matrix} {\bar{F}}^{P}_{0} = - ∯_{球面} P d \bar{s} (4) \end{matrix}$

由于球体周围气泡内的气压分布极其复杂,故由统计系统的角度考虑,小球表面的气压分布可用模型替换,

$\begin{matrix} \begin{matrix} P (θ, φ) = & P (θ) = \\ (P_{0} + \frac{4 σ}{r}) \frac{2 n_{o} + 1 - cosθ}{2 n_{o}} (5) \end{matrix} \end{matrix}$

该模型表明球表面的气压分布只与θ方向有关,而与φ向无关,气压的变化是余弦型,且在小球下面的气泡的内压比球上大出1/n₀。其中,P₀为肥皂泡体所处大气压。由

$\begin{matrix} \begin{matrix} {\bar{F}}^{P}_{0} = - ∯ P (θ) (sinθcosφ \bar{i} + sinθsinφ \bar{j} + \\ cosθ \bar{k}) R^{2} sinθdθdφ \end{matrix} \end{matrix}$

积分可得

$\begin{matrix} {\bar{F}}^{P}_{0} = \frac{2 R^{2}}{3 n_{0}} (P_{0} + \frac{4 σ}{r}) π \bar{k} \end{matrix}$

到此,可以得到由式(1)、(2)小球在肥皂泡体的动力学方程:

m $\begin{matrix} \frac{d^{2} \bar{r}}{d^{2} t} \end{matrix}$ = $\begin{matrix} \bar{F} \end{matrix}$ -mg $\begin{matrix} \bar{k} \end{matrix}$ =

$\begin{matrix} ({\bar{F}}_{0} - χ {(\frac{dr}{dt})}^{n - 1} (\frac{d \bar{r}}{dt})) \end{matrix}$ -mg $\begin{matrix} \bar{k} \end{matrix}$ (6)

此时选取小球的出发点为坐标原点,则初始条件为:

$\begin{matrix} \bar{r} = 0, \frac{d \bar{r}}{dt} = 0 \end{matrix}$

式中: $\begin{matrix} \overset{̅}{r} \end{matrix}$ 为球心的位置矢量。而肥皂泡体的弹性阻力为:

$\begin{matrix} F_{0} = {\bar{F}}^{n}_{0} + {\bar{F}}^{P}_{0} \end{matrix}$

小球在重力场中运动与坐标x以及y方向无关,所以可认为肥皂泡体给小球的作用只在于坐标正z方向,则由式(3)~(5)得:

$\begin{matrix} F_{0} = (\frac{const}{Φ^{\frac{1}{4}}} \frac{Rσ}{r} + \frac{2 R^{2} π}{2 n_{0}} (P_{0} + \frac{4 σ}{r})) \bar{k} (7) \end{matrix}$

因为与F₀相关的参数在特定环境下不变,与小球的速度等均无关。可见F₀在特定的实验环境之下是一个不变的矢量。而对于小球的动力学方程(6),其有级数形式的解析解。但是这种解的证伪过程将给实验带来诸多困难。但是仔细分析式(6)中的各项,可知其演化的解的形式必定为一个稳定解。在物理过程上表现为,当小球下落时间足够长时,小球在肥皂泡体中匀速下降,此时方程(6)的加速项为零,简化为代数方程,可直接解出小球在肥皂泡体之中下落的最终速度v_max满足:

$\begin{matrix} mg = F_{0} + χ v_{\max}^{n} (8) \end{matrix}$

2 实验验证

为了验证以上理论分析的正确性,实验上只需验证理论分析的最终结论式(8)所描述的关系。实际小球在运动时,式(6)所描述的加速阶段的持续时间是非常短的。所以实验上观察到的现象多为小球稳定之后的状态,即式(8)所描述的情况。

根据式(8),由分析知F₀只与小球的半径有关,控制球的半径和材质以及肥皂泡的特性不变。改变球的质量,测量球的终速。由于最终球将匀速下落,由 z = vt可得,测量小球运动等间距z时所用的时间t,从而测定v_max。

