Interfacial forces exceed gravitational forces on a scale small relative to the capillary length—two millimeters in the case of an air-water interface—and therefore dominate the physics of sub-millimetric systems. They are of paramount importance for various biological taxa and engineering processes where the motion of a liquid meniscus induces a viscous frictional force that exhibits a sublinear dependence in the meniscus velocity, i.e., a power law with an exponent smaller than one. Interested in the fundamental implications of this dependence, we use a liquid-foam sloshing system as a prototype to exacerbate the effect of sublinear friction on the macroscopic mechanics of multi-phase flows. In contrast to classical theory, we uncover the existence of a finite-time singularity in our system yielding the arrest of the fluid’s oscillations. We propose a minimal theoretical framework to capture this effect, thereby amending the paradigmatic damped harmonic oscillator model. Our results suggest that, although often not considered at the macroscale, sublinear capillary forces govern the friction at liquid-solid and liquid-liquid interfaces.

1.
H.
Lamb
,
Hydrodynamics
(
Cambridge University Press
,
1932
).
2.
R. A.
Ibrahim
,
Liquid Sloshing Dynamics: Theory and Applications
(
Cambridge University Press
,
2005
).
3.
K.
Case
and
W.
Parkinson
, “
Damping of surface waves in an incompressible liquid
,”
J. Fluid Mech.
2
,
172
184
(
1957
).
4.
A.
Sauret
,
F.
Boulogne
,
J.
Cappello
,
E.
Dressaire
, and
H. A.
Stone
, “
Damping of liquid sloshing by foams
,”
Phys. Fluids
27
,
022103
(
2015
).
5.
I.
Cantat
, “
Liquid meniscus friction on a wet plate: Bubbles, lamellae, and foams
,”
Phys. Fluids
25
,
031303
(
2013
).
6.
F.
Bretherton
, “
The motion of long bubbles in tubes
,”
J. Fluid Mech.
10
,
166
188
(
1961
).
7.
N. D.
Denkov
,
V.
Subramanian
,
D.
Gurovich
, and
A.
Lips
, “
Wall slip and viscous dissipation in sheared foams: Effect of surface mobility
,”
Colloids Surf., A
263
,
129
145
(
2005
).
8.
B.
Cocciaro
,
S.
Faetti
, and
M.
Nobili
, “
Capillarity effects on surface gravity waves in a cylindrical container: Wetting boundary conditions
,”
J. Fluid Mech.
231
,
325
343
(
1991
).
9.
L.
Landau
and
B.
Levich
, “
Dragging of a liquid by a moving plate
,”
Acta Phys. USSR
17
,
42
(
1942
).
10.
A. H.
Nayfeh
,
Perturbation Methods
(
John Wiley & Sons
,
2008
).
11.
H. K.
Moffatt
, “
Euler’s disk and its finite-time singularity
,”
Nature
404
,
833
834
(
2000
).

Supplementary Material

You do not currently have access to this content.