Thermocapillary motion of a Newtonian drop in a dilute viscoelastic fluid

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Abstract

In this work we investigate the role played by viscoelasticity on the thermocapillary motion of a deformable Newtonian droplet embedded in an immiscible, otherwise quiescent non-Newtonian fluid. We consider a regime in which inertia and convective transport of energy are both negligible (represented by the limit condition of vanishingly small Reynolds and Marangoni numbers) and free from gravitational effects. A constant temperature gradient is maintained by keeping two opposite sides of the computational domain at different temperatures. Consequently the droplet experiences a motion driven by the mismatch of interfacial stresses induced by the non-uniform temperature distribution on its boundary. The departures from the Newtonian behaviour are quantified via the “thermal” Deborah number, De T and are accounted for by adopting either the Oldroyd-B model, for relatively small De T, or the FENE-CR constitutive law for a larger range of De T. In addition, the effects of model parameters, such as the concentration parameter c=1−β (where β is the viscoelastic viscosity ratio), or the extensibility parameter, L 2, have been studied numerically using a hybrid volume of fluid-level set method. The numerical results show that the steady-state droplet velocity behaves as a monotonically decreasing function of De T, whilst its shape deforms prolately. For increasing values of De T, the viscoelastic stresses show the tendency to be concentrated near the rear stagnation point, contributing to an increase in its local interface curvature.

Original languageEnglish
Pages (from-to)8-22
Number of pages15
JournalJournal of Non-Newtonian Fluid Mechanics
Volume270
Early online date18 Jun 2019
DOIs
Publication statusPublished - 31 Aug 2019

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Viscoelastic Fluid
Droplet
Fluids
Motion
fluids
Gravitational effects
Stagnation Point
gravitational effects
stagnation point
Viscoelasticity
Level Set Method
Constitutive Law
Non-Newtonian Fluid
viscoelasticity
Temperature Distribution
inertia
Inertia
Thermal gradients
temperature gradients
Viscosity

Keywords

  • thermocapillary migration,
  • droplet dynamics
  • viscoelastic effects
  • level set-volume of fluid

Cite this

@article{62752ad2beab4b11ab7808fc155b8c8a,
title = "Thermocapillary motion of a Newtonian drop in a dilute viscoelastic fluid",
abstract = "In this work we investigate the role played by viscoelasticity on the thermocapillary motion of a deformable Newtonian droplet embedded in an immiscible, otherwise quiescent non-Newtonian fluid. We consider a regime in which inertia and convective transport of energy are both negligible (represented by the limit condition of vanishingly small Reynolds and Marangoni numbers) and free from gravitational effects. A constant temperature gradient is maintained by keeping two opposite sides of the computational domain at different temperatures. Consequently the droplet experiences a motion driven by the mismatch of interfacial stresses induced by the non-uniform temperature distribution on its boundary. The departures from the Newtonian behaviour are quantified via the “thermal” Deborah number, De T and are accounted for by adopting either the Oldroyd-B model, for relatively small De T, or the FENE-CR constitutive law for a larger range of De T. In addition, the effects of model parameters, such as the concentration parameter c=1−β (where β is the viscoelastic viscosity ratio), or the extensibility parameter, L 2, have been studied numerically using a hybrid volume of fluid-level set method. The numerical results show that the steady-state droplet velocity behaves as a monotonically decreasing function of De T, whilst its shape deforms prolately. For increasing values of De T, the viscoelastic stresses show the tendency to be concentrated near the rear stagnation point, contributing to an increase in its local interface curvature.",
keywords = "thermocapillary migration,, droplet dynamics, viscoelastic effects, level set-volume of fluid",
author = "Paolo Capobianchi and {T. Pinho}, Fernando and Marcello Lappa and Oliveira, {M{\'o}nica S. N.}",
year = "2019",
month = "8",
day = "31",
doi = "10.1016/j.jnnfm.2019.06.006",
language = "English",
volume = "270",
pages = "8--22",
journal = "Journal of Non-Newtonian Fluid Mechanics",
issn = "0377-0257",

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TY - JOUR

T1 - Thermocapillary motion of a Newtonian drop in a dilute viscoelastic fluid

AU - Capobianchi, Paolo

AU - T. Pinho, Fernando

AU - Lappa, Marcello

AU - Oliveira, Mónica S. N.

PY - 2019/8/31

Y1 - 2019/8/31

N2 - In this work we investigate the role played by viscoelasticity on the thermocapillary motion of a deformable Newtonian droplet embedded in an immiscible, otherwise quiescent non-Newtonian fluid. We consider a regime in which inertia and convective transport of energy are both negligible (represented by the limit condition of vanishingly small Reynolds and Marangoni numbers) and free from gravitational effects. A constant temperature gradient is maintained by keeping two opposite sides of the computational domain at different temperatures. Consequently the droplet experiences a motion driven by the mismatch of interfacial stresses induced by the non-uniform temperature distribution on its boundary. The departures from the Newtonian behaviour are quantified via the “thermal” Deborah number, De T and are accounted for by adopting either the Oldroyd-B model, for relatively small De T, or the FENE-CR constitutive law for a larger range of De T. In addition, the effects of model parameters, such as the concentration parameter c=1−β (where β is the viscoelastic viscosity ratio), or the extensibility parameter, L 2, have been studied numerically using a hybrid volume of fluid-level set method. The numerical results show that the steady-state droplet velocity behaves as a monotonically decreasing function of De T, whilst its shape deforms prolately. For increasing values of De T, the viscoelastic stresses show the tendency to be concentrated near the rear stagnation point, contributing to an increase in its local interface curvature.

AB - In this work we investigate the role played by viscoelasticity on the thermocapillary motion of a deformable Newtonian droplet embedded in an immiscible, otherwise quiescent non-Newtonian fluid. We consider a regime in which inertia and convective transport of energy are both negligible (represented by the limit condition of vanishingly small Reynolds and Marangoni numbers) and free from gravitational effects. A constant temperature gradient is maintained by keeping two opposite sides of the computational domain at different temperatures. Consequently the droplet experiences a motion driven by the mismatch of interfacial stresses induced by the non-uniform temperature distribution on its boundary. The departures from the Newtonian behaviour are quantified via the “thermal” Deborah number, De T and are accounted for by adopting either the Oldroyd-B model, for relatively small De T, or the FENE-CR constitutive law for a larger range of De T. In addition, the effects of model parameters, such as the concentration parameter c=1−β (where β is the viscoelastic viscosity ratio), or the extensibility parameter, L 2, have been studied numerically using a hybrid volume of fluid-level set method. The numerical results show that the steady-state droplet velocity behaves as a monotonically decreasing function of De T, whilst its shape deforms prolately. For increasing values of De T, the viscoelastic stresses show the tendency to be concentrated near the rear stagnation point, contributing to an increase in its local interface curvature.

KW - thermocapillary migration,

KW - droplet dynamics

KW - viscoelastic effects

KW - level set-volume of fluid

U2 - 10.1016/j.jnnfm.2019.06.006

DO - 10.1016/j.jnnfm.2019.06.006

M3 - Article

VL - 270

SP - 8

EP - 22

JO - Journal of Non-Newtonian Fluid Mechanics

JF - Journal of Non-Newtonian Fluid Mechanics

SN - 0377-0257

ER -