## Abstract

We show that emanating jets can be regarded as growing liquid towers, which are shaped by the twofold action of surface tension: first the emanated fluid is being accelerated back by surface tension force, herewith creating the boundary conditions to solve the shape of the liquid tower as a solution of an equation mathematically related to the hydrostatic Young-Laplace equation, known to give solutions for the shape of pending and sessile droplets, and wherein the only relevant forces are gravity g and surface tension γ. We explain that for an emanating jet under specific constraints all mass parts with density ρ will experience a uniform time dependent acceleration a(t). An asymptotic solution is subsequently numerically derived by making the corresponding Young-Laplace type equation dimensionless and by dividing all lengths by a generalized time dependent capillary length λ_{c}(t) = γ(t)/ρ(a(t)-g). The time dependent surface tension γ(t) can be derived by measuring both time dependent acceleration a(t) and time dependent capillary length λ_{c}(t). Jetting experiments with water and coffee show that the dynamic surface tension behavior according to the emanating jet method and with the well-known maximum bubble pressure method are the same, herewith verifying the proposed model.

Original language | English |
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Pages (from-to) | 13837-13844 |

Journal | Langmuir |

Volume | 34 |

Issue number | 46 |

Early online date | 8 Oct 2018 |

DOIs | |

Publication status | Published - 2018 |