## Abstract

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}/α_{0}). 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.

Original language | English |
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Article number | 107093 |

Journal | Minerals Engineering |

Volume | 171 |

DOIs | |

Publication status | Published - 1 Sept 2021 |

### Bibliographical note

Publisher Copyright:© 2021 The Author(s)

### Funding

This paper is supported by European Union’s Horizon 2020 research and innovation program under grant agreement No. 821265, project FineFuture (Innovative technologies and concepts for fine particle flotation: unlocking future fine-grained deposits and Critical Raw Materials resources for the EU). This paper is supported by European Union's Horizon 2020 research and innovation program under grant agreement No. 821265, project FineFuture (Innovative technologies and concepts for fine particle flotation: unlocking future fine-grained deposits and Critical Raw Materials resources for the EU).

Funders | Funder number |
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Horizon 2020 Framework Programme | |

European Commission | |

Horizon 2020 | 821265 |

## Keywords

- Critical coalescence concentration (CCC)
- Frother
- Gibbs elasticity
- Mean bubble diameter