Emanating Jets As Shaped by Surface Tension Forces

Cees J.M. van Rijn*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

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 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.

Original languageEnglish
Pages (from-to)13837-13844
JournalLangmuir
Volume34
Issue number46
Early online date8 Oct 2018
DOIs
Publication statusPublished - 2018

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Surface tension
interfacial tension
towers
Towers
coffee
Coffee
Laplace equation
Liquids
liquids
hydrostatics
Gravitation
bubbles
Boundary conditions
boundary conditions
gravitation
Fluids
Water
fluids
water
Experiments

Cite this

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title = "Emanating Jets As Shaped by Surface Tension Forces",
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 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.",
author = "{van Rijn}, {Cees J.M.}",
year = "2018",
doi = "10.1021/acs.langmuir.8b02413",
language = "English",
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}

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

In: Langmuir, Vol. 34, No. 46, 2018, p. 13837-13844.

Research output: Contribution to journalArticleAcademicpeer-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.

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DO - 10.1021/acs.langmuir.8b02413

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JO - Langmuir

JF - Langmuir

SN - 0743-7463

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