Hydro-Mechanical Properties of an Unsaturated Frictional Material

14 CHAPTER 2. STATE OF THE ART
Figure 2.4: Rise of water in capillary tubes of different diameter (Lu & Likos 2004)
Equilibrium between two interconnected drops of water is additionally presented in
Fig. 2.5. Two water drops with different radii (R1 > R2) are connected through a pipe
filled with water. The valve of the pipe is closed at first. Both drops have an internal pressure
uw1 and uw2. The water pressure in drop 1 is smaller than in drop 2 (uw1 < uw2), because the
radius of curvature for drop 1 is larger. When opening the valve the system will equilibrate.
The water will flow from higher pressure to smaller pressure. Thus the water will flow from
drop 2 to drop 1, drop 1 becomes larger and drop 2 becomes smaller. Equilibrium state is
reached, when the fluid of drop 2 enters the pipe and a convex meniscus with a radius equal
to R1 is formed (Lu & Likos 2004).
In Fig. 2.6 a capillary tube and a wide closed container are given. The interaction between
air, water and solid is shown. Two pressure points (1, 2) are observed in the tube and in the
container. The tube and the container are connected with a water filled pipe, where the valve
is at first closed. The air pressure in both systems is the same. Point 1 is located in the middle
and point 2 is located at the border of the container. The pressure in both points is equal
in the tube, because both points have the same spherical meniscus with the radius R. The
pressure difference can be calculated by using the meniscus geometry as ua − u w1/2 = 2Ts/R
R2 Water Air uw1 uw2 Valve is closed R1
R2=R1 Water Air uw1 uw2=uw1 R1
Valve is open
Figure 2.5: Equilibrium between two interconnected drops of water - the effect of drop’s radius
(Lu & Likos 2004)