Lecture 13 Flashcards
What is surface energy and surface tension, and how are they best described?
Surface energy is equivalent to tension which is exerted in all directions parallel to the surface!
Surface tension is the tendency of an interface to shrink
it is best explained by a heard being pulled in a circle due to surface tension when a needle is priced through the soap film it is o
What is the derivation for surface tension, work done, helm-holts free energy, entropy, and internal energy of the surface?
found in notes on page 1-2
What is the molecular origin of surface tension?
Read page 115
What is Laplace’s Law and its applications?
Laplace’s law is the quantitive relation of the pressure difference (between the two sides of the interface) and the curvature of the interface
applications:
- spherical droplets
- capillary rise and depression
- The Kelvin equation
What is the derivation of Laplace’s law for spherical droplets?
found in notes on page 2
what is the derivation for the capillary rise and depression?
found in notes on pages 3-4
Capillary length is the measure for the persistence length of the interface. For example, droplets larger than the capillary lose their spherical shape due to gravity. Also, the meniscus inside the tube is no longer spherical when the radius of the tube becomes comparable (or larger) than the capillary length
The capillary is also the measure of the meniscus height at the wall of the capillary.
What is the derivation of the Kelvin equation?
According to Laplace’s law, the pressure inside the droplet is larger than the pressure of a liquid with a flat surface.
Using that and the Maxwell relation: (δμ/δp) = molar volume and Laplace law, it is implied that the chemical potential of the liquid inside the droplet is larger than the chemical potential of the liquid with a flat surface. therefore at equilibrium, the chemical potential of the gas (that comes from the liquid droplet) will be larger as well. As the temp is constant that can only be achieved by increasing the vapour pressure
The rest of the derivation is in notes as well.
What is an important application of Kelvin’s equation?
It is well known that a vapour phase can remain in a supersaturated metastable phase for quite some time before it condenses. For the gas to condense the radius of the liquid droplet must equal the radius r(c) so that the vapour pressure of these droplets P(r(c)) is equal to the vapour pressure of the soundings. This radius r(c) of those critical liquid droplets is given by the Kelvin equation:
r(c) = (2yv(l)) / RTln(p/p*)
From this, the liquid droplet with r < r(c) evaporates again as its vapour pressure is larger than the vapour pressure of the surroundings. In contrast, the liquid droplets with r > r(c) will condense
What are contact angles and Young’s law?
A liquid droplet placed on a solid substrate will either contract or spread depending on the nature of the liquid and solid.
illustrated in the notes on page 6, there is a characteristic angle at which the liquid contacts the substrate, this is called the contact angle.
Multiple forces act on a droplet when it is placed on a solid. Mechanical equilibrium states that the forces parallel to the solid interface must be equal.
therefore we get the expression:
Y(sg) = Y(sl) + Y(lg) cos(angle)
rearranging gives us the contact angle of:
Cos(angle) = Y(sg)-Y(sl)/Y(lg)
this is known as Young Law
What is complete, partial, and non-wetting?
Following Young’s law:
Complete wetting:
Liquid will fully wet a surface (θ = 0) if
Y(sg) >= Y(sl) + Y(lg)
Polar surfaces which have a high Y(Ssg)
Partial wetting:
Liquid will partially wet a surface (0<θ<180) if: Y(sg) < Y(sl) + Y(lg)
This tells us that it is more thermodynamically favored to form a liquid-gas interface besides liquid-solid and liquid-gas interfaces
apolar surfaces which have a high Y(sl)
non-wetting:
When the liquid contracts to form a more or less spherical droplet (θ=180). This is the case when it is thermodynamically unfavoured to create a solid-liquid interface in addition to liquid-gas and gas-solid interfaces:
Ysl >= Ysg + Ylg