2.1 器材

研究器材有泡沫塑料小球(参数见表1)、标准计时器、大口径量筒(内径5.5 cm )、米尺、起泡剂(甘油,蒸馏水,液态洗涤剂)、蒸馏水。

表1 小球的参数

	编号
	1	2	3	4	5
质量/g	0.138 0	0.156 8	0.213 9	0.255 4	0.313 7
直径/cm	1.00±0.01

新窗口打开

2.2 实验方案

使用流量为50 mL/min氮气由口径1 mm的通气孔充入以体积比V_甘油∶ V_蒸馏水∶V_洗涤剂≈ 14∶72∶14的盛入量筒的起泡剂中。小球从液面以v = 0自由下落,在量筒A、B、C、D、E处安置光电门(见图3),用来多次重复测量小球等间距的经过AB、BC、CD、DE的时间值,然后对大量的数据进行平均。当D_内径≈ 5.5 cm > 2d_球时,小球在肥皂泡中的行为受到边界的影响微乎其微,可不予考虑^[16]。

显示原图| 下载原图ZIP| 生成PPT

图3 实验装置

2.3 结论分析

表2中,t_AB 、t_BC、t_CD、t_DE分别为对各小球下落过程进行了20次实验后,对小球经过AB、BC、CD、DE的时间进行统计平均的数据,其中,涂以颜色的表格是小球匀速运动的区域。v_max代表小球达到匀速运动后获得的最大速度。

表2 统计平均之后所得到的实验值

球	t_AB /s	t_BC /s	t_CD /s	t_DE /s	v_max/(cm·s^-1)
1号	3.3	2.0	2.1	1.9	3.75
2号	2.4	2.7	1.7	1.7	4.41
3号	1.7	1.5	1.1	1.2	6.52
4号	0.7	0.6	0.5	0.6	13.24
5号	0.3	0.4	0.4	0.4	18.75

新窗口打开

将实验数据依据式(8)在Matlab中使用非线性最小二乘法进行拟合,得到如图4的关系。从图中可以看出,若将实际的测量误差按照保守估计,则0.462 < n < 1的范围内,理论关系式与实验是相符合的。

显示原图| 下载原图ZIP| 生成PPT

图4 v_max-m实验数据与拟合图

为了进一步验证理论关系的正确性,n分别取0.462、0.47、0.50、0.60、0.70进行拟合,得到如图5所示的结果。从图中可以看出,拟合方程形式的最大范围为0.462 < n < 1。

显示原图| 下载原图ZIP| 生成PPT

图5 不同n值时v_max-m实验数据与拟合图

表3给出了n取不同值时,式(8)中系数F₀/ g和 χ / g的取值。

表3 不同n下F₀和 χ的取值

n	F₀/ g	χ / g
< 0.462	< 0	-
0.462	0.000 334 4	0.080 450 0
0.470	0.004 022 0	0.077 680 0
0.500	0.016 780 0	0.068 270 0
0.600	0.049 930 0	0.045 400 0
0.700	0.073 390 0	0.030 980 0
1.000	0.114 700 0	0.010 800 0

新窗口打开

从图4、5可以看出,当改变拟合理论关系中的未知参量n时,得到几乎重合的拟合方程。表4为n取不同数值时,实验参数和拟合曲线的均方误差。从表4可见,当n位于区间0.465~1之间时,实验数据与拟合方程之间的差距非常小,而且各n值对应的均方误差同样非常接近。这说明在给定的实验条件之下的肥皂泡体与球体的黏滞阻力关系呈现指数小于1的非线性关系。但对于具体的n值,可能像临界雷诺数一样是一个范围而非一个固定的值。

表4 不同n值时,实验参数和拟合曲线的均方误差

编号	n	均方误差
1	< 0.461 5	-
2	0.461 5	0.015 5
3	0.470 0	0.015 6
4	0.480 0	0.015 7
5	0.490 0	0.015 7
6	0.500 0	0.158 0
7	0.500 0	0.016 5
8	0.500 0	0.020 0
9	> 2.000 0	> 0.030 0

