Critical effects and scaling at meniscus osculation transitions
File(s)
Accepted version
Author(s)
Parry, Andrew
Malijevsky, Alexandr
Pospisil, Martin
Type
Journal Article
Abstract
We propose a simple scaling theory describing critical effects at rounded meniscus osculation transitions which occur when the Laplace radius of a condensed macroscopic drop of liquid coincides with the local radius of curvature
R
w
in a confining parabolic geometry. We argue that the exponent
β
osc
characterizing the scale of the interfacial height
ℓ
0
∝
R
β
osc
w
at osculation, for large
R
w
, falls into two regimes representing fluctuation-dominated and mean-field-like behavior, respectively. These two regimes are separated by an upper critical dimension, which is determined here explicitly and depends on the range of the intermolecular forces. In the fluctuation-dominated regime, representing the universality class of systems with short-range forces, the exponent is related to the value of the interfacial wandering exponent
ζ
by
β
osc
=
3
ζ
/
(
4
−
ζ
)
. In contrast, in the mean-field regime, which was not previously identified and which occurs for systems with longer-range forces (and higher dimensions), the exponent
β
osc
takes the same value as the exponent
β
co
s
for complete wetting, which is determined directly by the intermolecular forces. The prediction
β
osc
=
3
/
7
in
d
=
2
for systems with short-range forces (corresponding to
ζ
=
1
/
2
) is confirmed using an interfacial Hamiltonian model which determines the exact scaling form for the decay of the interfacial height probability distribution function. A numerical study in
d
=
3
, based on a microscopic model density-functional theory, determines that
β
osc
≈
β
co
s
≈
0.326
close to the predicted value of
1
/
3
appropriate to the mean-field regime for dispersion forces.
R
w
in a confining parabolic geometry. We argue that the exponent
β
osc
characterizing the scale of the interfacial height
ℓ
0
∝
R
β
osc
w
at osculation, for large
R
w
, falls into two regimes representing fluctuation-dominated and mean-field-like behavior, respectively. These two regimes are separated by an upper critical dimension, which is determined here explicitly and depends on the range of the intermolecular forces. In the fluctuation-dominated regime, representing the universality class of systems with short-range forces, the exponent is related to the value of the interfacial wandering exponent
ζ
by
β
osc
=
3
ζ
/
(
4
−
ζ
)
. In contrast, in the mean-field regime, which was not previously identified and which occurs for systems with longer-range forces (and higher dimensions), the exponent
β
osc
takes the same value as the exponent
β
co
s
for complete wetting, which is determined directly by the intermolecular forces. The prediction
β
osc
=
3
/
7
in
d
=
2
for systems with short-range forces (corresponding to
ζ
=
1
/
2
) is confirmed using an interfacial Hamiltonian model which determines the exact scaling form for the decay of the interfacial height probability distribution function. A numerical study in
d
=
3
, based on a microscopic model density-functional theory, determines that
β
osc
≈
β
co
s
≈
0.326
close to the predicted value of
1
/
3
appropriate to the mean-field regime for dispersion forces.
Date Issued
2022-11-14
Date Acceptance
2022-10-28
Citation
Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 2022, 106, pp.1-8
ISSN
1539-3755
Publisher
American Physical Society
Start Page
1
End Page
8
Journal / Book Title
Physical Review E: Statistical, Nonlinear, and Soft Matter Physics
Volume
106
Copyright Statement
©2022 American Physical Society
Identifier
https://journals.aps.org/pre/abstract/10.1103/PhysRevE.106.054802
Publication Status
Published
Date Publish Online
2022-11-14