Simple waves and shocks in a thin film of a perfectly soluble antisurfactant solution

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Abstract

We consider the dynamics of a thin film of a perfectly soluble anti-surfactant solution in the limit of large capillary and Peclet numbers in which the governing system of nonlinear equations is purely hyperbolic. We construct exact solutions to a family of Riemann problems for this system, and discuss the properties of these solutions, including the formation of both simple-wave and uniform regions within the flow, and the propagation of shocks in both the thickness of the film and the gradient of the concentration of solute.
Original languageEnglish
Pages (from-to)167-178
Number of pages12
JournalJournal of Engineering Mathematics
Volume107
Issue number1
Early online date3 Aug 2017
DOIs
Publication statusPublished - 31 Dec 2017

Fingerprint

System of Nonlinear Equations
Surfactant
Thin Films
Shock
Cauchy Problem
Exact Solution
Propagation
Gradient
Thin films
Peclet number
Nonlinear equations
Surface active agents
Family

Keywords

  • hyperbolic system
  • Riemann problems
  • simple waves
  • shocks
  • anti-surfactants
  • Marangoni effect

Cite this

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abstract = "We consider the dynamics of a thin film of a perfectly soluble anti-surfactant solution in the limit of large capillary and Peclet numbers in which the governing system of nonlinear equations is purely hyperbolic. We construct exact solutions to a family of Riemann problems for this system, and discuss the properties of these solutions, including the formation of both simple-wave and uniform regions within the flow, and the propagation of shocks in both the thickness of the film and the gradient of the concentration of solute.",
keywords = "hyperbolic system, Riemann problems, simple waves , shocks, anti-surfactants, Marangoni effect",
author = "Conn, {J. J. A.} and Duffy, {B. R.} and D. Pritchard and Wilson, {S. K.} and K. Sefiane",
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T1 - Simple waves and shocks in a thin film of a perfectly soluble antisurfactant solution

AU - Conn, J. J. A.

AU - Duffy, B. R.

AU - Pritchard, D.

AU - Wilson, S. K.

AU - Sefiane, K.

PY - 2017/12/31

Y1 - 2017/12/31

N2 - We consider the dynamics of a thin film of a perfectly soluble anti-surfactant solution in the limit of large capillary and Peclet numbers in which the governing system of nonlinear equations is purely hyperbolic. We construct exact solutions to a family of Riemann problems for this system, and discuss the properties of these solutions, including the formation of both simple-wave and uniform regions within the flow, and the propagation of shocks in both the thickness of the film and the gradient of the concentration of solute.

AB - We consider the dynamics of a thin film of a perfectly soluble anti-surfactant solution in the limit of large capillary and Peclet numbers in which the governing system of nonlinear equations is purely hyperbolic. We construct exact solutions to a family of Riemann problems for this system, and discuss the properties of these solutions, including the formation of both simple-wave and uniform regions within the flow, and the propagation of shocks in both the thickness of the film and the gradient of the concentration of solute.

KW - hyperbolic system

KW - Riemann problems

KW - simple waves

KW - shocks

KW - anti-surfactants

KW - Marangoni effect

UR - https://link.springer.com/journal/volumesAndIssues/10665

U2 - 10.1007/s10665-017-9924-8

DO - 10.1007/s10665-017-9924-8

M3 - Article

VL - 107

SP - 167

EP - 178

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JF - Journal of Engineering Mathematics

SN - 0022-0833

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ER -