新窗口打开

将实际测量的误差放到最大,则依据拟合方程(8)可以推导出当n = 1时, $\begin{matrix} {F_{0}}^{n} \end{matrix}$ < $\begin{matrix} {F_{0}}^{1} \end{matrix}$ =m_临界=0.11 g,此时小球在肥皂泡中无法运动。在实验中,也观察到m=0.106 5 g的泡沫塑料球在肥皂泡中无法运动。而标号球m=0.138 0 g的泡沫塑料球可以运动。这正好从实验上说明了理论的正确性。

3 结语

综上所述,通过理论建模、实验验证及数据模拟3种方式对小球在肥皂泡中的运动研究,得出了重力场作用下,小球在肥皂泡中运动的理论关系式,该式在0.462 < n < 1范围内具有普通普遍性。本文所得出的结论弥补了三维肥皂泡体研究的理论解释,对肥皂泡体中运动物体动力学行为的研究有着重要的实际意义。但本工作对 n > 1的情况研没有得出很好的结论,对n > 1的情况下,小球在肥皂泡的运动规律的研究同样具有不可估量的价值。

The authors have declared that no competing interests exist.

参考文献

原文顺序

文献年度倒序

文中引用次数倒序

被引期刊影响因子

[1]	郭平波. 肥皂泡筏中的力律与肥皂泡半径的关系 [D]. 重庆:重庆大学, 2008. [本文引用: 1]
[2]	张力,卢乾波,石戈. 实验验证肥皂膜与肥皂泡的两个物理特性 [J]. 大学物理实验,2013,26(1):55-58. DOI:10.3969/j.issn.1007-2934.2013.01.018 URL 摘要为了验证对称双漏斗肥皂膜实验在肥皂膜腰部半径自动变细之前的整个过程中肥皂膜的形状始终满足最小表面能原理,采用了四对半径不同的漏斗分别进行验证,利用FastStone Capture[1]软件对每种情况下的腰部半径随漏斗间距变化关系进行测量.通过拟合理论曲线与构建四种情况下分别对应的离散点,从而验证了这样一个结论:肥皂膜的形状在稳定区以内均满足最小表面能原理.此外,为了验证大小肥皂泡连通前后的半径关系,使用简易三通管,并使用 FastStoneCapture软件,测量了五次独立重复实验的数据.最后得到与理论计算相比较低误差的实验结果,从而验证了大小肥皂泡连通前后满足体积相加性.
[3]	游少平. 肥皂泡与建筑 [J]. 华中建筑,2008,26:20-23.
[4]	冷文秀,胡家晨,张鑫杰,等. 肥皂泡的光学和力学性质 [J]. 物理实验,2013,33(2):29-33.
[5]	唐玄之,王琦,魏良淑,等. 大小肥皂泡联通后的讨论与计算 [J]. 大学物理,2007,26(10):20-23. DOI:10.3969/j.issn.1000-0712.2007.10.007 URL [本文引用: 1] 摘要从弯曲液面附加压强、气体状态方程以及"球缺"的有关公式等出发,对大小肥皂泡连通后的变化作了全面的阐释,导出了最后大泡半径的近似公式,还介绍了演示实验,拍得了3个泡的照片,测出了它们的半径,验证了这个近似公式.并对产生误差的原因作了分析.
[6]	Hassan A, Dmitri L Vainchtein. The equation of state of a foam [J]. Physics of Fluids, 2000, 12(1):23-28. DOI:10.1063/1.870281 URL [本文引用: 1] 摘要 The equation of state of a dry foam with ideal gas in the bubbles, proposed by Ross, is proved. This equation suggests that a foam with a free boundary will expand to a maximum volume if the external pressure is lowered at constant temperature. The same foam enclosed in a container, on the other hand, can be expanded further but, as the volume is increased, will eventually become unstable. We speculate that this instability leads to a “bubble differentiation” transition of the kind observed by Herdtle in numerical simulations of two-dimensional foam with ideal gas in the bubbles. In the simulations the foam separated into two “phases,” one with a large number of small bubbles, another with a small number of very large bubbles.
[7]	Vainchteina D L, Arefb H. Morphological transition in compressible foam [J]. Physics of Fluids, 2001, 13(8):2152-2160. DOI:10.1063/1.1384881 URL 摘要 A theory is constructed to describe the morphological transition that occurs in a compressible foam when its volume is increased. The foam is observed to separate into two bubble populations or “phases,” one consisting of a large number of small bubbles, the “liquid” phase, the other consisting of a small number of large bubbles, the “gaseous” phase. First, working along lines similar to the van der Waals theory for a fluid system, approximate forms of the equation of state of the foam are derived and explored. These describe the weakly compressible range well, but fail to capture the nature of the transition. Taking a clue from the phenomenology, a theory of the “phase-separated” regime is then formulated working with the approximation that the two phases into which the foam separates are each relatively homogeneous. The successful single-phase formulas are applied to each phase, introducing an additional “order parameter” which gives the ratio of the average size of bubbles in the two phases. Approximate expressions are written for the Helmholtz free energy and the equilibria of the foam derived from these. The theory is compared to numerical simulations usingSURFACE EVOLVERwith very satisfying results. The transition from a uniform to a nonuniform configuration consists of avalanches of reconnections with smooth evolution between them. Hysteresis is observed as the foam is first expanded and then compressed.
[8]	Saugey A, Drenckhan W, Weaire D. Wall slip of bubbles in foams [J]. Physics of Fluids, 2006, 18,053101:1-12.
