Problem
Capillary rise is an important phenomenon in enhanced oil recovery, the recovery of non-aqueous-phase liquids from contaminated aquifers, the rise of sap in trees, and also in the determination of surface tension of liquids. This is based on the balance of forces between the surface tension and hydrostatic forces due to gravity.
(a) Consider a small capillary partially immersed in water. The water rises to an equilibrium height given by h. Equate the pressure given by the Young-Laplace equation for the hemispherical interface with that of the hydrostatic pressure and derive the equation σ = rgh/2Δρ, where r is the radius of the capillary, g is a gravitational constant, and Δρ is the difference in density between water and air.
(b) Soils are considered to have capillary size pores. Calculate the capillary rise of water in soil pores of diameters 100, 1000, and 10,000μm. This gives the shape of the boundary between air and water in soil pores. Repeat the calculation for a non-aqueous-phase contaminant such as chloroform in contact with groundwater. σ = 20 mN/m1 and Δρ = 150 kg/m3. What conclusions can you draw about the shape of the boundary in this case?
The response should include a reference list. Double-space, using Times New Roman 12 pnt font, one-inch margins, and APA style of writing and citations.