  We present a scaling theory for the long time behavior of spontaneous
imbibition in porous media consisting of interconnected pores with a large
length-to-width ratio. At pore junctions the meniscus propagation in one or
more branches can come to a halt when the Laplace pressure of the meniscus
exceeds the hydrostatic pressure within the junction. We derive the scaling
relations for the emerging arrest time distribution and show that the average
front width is proportional to the height, yielding a roughness exponent of
exactly beta=1/2 and explaining recent experimental results for nano-porous
Vycor glass (NVG). Extensive simulations of a pore network model confirm these
predictions.
