It is a common rule that the strength of the frother is assessed by either its dynamic foamability index (DFI) or its critical coalescence concentration (CCC). The smaller the value of CCC the stronger the frother is. This general rule (CCC rule) however is superficial although being well accepted. Yet, there are critical questions about the performance of the frothers on the bubbles:

1. Are the Gibbs elasticities stemming from the different frothers equally efficient in inhibiting the bubble coalescence?

2. How the Gibbs elasticity control the mean bubble diameter for every specific frother?

3. How the CCC value of the frothers and the mean bubble diameter are related?

This work raises these questions and suggests a rule based on the Gibbs elasticity performance (Gibbs elasticity rule). The performances of seven frothers (PPG 200, PPG 400, PPG 600, BDPG, BTPG, BTEG, and MIBC), whose surface tension isotherms, CCC values, bubble fraction coalescence, and Sauter mean bubble diameter vs. frother concentration were previously studied, were analyzed According to the CCC rule, these frothers follow the order of increasing strength: MIBC≈BTEG < BDPG < PPG 200 < BTPG < PPG 400 < PPG 600. The Gibbs elasticity rule questions what will be the bubble fraction coalescence at a certain fixed value of the Gibbs elasticity of a frother? The above mentioned frothers according to this rule follow the series of PPG 400 < BTPG ≈ BDPG < MIBC ≈ BTEG < PPG 200. Surprisingly, it was established that PPG 600 exhibits abnormal behavior, thus significantly inhibiting the bubble coalescence in a different way, not related to the Gibbs elasticity. For this reason, PPG 600 in the above series was not included. Moreover, correlations between the mean bubble diameter, the Gibbs elasticity, and the CCC value were established. Additionally, a new dimensionless parameter was developed. It estimates the strength of a frother – ζ = ln(Ks.l_CH2/α₀). A Surprising correlation between the CCC values of 21 frothers and their ζ values was developed. Moreover, it was established a correlation allowing us to calculate the bubble fraction coalescence vs. the frother concentration if the CCC value is known.

通常的规则是通过其动态发泡指数 (DFI) 或临界聚结浓度 (CCC) 来评估起泡剂的强度。CCC 值越小，泡沫越强。然而，这个一般规则（CCC 规则）虽然被广泛接受，但还是肤浅的。然而，关于起泡剂在气泡上的性能存在一些关键问题：

1. 不同起泡剂产生的吉布斯弹性在抑制气泡聚结方面是否同样有效？

2. Gibbs 弹性如何控制每个特定起泡剂的平均气泡直径？

3. 起泡剂的 CCC 值与平均气泡直径有什么关系？

这项工作提出了这些问题，并提出了基于吉布斯弹性性能的规则（吉布斯弹性规则）。先前研究了七种起泡剂（PPG 200、PPG 400、PPG 600、BDPG、BTPG、BTEG 和 MIBC）的性能，其表面张力等温线、CCC 值、气泡分数聚结和 Sauter 平均气泡直径与起泡剂浓度的关系，根据 CCC 规则，这些起泡剂遵循强度增加的顺序：MIBC≈BTEG < BDPG < PPG 200 < BTPG < PPG 400 < PPG 600。起泡剂的吉布斯弹性值？根据此规则，上述起泡剂遵循 PPG 400 < BTPG ≈ BDPG < MIBC ≈ BTEG < PPG 200 的系列。令人惊讶的是，已确定 PPG 600 表现出异常行为，从而以不同的方式显着抑制气泡聚结，与吉布斯弹性无关。因此，上述系列中的 PPG 600 不包括在内。此外，建立了平均气泡直径、吉布斯弹性和 CCC 值之间的相关性。此外，还开发了一个新的无量纲参数。它估计起泡剂的强度——ζ  = ln( Ks.l _CH2 / α ₀ )。21 个起泡剂的 CCC 值与其ζ值之间出现了惊人的相关性。此外，如果 CCC 值已知，则建立了相关性，允许我们计算气泡分数聚结与起泡剂浓度的关系。