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

J. J. A. Conn; B. R. Duffy; D. Pritchard; S. K. Wilson; K. Sefiane

doi:10.1007/s10665-017-9924-8

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

J. J. A. Conn, B. R. Duffy, D. Pritchard, S. K. Wilson, K. Sefiane

Mathematics And Statistics

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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 language	English
Pages (from-to)	167-178
Number of pages	12
Journal	Journal of Engineering Mathematics
Volume	107
Issue number	1
Early online date	3 Aug 2017
DOIs	https://doi.org/10.1007/s10665-017-9924-8
Publication status	Published - 31 Dec 2017

Keywords

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

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10.1007/s10665-017-9924-8Licence: CC BY 4.0

Conn-etal-JEM-2017-Simple-waves-and-shocks-in-a-thin-film-of-a-perfectlyFinal published version, 522 KBLicence: CC BY 4.0

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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. ",

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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

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SN - 0022-0833

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SP - 167

EP - 178

JO - Journal of Engineering Mathematics

JF - Journal of Engineering Mathematics

IS - 1

ER -

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

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