measurement of contact angles measurement of contact angles
The contact of
The contact of 4 4 He crystals with walls: He crystals with walls:
hysteresis of the contact angle hysteresis of the contact angle
S. Sasaki
S. Sasaki
aa, F. Caupin and S. Balibar , F. Caupin and S. Balibar
Laboratoire de Physique Statistique de l'ENS (Paris, France) Laboratoire de Physique Statistique de l'ENS (Paris, France)
a - now at North Western Univ. (USA) a - now at North Western Univ. (USA)
Abstract
Abstract : : We have measured the contact angle of the liquid-solid interface of helium 4 with different walls.
It was known to be about 45° but we have found that is rather hysteretic with advancing angles of about 25° and receding angles of about 55 ° . Although these angles are similar for copper, glass, and graphite substrates, the hysteresis seems to increase with roughness, as expected from the work of Rolley and Guthmann (Phys. Rev. Lett. 98, 166105, 2007). This angle is an important parameter for the existence of liquid channels where grain boundaries meet walls.
The hysteresis of the contact angle is known to increase with the The hysteresis of the contact angle is known to increase with the
substrate roughness (see, for example, the work of E. Rolley and C.
substrate roughness (see, for example, the work of E. Rolley and C.
Guthmann, PRL 98, 166105, 2007). We see perhaps such a tendancy.
Guthmann, PRL 98, 166105, 2007). We see perhaps such a tendancy.
The surface of our HOPG graphite was difficult to clean but, after 3 The surface of our HOPG graphite was difficult to clean but, after 3
days pumping of the cell at 100°C, we could observe frequent days pumping of the cell at 100°C, we could observe frequent
nucleation of oriented crystals on either one or the other graphite nucleation of oriented crystals on either one or the other graphite
piece (see photograph on the right). The contact angle on graphite is piece (see photograph on the right). The contact angle on graphite is
similar to that on glass or copper because the helium crystals are not similar to that on glass or copper because the helium crystals are not
oriented parallel to the graphite lattice.
oriented parallel to the graphite lattice.
The value of the contact angle
The value of the contact angle cc is important for the existence of is important for the existence of liquid channels where grain boundaries meet walls. Indeed, these liquid channels where grain boundaries meet walls. Indeed, these
channels exist only if the contact angle
channels exist only if the contact angle cc < < , where , where is half is half the dihedral angle of grooves appearing where GBs emerge at the
the dihedral angle of grooves appearing where GBs emerge at the liquid-solid interface.
liquid-solid interface.
a square hole (11 x 11 mm
a square hole (11 x 11 mm22) in a gold-plated ) in a gold-plated copper plate (either 10 mm or 3 mm thick)
copper plate (either 10 mm or 3 mm thick)
2 glass windows sealed with indium O-rings.
2 glass windows sealed with indium O-rings.
the cell stands pressures up to at least 64 bar the cell stands pressures up to at least 64 bar
and can be cooled down to 35 mK.
and can be cooled down to 35 mK.
see Sasaki, Caupin and Balibar, submitted to J.
see Sasaki, Caupin and Balibar, submitted to J.
Low Temp. Phys., July 2008.
Low Temp. Phys., July 2008.
the experimental cells the experimental cells
the shape of the liquid-solid interface depends on gravity and surface tension, as for an ordinary the shape of the liquid-solid interface depends on gravity and surface tension, as for an ordinary
liquid surface.
liquid surface.
The contact angle si measured thanks to a fit with the Laplace equation near the wall:
The contact angle si measured thanks to a fit with the Laplace equation near the wall:
where x is the horizontal distance to the reference x
where x is the horizontal distance to the reference x00, l, lcc ~ 1 mm~ 1 mm is the capillary length and z is is the capillary length and z is the vertical height.
the vertical height.
Results:
Results:
substrate
substrate advancing angleadvancing angle receding anglereceding angle copper
copper 7 < 7 < advadv < 30° < 30° 42 < 42 < recrec < 63° < 63°
glass
glass 13 < 13 < advadv < 38° < 38° 40 < 40 < recrec < 66° < 66°
graphite
graphite 31 < 31 < advadv < 43° < 43° 44 < 44 < recrec < 62° < 62°
During growth, the « advancing angle » is smaller than during melting (« receding angle »).
During growth, the « advancing angle » is smaller than during melting (« receding angle »).
We used either HOPG graphite which was difficult to clean properly since we coudl only warm We used either HOPG graphite which was difficult to clean properly since we coudl only warm
it at 100°C under moderate vacuum (3 days pumping through the fill line) it at 100°C under moderate vacuum (3 days pumping through the fill line)
Discussion Discussion
contact with a glass plate contact with a glass plate contact with a copper wall contact with a copper wall
growing (16
growing (16 m/s)m/s) melting (10 melting (10 m/s)m/s) fits with Laplace eq.
fits with Laplace eq.
growing (60
growing (60 m/s)m/s) melting (5 melting (5 m/s)m/s)
nucleation of an oriented helium nucleation of an oriented helium
crystal on HOPG graphite crystal on HOPG graphite the contact line of a grain boundary (GB)
the contact line of a grain boundary (GB) with a wall is in reality a liquid channel with a wall is in reality a liquid channel with triangular cross section if the wall is with triangular cross section if the wall is sufficiently favorable to the liquid phase sufficiently favorable to the liquid phase
(if (if cc < <
crystal grain 1 crystal grain 1
crystal grain 2 crystal grain 2 liquid
liquid
wallwall
mixing chamber mixing chamber
pressure gauge pressure gauge
fill line (0.6 mm ID) fill line (0.6 mm ID)