Liquid uptake by porous media is typically driven by surface tension. Suppose that a long, horizontal pore of radius a is initially filled with air, and that at t = 0 one end is immersed in a liquid. If the contact angle α is < π/2, there will be a liquid column of growing length L(t), as shown in Fig. P8.14. Assume that the far end of the pore is vented, keeping the air pressure constant at P₀, and that the liquid outside the pore is also at P₀.

(a) Relate dL/dt to the volume flow rate Q(t) of the liquid.

(b) Assuming that the flow in the pore is pseudosteady and fully developed, show that

which is called Washburn's law.

(c) Estimate how large t must be for the pseudosteady approximation to become valid. Washburn's law will be accurate if the observation time greatly exceeds that.

Transcribed Image Text:

Liquid Po Z a = a L(t) Figure P8.14 Capillary flow into a horizontal pore. Air Po (0)