Penetration dynamics through nanometer-scale hydrophilic capillaries: Beyond Washburn's equation and extended menisci.

The wicking velocity generally obeys Washburn's equation, but the dynamic contact angle (CA) has to be employed. The dynamic CA (θ) relies on the penetration rate and is always larger than the equilibrium CA. The breakdown of Washburn's equation occurs under two conditions, (i) the channel width close to molecular size and (ii) the positive spreading coefficient is large enough. Both cases come about when the wicking velocity in a nanoslit exceeds the maximum value corresponding to cos(θ) = 1. The failure of Washburn's equation is attributed to the invalidity of Young-Laplace equation associated with undefined meniscus. The extended meniscus will be developed as a wall of the nanoslit continues to extend outside the exit mouth. The shapes of extended menisci are discussed for both partial wetting and total wetting surfaces.