[9]	Jose' A Zapataa. Continuum spin foam model for 3d gravity [J]. Journal of Mathematical Physics, 2002, 43(11):5612-5623. DOI:10.1063/1.1509850 URL 摘要 An example illustrating a continuum spin foam framework is presented. This covariant framework induces the kinematics of canonical loop quantization, and its dynamics is generated by arenormalizedsum over colored polyhedra. Physically the example corresponds to 3d gravity with cosmological constant. Starting from a kinematical structure that accommodates local degrees of freedom and does not involve the choice of any background structure (e.g., triangulation), the dynamics reduces the field theory to have only global degrees of freedom. The result isprojectivelyequivalent to the Turaev iro model.
[10]	Davies I T, Cox S J. Sedimenting discs in a two-dimensional foam [J]. Colloids and Surfaces A: Physicochem Eng Aspects, 2009, 344:8-14. DOI:10.1016/j.colsurfa.2008.11.056 URL [本文引用: 1] 摘要 The sedimentation of circular discs in a dry two-dimensional, monodisperse foam is studied. This, a variation of the classical Stokes experiment, provides a prototype experiment to study a foam response. The interaction between two circular particles of equal size and weight is investigated as they fall through the foam under their own weight. Their positions are tracked and the lift and drag force measured in numerical calculations using the Surface Evolver. The initial placements of the discs are varied in each of two different initial configurations, one in which the discs are side by side and the second in which the discs are one above the other. It is shown that discs that are initially side-by-side rotate as a system during the descent in the foam. In the second scenario, the upper disc falls into the wake of the lower, after which the discs sediment as one with a constant non-zero separation. We present evidence that the foam screens this interaction for specific initial separations between the discs in both configurations. The force between a channel wall and a nearby sedimenting disc is also investigated.
[11]	Besson S, Debre'Geas G. Dissipation in a sheared foam: From bubble adhesion to foam rheology [J]. Physical Review Letter, 2008, 101,214504: 1-4. DOI:10.1103/PhysRevLett.101.214504 URL PMID: 19113415 [本文引用: 1] 摘要 The link between the rheology of 3D aqueous foam and the adhesion of neighboring bubbles is tested by confronting experiments at two different length scales. On the one hand, the dynamics of adhesion are probed by measuring how the shape of two bubbles in contact changes as their center-to-center distance is modulated. On the other hand, the linear viscoelastic behavior of 3D foam prepared with the same soapy solution is characterized by its complex shear modulus. To connect the two sets of data, we present a model of foam viscoelasticity taking into account bubble adhesion.
[12]	Taccoen N, Lequeux F, Gunes D Z, et al. Probing the mechanical strength of an armored bubble and its implication to particle-stabilized foams [J]. Physical Review X, 2016, 6,011010: 1-11. DOI:10.1103/PhysRevX.6.011010 URL 摘要 Bubbles are dynamic objects that grow and rise or shrink and disappear, often on the scale of seconds. This conflicts with their uses in foams where they serve to modify the properties of the material in which they are embedded. Coating the bubble surface with solid particles has been demonstrated to strongly enhance the foam stability, although the mechanisms for such stabilization remain mysterious. In this paper, we reduce the problem of foam stability to the study of the behavior of a single spherical bubble coated with a monolayer of solid particles. The behavior of this armored bubble is monitored while the ambient pressure around it is varied, in order to simulate the dissolution stress resulting from the surrounding foam. We find that above a critical stress, localized dislocations appear on the armor and lead to a global loss of the mechanical stability. Once these dislocations appear, the armor is unable to prevent the dissolution of the gas into the surrounding liquid, which translates into a continued reduction of the bubble volume, even for a fixed overpressure. The observed route to the armor failure therefore begins from localized dislocations that lead to large-scale deformations of the shell until the bubble completely dissolves. The critical value of the ambient pressure that leads to the failure depends on the bubble radius, with a scaling of Pcollapse 1, but does not depend on the particle diameter. These results