We consider the motion of a contact line between a fluid, gas, and solid, as it occurs when a drop advances
over a solid surface. This motion is controlled by a microscopic length scale near the contact line, such as a slip
length or the precursor thickness. The capillary profile inside the drop is linked to the contact line through an
intermediate region which is characterized by an interface slope which varies logarithmically. The intermediate
solution contains a single adjustable constant, which can be computed either by matching to the capillary
region or to the contact line. We describe a simple method to perform the matching and to compute the required
constant. This extends and/or simplifies results known previously. We apply our results to the case of a
spreading drop in the presence of an interface potential and derive the equation of motion by combining the
inner and outer expansions.
%0 Journal Article
%1 citeulike:3788752
%A Pismen, L. M.
%A Eggers, Jens
%D 2008
%I APS
%J Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)
%K moving-contact-line
%N 5
%R 10.1103/PhysRevE.78.056304
%T Solvability condition for the moving contact line
%U http://dx.doi.org/10.1103/PhysRevE.78.056304
%V 78
%X We consider the motion of a contact line between a fluid, gas, and solid, as it occurs when a drop advances
over a solid surface. This motion is controlled by a microscopic length scale near the contact line, such as a slip
length or the precursor thickness. The capillary profile inside the drop is linked to the contact line through an
intermediate region which is characterized by an interface slope which varies logarithmically. The intermediate
solution contains a single adjustable constant, which can be computed either by matching to the capillary
region or to the contact line. We describe a simple method to perform the matching and to compute the required
constant. This extends and/or simplifies results known previously. We apply our results to the case of a
spreading drop in the presence of an interface potential and derive the equation of motion by combining the
inner and outer expansions.
@article{citeulike:3788752,
abstract = {{We consider the motion of a contact line between a fluid, gas, and solid, as it occurs when a drop advances
over a solid surface. This motion is controlled by a microscopic length scale near the contact line, such as a slip
length or the precursor thickness. The capillary profile inside the drop is linked to the contact line through an
intermediate region which is characterized by an interface slope which varies logarithmically. The intermediate
solution contains a single adjustable constant, which can be computed either by matching to the capillary
region or to the contact line. We describe a simple method to perform the matching and to compute the required
constant. This extends and/or simplifies results known previously. We apply our results to the case of a
spreading drop in the presence of an interface potential and derive the equation of motion by combining the
inner and outer expansions.}},
added-at = {2017-06-29T07:13:07.000+0200},
author = {Pismen, L. M. and Eggers, Jens},
biburl = {https://www.bibsonomy.org/bibtex/2250d45cf88fe89d6d534b641a1cf9bd1/gdmcbain},
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citeulike-attachment-1 = {pismen_08_solvability_33521.pdf; /pdf/user/gdmcbain/article/3788752/33521/pismen_08_solvability_33521.pdf; b2d7327cef30b0120c4de2a30461c16d531f7a2a},
citeulike-linkout-0 = {http://dx.doi.org/10.1103/PhysRevE.78.056304},
citeulike-linkout-1 = {http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal\&id=PLEEE8000078000005056304000001\&idtype=cvips\&gifs=yes},
citeulike-linkout-2 = {http://link.aps.org/abstract/PRE/v78/e056304},
comment = {(private-note)PDF provided by SGM Mon. 15 Dec. 2008.},
doi = {10.1103/PhysRevE.78.056304},
file = {pismen_08_solvability_33521.pdf},
interhash = {c2c8d6cfbdfd48516b538da842400dc0},
intrahash = {250d45cf88fe89d6d534b641a1cf9bd1},
journal = {Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)},
keywords = {moving-contact-line},
number = 5,
posted-at = {2008-12-15 06:01:48},
priority = {2},
publisher = {APS},
timestamp = {2017-06-29T07:13:07.000+0200},
title = {{Solvability condition for the moving contact line}},
url = {http://dx.doi.org/10.1103/PhysRevE.78.056304},
volume = 78,
year = 2008
}