Fluids and Rocks - Introduction to Carbon Capture and Sequestration - page 402

the substrate. If the pores are below a certain thickness we see that this
wetting layer extends through the entire pore, and we observe capillary
condensation. A liquid is formed inside the pores at conditions where the
outside fl uid is still in the gas phase.
If we look in detail at the gas-liquid interface in the narrow pore (see
Figure 9.4.3 ), we see that because of the wetting of the fl uid with the
walls our meniscus is curved. Such a curved interface causes a pressure
difference between the liquid and gas phase, called the capillary pres-
sure . Consider a balloon: the surface tension of the skin of the balloon is
compensating for the fact that the pressure inside the balloon is higher
than the pressure outside. For our fl uid in a pore, we can relate this pres-
sure difference to the liquid-gas surface tension using the Young-
Laplace equation (see Box 9.4.1 ), which reads for a cylindrical pore and
a fully wetting fl uid (zero contact angle):

2

p − p = γ ,

gas liquid LG

R

where R is the radius of the pore. If we observe a non-zero contact angle,
the surface has a slightly different shape and the Young-Laplace equa-
tion becomes:

2 γ R

LG

pp p = − = ,

C gas liquid

cos θ

where is now the radius of curvature of

the fi lm. This difference in pressure is called the capillary pressure, p C . See
Question 9.4.1 for a biological application of the Young-Laplace equation.

θ is the contact angle and R/ cos θ

Box 9.4.1 Young-Laplace equation

Let us assume that our pore, gas, and liquid are at constant temperature. In addition,
the total volume and the total number of particles are constant. From thermodynamics,
we know that at these conditions the Helmholtz free energy ( A ) takes its minimum value:

dA =− SdT − pdV +γ dA ,

where we see two work terms: one if we change the volume V and one if we change
the area A .

( Continued )