disagree with the generally used elastic models to describe particle-covered interfaces. Instead, the experimental measurements are accounted for by an original theoretical description that equilibrates the energy gained from the gas dissolution with the capillary energy cost of displacing the individual particles. The model recovers the short-wavelength instability, the scaling of the collapse pressure with bubble radius, and the insensitivity to particle diameter. Finally, we use this new microscopic understanding to predict the aging of particle-stabilized foams, by applying classical Ostwald ripening models. We find that the smallest armored bubbles should fail, as the dissolution stress on these bubbles increases more rapidly than the armor strength. Both the experimental and theoretical results can readily be generalized to more complex particle interactions and shell structures.
[13]	Burnett G D, Chae J J, Tam W Y. Structure and dynamics of breaking foams [J]. Physical Review E, 1995, 51(6):5788-5796. DOI:10.1103/PhysRevE.51.5788 URL PMID: 9963315 [本文引用: 1] 摘要 ABSTRACT Experimental results are presented for the relaxation of a two dimensional soap foam in which wall breakage is initiated through gentle warming of the foam cell. Significantly different phenomenology from the relaxation of nonbreaking foams is observed. At a critical ‘‘break time,’’ which depends on the temperature ramping rate and initial conditions, a large scale mechanical cascade of wall rupture sets in, leading to a rapid disintegration of the foam. In the cascade regime, whose behavior is essentially independent of the ramping rate, a dynamical scaling behavior, associated with the distribution of cell edge lengths, is proposed.
[14]	Weaire D, Phelan R. The physics of foam [J]. Journal of Physics Condensed Matter, 1999, 47(8):9519-9524. [本文引用: 1]
[15]	Dollet B,Elias F,Quilliet C M, et al. Aubouy two-dimensional flow of foam around an obstacle: Force measurements [J]. Physical Review E Statistical Nonlinear & Soft Matter Physics, 2005, 71:142-154. DOI:10.1103/PhysRevE.71.031403 URL PMID: 15903427 [本文引用: 1] 摘要 Abstract: A Stokes experiment for foams is proposed. It consists in a two-dimensional flow of a foam, confined between a water subphase and a top plate, around a fixed circular obstacle. We present systematic measurements of the drag exerted by the flowing foam on the obstacle, \emph{versus} various separately controlled parameters: flow rate, bubble volume, bulk viscosity, obstacle size, shape and boundary conditions. We separate the drag into two contributions, an elastic one (yield drag) at vanishing flow rate, and a fluid one (viscous coefficient) increasing with flow rate. We quantify the influence of each control parameter on the drag. The results exhibit in particular a power-law dependence of the drag as a function of the bulk viscosity and the flow rate with two different exponents. Moreover, we show that the drag decreases with bubble size, and increases proportionally to the obstacle size. We quantify the effect of shape through a dimensioned drag coefficient, and we show that the effect of boundary conditions is small.
[16]	John R, de Bruyn. Transient and steady-state drag in foam [J]. Rheologica Acta, 2004, 44(2):150-159. DOI:10.1007/s00397-004-0391-6 URL Magsci [本文引用: 1] 摘要 The steady-state force exerted on a sphere moving at constant speed through an aqueous foam is studied experimentally. The dependence of the force on container size indicates that the moving sphere is surrounded by a fluidised region that extends approximately one sphere radius into the foam. The force increases with the speed of the sphere, but with a finite zero-speed intercept which is a measure of the yield stress of the foam. The steady-state force as a function of pulling speed yields a flow curve which can be described by a Herschel-Bulkley constitutive relation. The transient build-up of the force when motion starts, and its relaxation when motion stops, are also studied. While the initial build-up has a single time constant inversely proportional to the imposed shear rate, the relaxation involves three distinct processes which we relate to events on the scale of the individual bubbles making up the foam.

