Immersion microscopy optics may include liquid droplets (e.g., water) to control the light pathway and the numerical aperture of an optical system. Changing the distances between the optical system and an object slide for image focusing also changes the shape (especially the diameter) of the droplet and the surface energy, thus leading to forces acting on both optics and object slides. We examine these effects analytically and derive a numerical model using numerical integration of a recursive integral to predict the force resulting from a liquid droplet changing its shape in the system. Our solutions show that an alteration of the distance leads to a time-dependency of the droplet surface, which is reflected in the corresponding surface and meniscus energies. With this, we can calculate the hydrostatic force that pulls both optical surfaces closer to each other and simulate the time-dependent equilibration of the system.

1.
V. G.
Levich
and
V. S.
Krylov
,
Annu. Rev. Fluid Mech.
1
,
293
(
1969
).
2.
T.
Gillespie
and
W. J.
Settineri
,
J. Colloid Interface Sci.
24
,
199
(
1967
).
3.
A.
de Lazzer
,
M.
Dreyer
, and
H. J.
Rath
,
Langmuir
15
,
4551
(
1999
).
4.
Y. I.
Rabinovich
,
T. G.
Movchan
,
N. V.
Churaev
, and
P. G.
Ten
,
Langmuir
7
,
817
(
1991
).
5.
K. L.
Johnson
,
K.
Kendall
, and
A. D.
Roberts
,
Proc. R. Soc. Lond.
324
,
301
(
1971
).
6.
Y. I.
Rabinovich
,
J. J.
Adler
,
M. S.
Esayanur
,
A.
Ata
,
R. K.
Singh
, and
B. M.
Moudgil
,
Adv. Colloid Interface Sci.
96
,
213
(
2002
).
7.
L.
Sirghi
,
N.
Nakagiri
,
K.
Sugisaki
,
H.
Sugimura
, and
O.
Takai
,
Langmuir
16
,
7796
(
2000
).
8.
M.
Fuji
,
K.
Machida
,
T.
Takei
,
T.
Watanabe
, and
M.
Chikazawa
,
Langmuir
15
,
4584
(
1999
).
9.
X.
Xiao
and
L.
Qian
,
Langmuir
16
,
8153
(
2000
).
10.
M.
Pasandideh-Fard
,
Y. M.
Qiao
,
S.
Chandra
, and
J.
Mostaghimi
,
Phys. Fluids
8
,
650
(
1996
).
11.
R.
Pericet-Cámara
,
A.
Best
,
H.-J.
Butt
, and
E.
Bonaccurso
,
Langmuir
24
,
10565
(
2008
).
12.
J. F.
Joanny
and
P. G.
de Gennes
,
J. Chem. Phys.
81
,
552
(
1984
).
13.
J. A.
Marsh
,
S.
Garoff
, and
E. B.
Dussan V.
,
Phys. Rev. Lett.
70
,
2778
(
1993
).
14.
E.
Ramé
,
S.
Garoff
, and
K. R.
Willson
,
Phys. Rev. E
70
,
031608
(
2004
).
15.
K.
Stoev
,
E.
Ramé
, and
S.
Garoff
,
Phys. Fluids
11
,
3209
(
1999
).
16.
S.
Somalinga
and
A.
Bose
,
Phys. Fluids
12
,
499
(
2000
).
17.
D. E.
Finlow
,
P. R.
Kota
, and
A.
Bose
,
Phys. Fluids
8
,
302
(
1996
).
18.
J.-B.
Dupont
and
D.
Legendre
,
J. Comput. Phys.
229
,
2453
(
2010
).
19.
Q.
Chen
,
E.
Ramé
, and
S.
Garoff
,
Phys. Fluids
7
,
2631
(
1995
).
20.
Taschenbuch der Physik, 5th ed., edited by H. Stöcker (Verlag Harri Deutsch, Frankfurt am Main, 2005), p. 171ff.
21.
T.
Young
,
Philos. Trans. R. Soc.
95
,
65
(
1805
).
22.
Olympus Lifescience
, see www.olympus-lifescience.com/de/objectives/lumplfln-w for “(L)UMPLFLN-W/XLUMPLFLN-W/LUMFLN-W Semi Apochromatic Water Immersion Optics Series” (Olympus, 2019).
23.
E.
Hänel
et al., see https://sourceforge.net/projects/numere/ for “NumeRe,” v1.1.2rc3, SourceForge (2020).
24.
M.
Kalin
and
M.
Polajnar
,
Appl. Surf. Sci.
293
,
97
(
2014
).
You do not currently have access to this content.