The three-dimensional shape of bubbles in foam; an analysis of the role of surface forces in three-dimensional cell shape determination.
The three-dimensional shape of bubbles in foam; an analysis of the role of surface forces in three-dimensional cell shape determination.
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DOI：
10.1002/j.1537-2197.1946.tb10347.x
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发表时间：
1946
影响因子：
3
通讯作者：
E. B. Matzke
中科院分区：
文献类型：
--
作者：
E. B. Matzke
通过将由特殊肥皂溶液制成的气泡一个接一个地放入圆柱形盘中来构造均匀的泡沫。通过将耶鲁结核菌素注射器的柱塞设定为1/10（或1/20）cc来控制每个气泡的体积，用封闭的空气制造气泡。用这种方法，一个培养皿中充满了近2000个（或4000个）气泡，每个气泡的体积都是相同的。然后用解剖显微镜，通过聚焦，可以挑出这样一团气泡中的任何一个，并精确地记录其表面的数量和种类。泡沫中气泡的确切三维形状多年来一直是数学物理学家（Plateau，Kelvin），植物学家，植物和动物组织学家以及原生质结构学生讨论和推测的主题。以这种方式研究，400个外围（表皮）气泡，其中200个是自由的，200个与圆柱体的壁接触，平均10.99面，范围从7到14。超过一半的表面是五边形，98%是四边形、五边形或六边形。在那些被发现的面孔中，没有一种面孔组合占主导地位，或者可以被认为是“类型”。在所发现的43种面的组合中，最常见的有11种面，其中3种是四边形，6种是五边形，2种是六边形;通常上面有一个六边形面，除了6个侧面接触和4个基底面。这种结合发生了67次，占研究总数的17%。在400个外围气泡中，五角十二面体出现了11次。对泡沫中的外周气泡、外周压缩铅丸和组织中的细胞进行了比较。气泡比子弹或细胞更均匀。细胞表现出更接近的相似性，比周边的气泡，强烈表明，表面力，这是相对更重要的气泡比在拍摄，也明显显着时，细胞形状正在确定。平均面孔数量为10.99个，与刘易斯之前报道的11面表皮细胞一致。600个中心气泡的平均接触数为13.70，范围为11 - 17。在600个泡沫单元中，超过三分之一（218个）有14个面，超过六分之五有13、14或15个触点。超过三分之二的面是五边形，99.6%的面是四边形、五边形和六边形。列表中的600个中央气泡出现在36种不同的面部组合中。与周围气泡一样，没有一种组合是强烈占优势的，可以被认为是“类型”。“最丰富的组合是一个13面的泡沫细胞，其中1个四边形，10个五边形和2个六边形面（1-10-2），在600个泡沫中出现了118次。第二和第三最常见的组合是14面的气泡，1-10-3和2-8-4，分别被发现73次和64次。五角十二面体，有12个面都是五边形，出现了50次。这4种组合占600个气泡中的305个。当大量体积相等的气泡被放入一个圆柱形的盘子中，使它们可以自由地滑动和调整自己时，它们不会呈现开尔文勋爵的正四面体或最小四面体的形式。相反，它们排列成一团有点不规则的泡沫细胞，至少近似地满足高原的平衡条件。在这个系统中，五边形面占主导地位;因此...
A uniform foam was constructed by placing bubbles made of a special soap solution, one by one, into a cylindrical dish. The volume of each bubble was controlled by setting the plunger of a Yale tuberculin syringe at 1/10 (or 1/20) of a cc., and making a bubble with the enclosed air. In this way a dish was filled with nearly 2000 (or 4000) bubbles, each of the same controlled volume. Then with a dissecting microscope it was possible to single out, by focusing, any bubble in such a mass and record with precision the number and kinds of its faces. The exact three-dimensional shape of bubbles in foam has been for many years a subject of discussion and speculation among mathematical physicists (Plateau, Kelvin), metallurgists, plant and animal histologists, and students of protoplasmic structure. Studied in this way, 400 peripheral (epidermal) bubbles, of which 200 were free and 200 in contact with the walls of the cylinder, averaged 10.99 faces, with a range from 7 to 14. More than half of the faces of the pcripheral bubbles were pentagonal, and 98 per cent were quadrilateral, pentagonal, or hexagonal. No one combination of faces among those found strongly predominated or could be considered "the type." The commonest of the 43 combinations of faces which were found had 11 faces, of which 3 were quadrilateral, 6 pentagonal, and 2 hexagonal; there was normally one hexagonal face above, in addition to 6 lateral contacts and 4 basal ones. This combination occurred 67 times and constituted 17 per cent of the total number studied. Pentagonal dodecahedra occurred 11 times among the 400 peripheral bubbles. Comparisons were made between peripheral bubbles in foam, peripheral compressed lead shot, and cells in tissues. The bubbles were more uniform than the shot or than the cells. The cells showed a much closer resemblance to the peripheral bubbles than to the peripheral shot, suggesting strongly that surface forces, which are of relatively greater importance in the bubbles than in the shot, are also distinctly significant when cell shapes are being determined. The average number of faces, 10.99, agreed with 11-faceted epidermal cells previously reported by Lewis. The average number of contacts of 600 central bubbles was 13.70, the range being from 11 to 17. More than a third (218) of the 600 foam cells had 14 faces, and more than five-sixths had 13, 14, or 15 contacts. More than two-thirds of all the faces were pentagonal, and 99.6 per cent of all the faces were quadrilateral, pentagonal, and hexagonal. The 600 central bubbles tabulated occurred in 36 different combinations of faces. As in the peripheral bubbles, there was no one combination of those occurring that was strongly preponderant and that could be considered as "the type." The most abundant combination was a 13-faceted foam cell with 1 quadrilateral, 10 pentagonal, and 2 hexagonal faces (1-10-2) which occurred 118 times among the 600 bubbles. The second and third most frequent combinations were of bubbles with 14 faces, 1-10-3 and 2-8-4, which were found 73 and 64 times, respectively. The pentagonal dodecahedron, with 12 faces all pentagons, occurred 50 times. These 4 combinations accounted for 305 of the 600 bubbles. When a large number of bubbles, all of equal volume, are placed into a cylindrical dish so that they are free to glide and adjust themselves, they do not assume the form of the orthic or of the minimal tetrakaidecahedra of Lord Kelvin. Instead, they become arranged in a mass of somewhat irregular foam cells, satisfying, in approximation at least, the equilibrium conditions of Plateau. In this system pentagonal faces predominate; consequently the …