肥皂泡筏中的力律与肥皂泡半径的关系

2008

... 肥皂泡体类似于普通的流体,但又有普通流体无法相比拟的特性.近年来,肥皂泡体常用于粉体矿物分离、消防器材、工业清洁、交通工具的生产和油井中原油的回收等^[1-5].同时,肥皂泡体作为复杂流体介质的典型例子,普遍受到国内外理论研究领域的关注,尤其是肥皂泡体对其中运动物体的动力学行为的影响^[6-10].然而,肥皂泡体作为非线性流体,其对于外界的作用有着极其复杂的非线性响应,从而导致动力学系统近乎无规律的随时演化行为,这是肥皂泡体对动力学系统的影响描述的困难所在.对此无序三维肥皂泡体的研究,国内外的研究人员大多并未从理论上进行系统的描述,而是从实验的角度,采取唯象的研究策略,从而得到描述三维肥皂泡体对动力学的经验关系^[11-13].本文论述了在重力场作用下球体在肥皂泡体中的运动现象,从统计力学的系综角度上给出理论的解释,并从实验上证明其合理性. ...

实验验证肥皂膜与肥皂泡的两个物理特性

2013

肥皂泡与建筑

2008

肥皂泡的光学和力学性质

2013

大小肥皂泡联通后的讨论与计算

2007

The equation of state of a foam

2000

Morphological transition in compressible foam

2001

Wall slip of bubbles in foams

2006

Continuum spin foam model for 3d gravity

2002

Sedimenting discs in a two-dimensional foam

2009

Dissipation in a sheared foam: From bubble adhesion to foam rheology

2008

Probing the mechanical strength of an armored bubble and its implication to particle-stabilized foams

2016

Structure and dynamics of breaking foams

1995

The physics of foam

1999

... 其中:σ_f是肥皂泡体的传导性度量;σ_l是流体中无气体时的传导性^[14]. ...

Aubouy two-dimensional flow of foam around an obstacle: Force measurements

2005

... 对于二维气泡壁的净合力的经验关系为^[15]: ...

Transient and steady-state drag in foam

2004

... 使用流量为50 mL/min氮气由口径1 mm的通气孔充入以体积比V_甘油∶ V _蒸馏水∶V_洗涤剂≈ 14∶72∶14的盛入量筒的起泡剂中.小球从液面以v = 0自由下落,在量筒A、B、C、D、E处安置光电门(见图3),用来多次重复测量小球等间距的经过AB、BC、CD、DE的时间值,然后对大量的数据进行平均.当D_内径≈ 5.5 cm > 2d_球时,小球在肥皂泡中的行为受到边界的影响微乎其微,可不予考虑^[16]. ...

〈

〉

球体在肥皂泡体中的运动

A Study on the Movement of the Sphere in Soap Bubbles

0 引 言

1 理论分析

2 实验验证

2.1 器 材

2.2 实验方案

2.3 结论分析

3 结 语

参考文献 文献选项 原文顺序 文献年度倒序 文中引用次数倒序 被引期刊影响因子

0 引言

2.1 器材

3 结语

参考文献

原文顺序

文献年度倒序

文中引用次数倒序

被引期刊影响因子