# Modelling of Miscible Liquids with the Korteweg Stress

Ilya Kostin; Martine Marion; Rozenn Texier-Picard; Vitaly A. Volpert

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 37, Issue: 5, page 741-753
- ISSN: 0764-583X

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topKostin, Ilya, et al. "Modelling of Miscible Liquids with the Korteweg Stress." ESAIM: Mathematical Modelling and Numerical Analysis 37.5 (2010): 741-753. <http://eudml.org/doc/194189>.

@article{Kostin2010,

abstract = {
When two miscible fluids, such as glycerol (glycerin) and water,
are brought in contact, they immediately diffuse in each other.
However if the diffusion is sufficiently slow, large concentration gradients exist
during some time. They can lead to the appearance of an
“effective interfacial tension”. To study these phenomena we
use the mathematical model
consisting of the diffusion equation with convective terms and of
the Navier-Stokes equations with the Korteweg stress.
We prove the global existence and uniqueness of the solution for the
associated initial-boundary value problem in a two-dimensional bounded domain.
We study the longtime behavior of the solution and show that it converges
to the uniform composition distribution with zero velocity field.
We also present numerical simulations of miscible drops and show how
transient interfacial phenomena can change their shape.
},

author = {Kostin, Ilya, Marion, Martine, Texier-Picard, Rozenn, Volpert, Vitaly A.},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Miscible liquids; Korteweg stress; drops.},

language = {eng},

month = {3},

number = {5},

pages = {741-753},

publisher = {EDP Sciences},

title = {Modelling of Miscible Liquids with the Korteweg Stress},

url = {http://eudml.org/doc/194189},

volume = {37},

year = {2010},

}

TY - JOUR

AU - Kostin, Ilya

AU - Marion, Martine

AU - Texier-Picard, Rozenn

AU - Volpert, Vitaly A.

TI - Modelling of Miscible Liquids with the Korteweg Stress

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2010/3//

PB - EDP Sciences

VL - 37

IS - 5

SP - 741

EP - 753

AB -
When two miscible fluids, such as glycerol (glycerin) and water,
are brought in contact, they immediately diffuse in each other.
However if the diffusion is sufficiently slow, large concentration gradients exist
during some time. They can lead to the appearance of an
“effective interfacial tension”. To study these phenomena we
use the mathematical model
consisting of the diffusion equation with convective terms and of
the Navier-Stokes equations with the Korteweg stress.
We prove the global existence and uniqueness of the solution for the
associated initial-boundary value problem in a two-dimensional bounded domain.
We study the longtime behavior of the solution and show that it converges
to the uniform composition distribution with zero velocity field.
We also present numerical simulations of miscible drops and show how
transient interfacial phenomena can change their shape.

LA - eng

KW - Miscible liquids; Korteweg stress; drops.

UR - http://eudml.org/doc/194189

ER -

## References

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- P. Petitjeans, Une tension de surface pour les fluides miscibles. C. R. Acad. Sci. Paris Sér. I Math.322 (1996) 673-679.
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- V. Volpert, J. Pojman and R. Texier-Picard, Convection induced by composition gradients in miscible liquids. C. R. Acad. Sci. Paris Sér. I Math.330 (2002) 353-358.

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