### 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 |
---|---|

Pages (from-to) | 13837-13844 |

Journal | Langmuir |

Volume | 34 |

Issue number | 46 |

Early online date | 8 Oct 2018 |

DOIs | |

Publication status | Published - 2018 |

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### Cite this

*Langmuir*,

*34*(46), 13837-13844. https://doi.org/10.1021/acs.langmuir.8b02413

}

*Langmuir*, vol. 34, no. 46, pp. 13837-13844. https://doi.org/10.1021/acs.langmuir.8b02413

**Emanating Jets As Shaped by Surface Tension Forces.** / van Rijn, Cees J.M.

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - Emanating Jets As Shaped by Surface Tension Forces

AU - van Rijn, Cees J.M.

PY - 2018

Y1 - 2018

N2 - 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 λc(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 λc(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.

AB - 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 λc(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 λc(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.

U2 - 10.1021/acs.langmuir.8b02413

DO - 10.1021/acs.langmuir.8b02413

M3 - Article

VL - 34

SP - 13837

EP - 13844

JO - Langmuir

JF - Langmuir

SN - 0743-7463

IS - 46

ER -