measurement of contact anglesmeasurement of contact angles

The contact of The contact of 44He crystals with walls:He crystals with walls:hysteresis of the contact anglehysteresis 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)

AbstractAbstract:: 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 mma 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 xwhere 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:

substratesubstrate advancing angleadvancing angle receding anglereceding anglecoppercopper 7 < 7 < advadv < 30° < 30° 42 < 42 < recrec < 63° < 63°

glassglass 13 < 13 < advadv < 38° < 38° 40 < 40 < recrec < 66° < 66°

graphitegraphite 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)

DiscussionDiscussion

contact with a glass platecontact with a glass plate

contact with a copper wallcontact 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 graphitecrystal 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 1crystal grain 1

crystal grain 2crystal grain 2

liquidliquidwal

lw

all

mixing chambermixing chamber

pressure gaugepressure gauge

fill line (0.6 mm ID)fill line (0.6 mm ID)