Post on 18-Jun-2020
transcript
Jacco Snoeijer, University of Twente
force and energy interpretations of capillarity
“Why is surface tension a force parallel to the interface?”Marchand, Weijs, Snoeijer & Andreotti (submitted to Am. J. Physics)
Young’s force construction
force and energy interpretations of capillarity
surface tension γ
[γ] = energy/area[γ] = force/length
from DVD “Interfaces mobiles”, Quere, Fermigier & Clanet
[γ] = energy/area[γ] = force/length
surface tension γ
dE = 2 γL dx
[γ] = energy/area[γ] = force/length
surface tension γ
force
dE = 2 γL dx
a liquid puddle
less obvious cases
De Gennes, Brochard-Wyart & Quere
a liquid puddle
is the solid-vapor interface really pulling on the liquid?
less obvious cases
De Gennes, Brochard-Wyart & Quere
less obvious cases
tensiometer
Young’s law
less obvious cases
tensiometer
why only γLV?
γSV and γSL ?
energy always works!
★ at equilibrium, minimize dE=0
• p = const (Laplace, gravity, disjoining...)• boundary condition: Young’s law
my guide to capillarity
energy always works!
★ at equilibrium, minimize dE=0
• p = const (Laplace, gravity, disjoining...)• boundary condition: Young’s law
★ non-equilibrium, dE = Ftot dx (virtual work)
my guide to capillarity
energy always works!
my guide to capillarity
force interpretion: be careful!
★ specify the “system” to which forces are applied
★ know the rules of the game!
“Why is surface tension a force parallel to the interface?” Marchand, Weijs, Snoeijer & Andreotti (Submitted to Am. J. Phys.)
hydrostatic & Laplace pressure
from pressure to force
De Gennes, Brochard-Wyart & Quere
-γ κ(x) + ρg { h(x) - e } = 0
can we identify the capillary forces e.g. in the stress tensor?
physical reality of forces
liquid/vapor interface
Molecular Dynamics (LJ molecules)Joost Weijs
liquid/vapor interface
liquid/vapor interface
bulk: isotropic stress
liquid/vapor interface
bulk: isotropic stresssurface: anisotropic stress
liquid/vapor interface
bulk: isotropic stresssurface: anisotropic stress surface tension
mechanical definition
surface tension force is due to normal stress difference
near the interface:
γ = ∫ dz (pT-pN)
Kirkwood & Buff 1949
a liquid drop (2D)
a liquid drop (2D)
subsystem
a liquid drop (2D)
surface tension: γ
a liquid drop (2D)
surface tension: γ
Laplace pressure:
γ/R
a liquid drop (2D)
surface tension: γ
Laplace pressure:
γ/R
perfect mechanical equilibrium:• x direction• y direction• torque balance!!
a liquid drop (2D)
new subsystem
a liquid drop (2D)
a liquid drop (2D)
free drop partial wetting
solid
liquid
θ
a liquid drop (2D)
free drop partial wetting
solid
solid-on-liquid forces: normal to interface
θ
γsinθ γsinθ
liquid
solid-on-liquid force
the solid exerts a purely normal force on the liquid, which near the contact line
has a strength γsinθ
Young’s law
solid
θ
γsinθ γsinθ
liquid
γ cos θ = γsv -γsl
Young’s law
solid
θ
γsinθ γsinθ
liquid
γ cos θ = γsv -γsl
• incomplete: vertical/torque balance? • subsystem: what is pulling on what?
Young’s law: liquid wedge
θ
Young’s law: liquid wedge
θ
subsystem
Young’s law: liquid wedge
γsinθ
θ
γ
solid-on-liquid force
liquid-on-liquid force
Young’s law: liquid wedge
γsinθ
θ
γ
γsv-γsl
solid-on-liquid force
liquid-on-liquid force
liquid-on-liquid force
valid for inert solids, see Nijmeijer, Bruin, Bakker & van Leeuwen, Phys. Rev. A 1990
Young’s law: liquid wedge
γsinθ
θ
γ
γsv-γsl
solid-on-liquid force
liquid-on-liquid force
liquid-on-liquid force
perfect mechanical equilibrium:• x direction• y direction• torque balance!!
Young’s law
incomplete & misleading complete & physical
floating pin paradox
Finn, Phys. Fluids 2006,
floating pin paradox
Finn, Phys. Fluids 2006,
commented: Lunati, Phys. Fluids 2007 Shikmurzaev, Phys. Lett. A 2008 Wente, J. Math. Fluid Mech. 2008
floating pin paradox
Finn, Phys. Fluids 2006,
commented: Lunati, Phys. Fluids 2007 Shikmurzaev, Phys. Lett. A 2008 Wente, J. Math. Fluid Mech. 2008
response by Finn.... pfff...
floating pin paradox
θzero gravity: flat interface θ
floating pin paradox
θzero gravity: flat interface
energy dE=0: position determined by θeq
θ
floating pin paradox
θzero gravity: flat interface θ
force picture?
floating pin paradox
θzero gravity: flat interface θ
floating pin paradox
resultant upward force on the solid !?
θzero gravity: flat interface θ
macroscopic view
θzero gravity: flat interface θ
• the “system” is the solid• γSV and γSL do not pull on the solid
γLV γLV
Young’s law: liquid corner
system!
tensiometer
Q: why only γLV?
A: system = the solid
liquid-on-solid force
macrosopic view:
the surface tensions γSV and γSL do not pull on the
solid
★ energy route always gives correct answer
★ force interpretation: define “system”
• Young’s law: system = liquid corner
summary
★ energy route always gives correct answer
★ force interpretation: define “system”
• Young’s law: system = liquid corner
• macroscopic view: γSV and γSL do not pull on solid
summary
★ energy route always gives correct answer
★ force interpretation: define “system”
• Young’s law: system = liquid corner
• macroscopic view: γSV and γSL do not pull on solid
★ microscopic view of force-on-solid:
• beyond wetting: theory for the solid!• experimentally: elastic deformations
summary
elastic solids
silicone elastomer
Pericet-Camera et al, Langmuir 2008
silicone gel
elastic solids
silicone elastomer
Pericet-Camera et al, Langmuir 2008 Jerison et al, PRL 2011
model for the solid
unexpected tangential forces
Das, Marchand, Andreotti and Snoeijer, submitted
model for the solid
Das, Marchand, Andreotti and Snoeijer, submitted
unexpected tangential forces